# Natural and magnetically induced entanglement of hyperfine-structure states
in atomic hydrogen

Yusef Maleki,1 Sergei Sheludiakov,1 Vladimir V. Khmelenko,1 Marlan O.
Scully,1,2 David M. Lee,1 and Aleksei M. Zheltikov1,3,4,5
1Institute of Quantum Science and Engineering, Department of Physics and
Astronomy, Texas A&M University, College Station, Texas 77843-4242, USA
2Princeton University, Princeton, NJ 08544, USA
3Physics Department, M.V. Lomonosov Moscow State University, Moscow 119992,
Russia
4Advanced Photonics Laboratory, Russian Quantum Center, Skolkovo, Moscow
Region 143025, Russia
5Kazan Quantum Center, A.N. Tupolev Kazan National Research Technical
University, 420126 Kazan, Russia

###### Abstract

The spectrum of atomic hydrogen has long been viewed as a Rosetta stone that
bears the key to decode the writings of quantum mechanics in a vast variety of
physical, chemical, and biological systems. Here, we show that, in addition to
its role as a basic model of quantum mechanics, the hydrogen atom provides a
fundamental building block of quantum information. Through its electron and
nuclear spin degrees of freedom, the hydrogen atom is shown to lend a
physically meaningful frame and a suitable Hilbert space for bipartite
entanglement, whose two-qubit concurrence and quantum coherence can be
expressed in terms of the fundamental physical constants – the Planck and
Boltzmann constants, electron and proton masses, the fine-structure constant,
as well as the Bohr radius and the Bohr magneton. The intrinsic, natural
entanglement that the hyperfine-structure (HFS) states of the H atom store at
low temperatures rapidly decreases with a growth in temperature, vanishing
above a $\tau_{c}$ $\approx$ 5.35 $\mu$eV threshold. An external magnetic
field, however, can overcome this thermal loss of HFS entanglement. As one of
the central findings of this work, we show that an external magnetic field can
induce and sustain an HFS entanglement, against all the odds of thermal
effects, at temperatures well above the $\tau_{c}$ threshold, thus enabling
magnetic-field-assisted entanglement engineering in low-temperature gases and
solids.

##  I Introduction

In its capacity as the simplest of atoms, atomic hydrogen plays a central role
in physics, serving as an ultimate reference point, a basic model of a bound
quantum system, and a source of closed-form analytical solutions for quantum
theories Bohr ; Bethe . The significance of the H atom for the development of
quantum concepts is well-documented in the canonical accounts of the early era
of quantum mechanics Bethe ; Series ; Landau . In a more recent history,
atomic hydrogen has continued to stay one of the most extensively studied
objects of fundamental Hansch72 ; Udem ; Fischer  and applied Marowsky ;
Gladkov  spectroscopy, as well as attosecond physics Sansone ; attoH2 ; attoH3
, serving as the basis for understanding the structure of matter and a highly
sensitive probe for experimental tests of the quantum theory LeeRMP ;
Hansch2006 .

As a fundamental connection to solid-state and low-temperature physics, recent
studies reveal nuclear-polarized phases of hydrogen atoms embedded in solid H2
films Bigelow ; Sheludiakov  with remarkably large deviations of the low-
temperature nuclear spin polarization of H atoms from the Boltzmann
distribution Sheludiakov ; Ahokas ; Ahokas2 . This finding raises a number of
interesting and important questions regarding the role of quantum effects in
systems of this class, including the feasibility of quantum entanglement of H
at thermal equilibrium. Important insights into this question can be found in
earlier studies on electron-spin dynamics in two-electron double-quantum-dot
systems Johnson ; Petta , which have been shown to offer much promise as
prospective qubits and advantageous building blocks for quantum information
technologies Taylor ; Ladd ; Bennett2 . In search of the insights into these
questions, we are led to revisit the entanglement capacity of the basic
building block of such a hypothetical quantum interface – a single hydrogen
atom. As we show below in this paper, the electron and nuclear spin degrees of
freedom in a hydrogen atom provide both a physically meaningful frame and a
suitable Hilbert space for bipartite entanglement. We quantify this
entanglement in terms of a two-qubit concurrence and quantum coherence,
revealing a connection of H-atom entanglement to the fundamental physical
constants – the Planck and Boltzmann constants, electron and proton masses,
the fine-structure constant, as well as the Bohr radius and the Bohr magneton.
The intrinsic, natural entanglement that the hyperfine-structure (HFS) states
of the H atom store at low temperatures rapidly decreases with a growth in
temperature, vanishing above a $\tau_{c}$ $\approx$ 5.35 $\mu$eV threshold. An
external magnetic field, however, can overcome this thermal loss of HFS
entanglement above $\tau_{c}$, enabling magnetic-field-assisted entanglement
engineering in low-temperature gases and solids.

As one of the prominent earlier efforts to understand quantum-entanglement
properties of the H atom, Tommassini et al. Tommassini  have analyzed the
electron–proton coordinate entanglement, understood as correlations in the
electron–proton motion in the H atom. While the behavior of this
electron–proton position entanglement as a function of temperature is yet to
be understood, here, we focus on another type of quantum entanglement built
into the H atom – entanglement related to the nuclear and electron spin
degrees of freedom. An illuminating analysis of entanglement of this type has
been earlier presented by Zhu et al. Zhu , who developed a helpful formalism
for the description of electron–nuclear spin entanglement in the H atom and
examined important properties of his entanglement. Entanglement involving
nuclear degrees of freedom is in no way unique to the H atom. As one prominent
example, nuclear spins in nitrogen–vacancy centers in diamond have been shown
to offer a powerful resource for quantum information, attracting much interest
in the context of rapidly growing quantum technologies Childress ; Dutt ;
Neumann ; Fuchs .

As one of the central findings of our work, which goes well beyond the scope
of Ref. Zhu , we demonstrate that an external magnetic field can induce and
sustain an HFS entanglement, against all the odds of thermal effects, at
temperatures well above the $\tau_{c}$ threshold, thus enabling magnetic-
field-assisted entanglement engineering in low-temperature gases and solids.
Since this in many ways counterintuitive behavior of entanglement in the H
atom is due to the interaction of the electron and nuclear spins with an
external magnetic field, this effect is not foreseen for the electron–proton
coordinate entanglement, such as the one studied by Tommassini et al.
Tommassini . Moreover, we extend the analysis of the HFS entanglement in the H
atom to show that the criterion of this entanglement can be meaningfully
expressed in terms of a suitably defined quantum coherence, providing useful
insights into the behavior of the HFS entanglement as a function of
temperature and helping better understand the phenomenon of magnetically
induced entanglement above the $\tau_{c}$ threshold.

##  II THE HAMILTONIAN AND THE HYPERFINE STRUCTURE OF H

In our analysis of the HFS entanglement of the H atom, we resort to the
standard equation for the spin part of its ground-state Hamiltonian in an
external magnetic field $B$ Feynman ,

$\displaystyle
H_{HF}=\mathcal{A}(\sigma_{e}\cdot\sigma_{p})+\mu_{B}\sigma_{e}\cdot B.$ (1)

Here, $\sigma_{q}$ = ($\sigma_{q}^{x}$, $\sigma_{q}^{y}$, $\sigma_{q}^{z}$) is
the vector composed of the Pauli operators $\sigma_{j}^{x}$, $\sigma_{j}^{y}$,
and $\sigma_{j}^{z}$, $q=e$ and $p$ for the electron and proton, respectively,
$\mu_{B}=e\hbar/2m_{e}c$ is the Bohr magneton,

$\mathcal{A}={A\hbar^{2}}/{4}=\left[\left(\frac{2\pi}{3}\right)\left(\frac{1}{4\pi\varepsilon_{0}}\right)\left(\frac{\hbar^{2}}{c\pi
a_{0}^{3}}\right)\left(\frac{g_{e}e}{2m_{e}}\right)\left(\frac{g_{p}e}{2m_{p}}\right)\right]$

is the HFS constant, $e$ is the electron charge, $m_{e}$ and $m_{p}$ are the
electron and proton masses, $g_{e}=-\gamma_{e}\mu_{B}/\hbar$,
$g_{p}=\gamma_{p}\mu_{N}/\hbar$, $\gamma_{e}$ and $\gamma_{p}$ are the
electron and proton gyromagnetic ratios, $\mu_{N}=e\hbar/2m_{p}c$ is the
nuclear magneton, $c$ is the speed of light in vacuum, and $a_{0}$ is the Bohr
radius.

The first term in Eq. (1) describes the interaction between the electron and
nuclear spins, $\hat{S}$ and $\hat{I}$, $H_{1}=A\hat{S}\cdot\hat{I}$, with
$\mathcal{A}={A\hbar^{2}}/{4}$. The second term accounts for the interaction
between the electron spin and the external magnetic field $B$,
$H_{2}=-\gamma_{e}S\cdot B$. Interaction between the nuclear spin and $B$ is
much weaker and is neglected.

The energy eigenvalues $E_{u}$ of the Hamiltonian (1) are found as solutions
to $H_{HF}|u\rangle=E_{u}|u\rangle$, yielding Feynman ; Breit  four energy
eigenstates (Fig. 1a), $u=a,b,c,d$, with $E_{a,c}=\mathcal{A}(-1\mp
2\sqrt{1+\xi^{2}})$, $E_{b,d}=\mathcal{A}(1\mp 2\xi)$, where
$\xi=\mu_{B}B/(2\mathcal{A})$, the ”–” sign is taken for $u=a$ and $b$ and the
”+” sign is taken for $u=c$ and $d$.

The eigenstates of the Hamiltonian (1) can now be represented as

$\displaystyle\left(\begin{array}[]{c}|d\rangle\\\ |b\rangle\\\ |c\rangle\\\
|a\rangle\\\ \end{array}\right)$
$\displaystyle=\left(\begin{array}[]{cccc}1&0&0&0\\\ 0&1&0&0\\\
0&0&x_{+}&y_{+}\\\ 0&0&x_{-}&y_{-}\\\
\end{array}\right)\left(\begin{array}[]{c}|\uparrow_{e}\uparrow_{p}\rangle\\\
|\downarrow_{e}\downarrow_{p}\rangle\\\ |\uparrow_{e}\downarrow_{p}\rangle\\\
|\downarrow_{e}\uparrow_{p}\rangle\\\ \end{array}\right),$ (14)

where
$x_{\pm}=\frac{\sqrt{1+\xi^{2}}\pm\xi}{\sqrt{1+(\sqrt{1+\xi^{2}}\pm\xi)^{2}}}$
and $y_{\pm}=\frac{\pm 1}{\sqrt{1+(\sqrt{1+\xi^{2}}\pm\xi)^{2}}}$.

Figure 1: (a) Energy level diagram of the hyperfine structure of a ground-
state H atom driven by a magnetic field $B$. (b) The concurrence of the HFS
states of the H atom as a function of the temperature $T$ for different values
of the normalized magnetic field $\xi$.

To describe the entanglement of the HFS states of the hydrogen atom, we
consider a four-dimensional Hilbert space with a basis $\mathcal{Q}(e,p)=$
$\\{|\uparrow_{e}\uparrow_{p}\rangle,|\uparrow_{e}\downarrow_{p}\rangle,|\downarrow_{e}\uparrow_{p}\rangle,|\downarrow_{e}\downarrow_{p}\rangle\\}$,
where $|\uparrow_{q}\rangle$ and $|\downarrow_{q}\rangle$ are the electron
($q=e$) and proton ($q=p$) spin-up and spin-down states,
$|\uparrow_{e}\uparrow_{p}\rangle$ is a state where both the electron and
proton spins are up, $|\uparrow_{e}\downarrow_{p}\rangle$ is a state where the
electron spin is up, while the proton spin is down,
$|\uparrow_{e}\uparrow_{p}\rangle=|\uparrow_{e}\rangle\otimes|\uparrow_{p}\rangle$,
and
$|\uparrow_{e}\downarrow_{p}\rangle=|\uparrow_{e}\rangle\otimes|\downarrow_{p}\rangle$.
Each state ket in this four-dimensional space can thus be considered as a two-
qubit state.

##  III the concurrence

We now consider a hydrogen atom in equilibrium with a heat reservoir at a
temperature $\tau$. Pertinent to the hyperfine structure of an H atom at such
thermal equilibrium is the density operator
$\rho(\tau)=\frac{1}{Z}e^{-\beta{H_{HF}}}$, where $Z=Tr(e^{-\beta{H_{HF}}})$
is the partition function, $\beta=1/(k_{B}\tau)$, and $k_{B}$ is the Boltzmann
constant. While quantum entanglement in pure quantum states is adequately
understood in terms of the von Neumann entropy Bennett ; Nielsen , a suitable
quantifier for the entanglement of mixed states is much harder to define. Yet,
the entanglement of formation has been shown to satisfactorily address this
problem Wootters ; Hill , providing a closed-form computable measure for the
entanglement of mixed states, fully applicable to thermal states as defined by
the density operator $\rho(\tau)$ Arnesen ; Werlang . Specifically, given
$\rho$ = $\rho(\tau)$, the entanglement of such states is meaningfully
quantified via the concurrence Wootters ; Hill
$C=\textrm{max}\\{0,\lambda_{1}-\lambda_{2}-\lambda_{3}-\lambda_{4}\\}$, where
$\lambda_{i}$, enumerated such that,
$\lambda_{1}\geq\lambda_{2}\geq\lambda_{3}\geq\lambda_{4}$, are the
eigenvalues of the Hermitian matrix
$R=\sqrt{\sqrt{\rho}\tilde{\rho}\sqrt{\rho}}$ and
$\tilde{\rho}=(\sigma_{y}\otimes\sigma_{y})\rho^{*}(\sigma_{y}\otimes\sigma_{y})$.

With $H_{HF}$ as defined by Eq. (1), the concurrence $C$ becomes

$\displaystyle
C=\frac{1}{\mathcal{G}}\textrm{max}\\{0,\frac{\sinh[2\beta\mathcal{A}\sqrt{1+\xi^{2}}]}{\sqrt{1+\xi^{2}}}-e^{-2\beta\mathcal{A}}\\},$
(15)

where,
$\mathcal{G}=e^{-2\beta\mathcal{A}}\cosh(2\beta\mathcal{A}\xi)+\cosh[2\beta\mathcal{A}\sqrt{1+\xi^{2}}].$

In Fig. 1(b), we plot the concurrence $C$ calculated with the use of Eq. (3)
as a function of temperature $T=1/(\beta\mathcal{A})$. Entanglement is seen to
decrease with a rise in $T$, vanishing as the temperature is allowed to grow
above a critical value $T_{c}$. When no magnetic field is applied, $\xi=0$,
Eq. (3) yields $T_{c}$ = 4/ln3. It is instructive to rewrite this relation as
$k_{B}\tau_{c}=\Delta E$/ln3, where $\Delta E$ = $E_{b,c,d}-E_{a}$ =
$4\mathcal{A}$ is the energy gap between the highest- and lowest-energy HFS
levels at $B$=0. To articulate the connection of the critical temperature
$\tau_{c}$ to the fundamental physical constants, we express it as

$\tau_{c}=\frac{2}{3\ln{3}}\frac{\alpha^{2}\hbar^{2}}{k_{B}a_{0}^{2}}\frac{g_{e}g_{p}}{m_{p}}=\frac{4\alpha^{2}\hbar
c}{3k_{B}\ln{3}}\frac{m_{e}}{m_{p}}g_{e}g_{p}R_{\infty},$

where $\alpha$ is the fine-structure constant and
$R_{\infty}=m_{\text{e}}e^{4}/(8\varepsilon_{0}^{2}h^{3}c)$ is the Rydberg
constant.

The HFS entanglement can thus survive only as long as the thermal energy
$k_{B}\tau$ is much lower than the HFS splitting $\Delta E$. The maximum
thermal energy that the natural HFS entanglement (i.e., the HFS entanglement
at $B$ = 0) of the H atom can withstand is $k_{B}\tau_{c}\approx 5.35\times
10^{-6}$ eV, or $\tau_{c}\approx 60$ mK.

The effect of the magnetic field on the concurrence $C$ is much more complex
and much less transparent. At very low $T$, where the natural HFS entanglement
is high ($T\leq$ 3 in Fig. 1b), the concurrence $C$ is a rapidly decreasing
function of $\xi$. However, as $T$ increases, approaching $T_{c}$, $C$($\xi$)
gradually flattens out (Fig. 2a), eventually becoming nonmonotonic (for
$T\geq$ 3.5 in Fig. 2a). This behavior of $C$($\xi$) is in agreement with the
earlier observations by Zhu et al. Zhu .

It is, however, above the $\tau_{c}$ threshold that the magnetic field can
have the most dramatic and in many ways counterintuitive effect on the HFS
entanglement of the H atom. As one of the central findings of our analysis,
which goes well beyond the scope of Ref. Zhu , when applied to an H atom at
temperatures $T$ $\succsim$ $T_{c}$, an external magnetic field can induce an
entanglement of HFS states against all the odds of thermal effects, which
become strong enough at these temperatures to completely suppress the
entanglement of HFS states in the $B$ = 0 regime.

This effect is illustrated in Fig. 2b. Here, the temperature $T$ is set above
the $T_{c}$ threshold. Thus, as long as $B$ = 0, and, hence $\xi$ = 0, the H
atom features no HFS entanglement, $C$ = 0 (see Fig. 1b). Yet, even though all
the natural HFS entanglement has been lost at these temperatures, an external
magnetic field can overcome this loss and induce an entanglement in the HFS
manifold. This effect will be referred to hereinafter as magnetically induced
entanglement (MIE). The highest MIE concurrences $C$ are achieved at
temperatures right above $T_{c}$ (the solid curve in Fig. 2b, corresponding to
$T$ = 4). At higher $T$, thermal effects, once again, take their toll,
reducing the maximum attainable MIE. Higher $T$, as can be seen in Fig. 2b,
require stronger magnetic fields for the onset of MIE. Finally, in the regime
of very strong magnetic fields ($\xi>$ 25 in Fig. 2b), $C$($\xi$) is seen to
display a temperature-independent asymptotic behavior, with $C$($\xi$) curves
plotted for different $T$ bunching together as a part of this asymptotic
behavior to a $T$-independent universal $C_{0}$($\xi$) curve.

Figure 2:  The concurrence of the HFS states of the H atom as a function of
the normalized magnetic field $\xi$ below (a) and above (b) the critical
temperature $T_{c}$.

To gain insights into the physics behind this behavior of the HFS entanglement
as a function of the temperature and the magnetic field, we first examine the
concurrence of the HFS states with no magnetic field applied, $B$ = 0. As one
important finding, we see that, in this case,
$|c\rangle=\frac{1}{\sqrt{2}}(|\uparrow_{e}\downarrow_{p}\rangle+|\downarrow_{e}\uparrow_{p}\rangle)$
and
$|a\rangle=\frac{1}{\sqrt{2}}(|\uparrow_{e}\downarrow_{p}\rangle-|\downarrow_{e}\uparrow_{p}\rangle)$
are maximally entangled, with their concurrence $C$ = 1. At low temperatures,
such that $k_{B}\tau_{c}<<\Delta E$ = $E_{b,c,d}-E_{a}$, the population of the
lower-energy $|a\rangle$ singlet state is much higher than the population of
the $|b\rangle$, $|c\rangle$, and $|d\rangle$ HFS triplet. As the temperature
increases, however, the population of the HFS triplet grows, leading to a
decrease in the HFS entanglement. Eventually, at $k_{B}\tau_{c}\approx\Delta
E$, the population of the HFS triplet becomes comparable to the population of
the $|a\rangle$ state, and the entanglement is completely lost, $C$ = 0.

An external magnetic field lifts the degeneracy of the $|b\rangle$,
$|c\rangle$, and $|d\rangle$ states, splitting this triplet into three states
with different, $B$-dependent energies (Fig. 1a). As the magnetic field
increases, the energy gaps $\delta E_{c,d}$ = $E_{c,d}-E_{a}$ grow. It is
straightforward to see from Eq. (3) that, in the low-temperature limit, $T<<$
1, the temperature dependence of the concurrence is suppressed, $C$ $\approx$
$1/\sqrt{1+\xi^{2}}$, explaining the low-$T$ plateaus in the $C$($T$) plots in
Fig. 1b.

When the magnetic field is strong enough to induce $\delta E_{c,d}$ $\succsim$
$k_{B}\tau_{c}$, the temperature $\tau_{c}$ is no longer sufficient for
complete entanglement suppression. More rigorously, as can be seen from Eq.
(3), the HFS manifold retains entanglement as long as

$\displaystyle{\sinh[2\beta\mathcal{A}\sqrt{1+\xi^{2}}]}-\sqrt{1+\xi^{2}}e^{-2\beta\mathcal{A}}>0.$
(16)

Thus, the critical magnetic field, $\xi_{c}$, needed to induce an HFS
entanglement above the $\tau_{c}$ threshold can be found from

$\displaystyle\sinh[2\beta\mathcal{A}\sqrt{1+\xi_{c}^{2}}]=e^{-2\beta\mathcal{A}}\sqrt{1+\xi_{c}^{2}}.$
(17)

In the $T>>$ 1 regime, high magnetic fields are required to induce HFS
entanglement, $\xi_{c}>>1$. In this limit, Eq. (5) reduces to
$2\beta\mathcal{A}\approx\ \ln{2\xi_{c}}/(\xi_{c}+1)$.

Specifically, with $\xi_{c}$ set at $\xi_{c}\approx 16.5$, this approximation
yields an estimate, $T\approx 10.01$, that agrees very well with the results
of numerical simulations presented in Fig. 2b, where the dotted line, plotted
for $T=10$, is seen to take off from the $C$ = 0 level at precisely
$\xi_{c}\approx 16.5$.

##  IV coherence

As a useful insight, the inequality of Eq. (4), which guarantees the existence
of HFS entanglement, can be expressed via the Manhattan-norm coherence,
$D=\sum_{{i\neq j}}|\rho_{i,j}|$, also referred to as the $l_{1}$-norm
coherence Baumgratz . For the HFS states of the H atom at thermal equilibrium
with a temperature $\tau$, this coherence is given by

$\displaystyle
D=\frac{\sinh[2\beta\mathcal{A}\sqrt{1+\xi^{2}}]}{\mathcal{G}\sqrt{1+\xi^{2}}}.$
(18)

Eq. (4) is thus equivalent to $D>e^{-2\beta\mathcal{A}}/\mathcal{G}$. Figures
3a and 3b illustrate the behavior of $D$ as a function of the temperature $T$
and the normalized magnetic field $\xi$. In the low-temperature limit, $T<<$
1, $D$ is indistinguishable from the concurrence, $D$ $\approx$ $C$ $\approx$
$1/\sqrt{1+\xi^{2}}$. In this limit, the temperature dependence of the
coherence is suppressed, leading to well-resolved plateaus in the $D$($T$)
plots at low $T$ (Fig. 3a).

In the limit of a strong magnetic field, $\xi>>$ 1, the coherence can be
approximated as $D\approx(1-e^{-2\beta\mathcal{A}})/\xi$. In this limit, the
$D$($\xi$) plots bunch together (Fig. 3b) as $D$ tends to zero regardless of
$T$. This behavior of $D$ in the $\xi>>$ 1 limit provides deeper insights into
the properties of MIE at high $T$. Indeed, since the critical magnetic field
$\xi_{c}$ needed to induce HFS entanglement can be found from
$D(\xi_{c})=e^{-2\beta\mathcal{A}}/\mathcal{G}$, the maximum concurrence
attainable in the MIE regime (Fig. 2b) is bound to follow a rapid roll-off of
$D$($\xi$) as a function of $\xi$ (cf. Fig. 3b).

##  V THE PHYSICS BEHIND MAGNETICALLY INDUCED ENTANGLEMENT OF H

To better connect to the HFS physics behind the properties of MIE concurrence,
it is instructive to examine Eq. (3) for $C$ jointly with the equations for
the energy eigenvalues $E_{u}$. When no magnetic field is applied, $\xi$ = 0,
the $|a\rangle$ and $|c\rangle$ states are maximally entangled, with their
concurrence $C$ = 1. In the opposite limit of $\xi>>1$, however, the
$|a\rangle$ and $|c\rangle$ state kets tend to
$|c\rangle\approx|\uparrow_{e}\downarrow_{p}\rangle$ and
$|a\rangle\approx|\downarrow_{e}\uparrow_{p}\rangle$, with their energy
eigenvalues given by $E_{c}\approx\mathcal{A}(-1+2\xi)$ and
$E_{a}\approx\mathcal{A}(-1-2\xi)$. It is straightforward to see that the
concurrence of these states tends to zero. Physically, this result is
understood in terms of a strong coupling of electron and nuclear spins to the
external magnetic field, which eventually breaks the spin–spin
electron–nucleus coupling.

Figure 3:  The $l_{1}$-norm coherence of the HFS states of the H atom as a
function of the temperature $T$ (a) and the normalized magnetic field $\xi$
(b).

We will now benchmark the HFS entanglement of the H atom against the two-qubit
spin–spin entanglement in a one-dimensional (1D) Heisenberg chain (HC) Arnesen
. To this end, we consider two spins in a 1D Heisenberg chain driven by an
external magnetic field $B$ governed by an interaction Hamiltonian

$\displaystyle
H_{s}=J\sigma_{1}\cdot\sigma_{2}+\mu_{B}B(\sigma_{1}^{z}+\sigma_{2}^{z}),$
(19)

with a coupling constant $J<$ 0 ($J>$ 0) for a ferromagnetic
(antiferromagnetic) system.

Solving $H_{s}|v\rangle=E_{v}|v\rangle$, we find four energy eigenstates, $v=$
1, 2, 3, 4, $|1\rangle=|\uparrow_{1}\uparrow_{2}\rangle$,
$|2\rangle=|\downarrow_{1}\downarrow_{2}\rangle$,
$|3\rangle=\frac{1}{\sqrt{2}}(|\uparrow_{1}\downarrow_{2}\rangle+|\downarrow_{1}\uparrow_{2}\rangle)$,
$|4\rangle=\frac{1}{\sqrt{2}}(|\uparrow_{1}\downarrow_{2}\rangle-|\downarrow_{1}\uparrow_{2}\rangle)$,
with energy eigenvalues $E_{1}=J(1+4\xi)$, $E_{2}=J(1-4\xi)$, $E_{3}=J$, and
$E_{4}=-3J$, and the normalized magnetic field $\xi$ redefined as
$\xi=\frac{\mu_{B}B}{2J}$.

A two-qubit spin–spin entanglement in such a system is quantified in terms of
the concurrence Arnesen

$C=\textrm{max}\\{0,\frac{e^{4\beta J}-3}{1+e^{4\beta J\xi}+e^{-4\beta
J\xi}+e^{4\beta J}}\\}.$ (20)

The behavior of this concurrence as a function of the temperature $T$ and the
normalized magnetic field $\xi$ is illustrated in Figs. 4a and 4b. As one of
its central properties, readily seen from Eq. (8), $C$ = 0 for
$k_{B}\tau_{c}>4J$/ln3 and $C=(e^{4\beta J}-3)/(1+e^{4\beta J\xi}+e^{-4\beta
J\xi}+e^{4\beta J})$ for $k_{B}\tau_{c}<4J$/ln3.

The spins thus remain entangled only for temperatures below
$\tau_{c}=4J/(k_{B}$ln3).

Similar to the HFS states of the H atom, the 1D Heisenberg chain is permissive
of low-temperature spin–spin entanglement. The key properties of this
entanglement, however, are profoundly different from the properties of HFS
entanglement. The origins of these differences trace back to the physics of
hyperfine splitting vis-à-vis the physics embodied by the 1D Heisenberg chain.
Reflecting the difference in the physical contents of the two systems are the
properties of the eigenfunctions $|u\rangle$ and $|v\rangle$ as dictated by
the respective Hamiltonians $H_{HF}$ and $H_{s}$. When expanded in the basis a
suitable for the description of spin–spin entanglement, viz., the
$\mathcal{Q}(1,2)$ basis, the $|u\rangle$ eigenkets manifest a strong,
explicit dependence on the magnetic field. By contrast, the $|v\rangle$
eigenkets in the same representation are $B$-independent. As a consequence, at
$T$ = 0, the 1DHC concurrence is $C$ = 1 for any $\xi<$ 1 and $C$ = 0 for all
$\xi>$ 1 (Fig. 4a). This property of $C$ is in stark contrast with the low-$T$
behavior of the HFS concurrence, which decreases monotonically with $\xi$ at
any $T<<$ 1, $C$ $\approx$ $1/\sqrt{1+\xi^{2}}$ (Fig. 2a). When plotted as a
function of the dimensionless magnetic field $\xi$ at $T\approx$ 0, the 1DHC
concurrence displays a steep, almost stepwise change at $\xi$ = 1 (Fig. 4b).
The HFS concurrence, on the other hand, is always a smooth, well-behaved
function of $\xi$ (Figs. 2a, 2b).

Because the magnetic field makes no imprint on the expansion coefficients of
the $|v\rangle$ eigenkets in the $\mathcal{Q}(1,2)$ basis, the critical
temperature for the 1DHC entanglement, $\tau_{c}=4J/(k_{B}$ln3), is
independent of the magnetic field. Thus, unlike the natural HFS entanglement,
whose critical temperature, i.e., the temperature at which $C$ = 0, is a
function of $\xi$ (Fig. 1b), the 1DHC entanglement vanishes at the same
temperature regardless of $\xi$ (Fig. 4a). Importantly, once it is gone with
$\tau$ increased above $\tau_{c}$, the 1DHC entanglement never comes back no
matter how strong the external magnetic field is.

In this regard, the magnetically induced entanglement of HFS states of the H
atom identified in this work is fundamentally different, as it is induced at
temperatures above the critical point $\tau_{c}$, rising from zero (Fig. 2b).
Once induced by a magnetic field with a critical magnitude $\xi_{c}$, the MIE
of HFS states grows with $\xi$, reaches its temperature-dependent maximum,
then decreases and eventually vanishes (Fig. 2b) as the magnetic field becomes
strong enough to break the spin–spin coupling of the electron and its nucleus
in the H atom.

##  VI conclusion

To summarize, we have shown that the electron and nuclear spin degrees of
freedom in a hydrogen atom provide a physically meaningful frame and lend a
suitable Hilbert space for bipartite entanglement, whose two-qubit concurrence
and quantum coherence can be expressed in terms of the fundamental physical
constant. The intrinsic, natural entanglement that the hyperfine-structure
states of the H atom store at low temperatures is shown to rapidly decrease
with a growth in temperature, vanishing above a critical temperature of
$T_{c}$ $\approx$ 5.35 $\mu$eV. An external magnetic field, however, can
overcome this thermal loss of HFS entanglement. As one of the central findings
of this work, an external magnetic field can induce and sustain the
entanglement of HFS states, against all the odds of thermal effects, at
temperatures well above the $\tau_{c}$ threshold, thus enabling magnetic-
field-assisted entanglement engineering in low-temperature gases and solids.
Experiments to isolate spectroscopic signatures of entanglement in hydrogen
and hydrogen-containing systems are currently in progress as a follow-up to
the earlier studies Sheludiakov ; Ahokas ; Ahokas2 .

This research was supported in part by the Russian Foundation for Basic
Research (projects Nos. 18-29-20031, 19-02-00473), Russian Science Foundation
(project No. 20-12-00088 – ultrabroadband optical science), Ministry of
Science and Higher Education of the Russian Federation (project
14.Z50.31.0040, Feb. 17, 2017), and the Welch Foundation (grant
A-1801-20180324).

Figure 4: The concurrence $C$ quantifying the two-qubit entanglement in a 1D
Heisenberg model as a function of the temperature $T$ (a) and the normalized
magnetic field $\xi$ (b).

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# An Evaluation Framework for Mapping News Headlines
to Event Classes in a Knowledge Graph

Steve Fonin Mbouadeu
St. John’s University
<EMAIL_ADDRESS>
Martin Lorenzo
IBM Research
<EMAIL_ADDRESS>
Ken Barker
IBM Research
<EMAIL_ADDRESS>
Oktie Hassanzadeh
IBM Research
<EMAIL_ADDRESS>
###### Abstract

Mapping ongoing news headlines to event-related classes in a rich knowledge
base can be an important component in a knowledge-based event analysis and
forecasting solution. In this paper, we present a methodology for creating a
benchmark dataset of news headlines mapped to event classes in Wikidata, and
resources for the evaluation of methods that perform the mapping. We use the
dataset to study two classes of unsupervised methods for this task: 1)
adaptations of classic entity linking methods, and 2) methods that treat the
problem as a zero-shot text classification problem. For the first approach, we
evaluate off-the-shelf entity linking systems. For the second approach, we
explore a) pre-trained natural language inference (NLI) models, and b) pre-
trained large generative language models. We present the results of our
evaluation, lessons learned, and directions for future work. The dataset and
scripts for evaluation are made publicly available.

An Evaluation Framework for Mapping News Headlines
to Event Classes in a Knowledge Graph

Steve Fonin Mbouadeu St. John’s University<EMAIL_ADDRESS>Martin
Lorenzo IBM Research<EMAIL_ADDRESS>

Ken Barker IBM Research<EMAIL_ADDRESS>Oktie Hassanzadeh IBM Research
<EMAIL_ADDRESS>

##  1 Introduction

Businesses and organizations can benefit from seeking knowledge of new events
that may have an impact on their business. To assist in this task, there are
several media monitoring solutions with features that can provide alerts and
real-time analysis for ongoing events. The majority of existing solutions are
centered around entities and/or topics. For example, they identify mentions of
key companies or people, group texts by topics, and analyze contents for
sentiment. On the other hand, there is great value in an event-centric
solution that identifies ongoing events and analyzes the characteristics of
the identified events to enable event-based reasoning. In particular, such a
solution would enable causal reasoning to determine the causes and
consequences of ongoing events and identify potential risks and opportunities
Hassanzadeh et al. (2022).

To enable a knowledge-driven event-centric news analysis and monitoring
solution, a key requirement is the ability to accurately map ongoing news to
event-related classes in a knowledge base. One way to perform this mapping is
to treat event-related classes as a set of categories (or topics) and classify
news headlines into these categories. Prior work has studied classification
methods for news headlines (e.g., see Awasthy et al. (2021); Rana et al.
(2014) and references therein). The majority of existing methods rely on
supervised learning and therefore require a training corpus. For a generic
solution that can adapt to changing event classes or one that can be tuned
easily for different domains, it is not feasible to rely on the availability
of training corpora large enough for accurate classification.

In the absence of training data, the alternative solution is to apply
unsupervised or weakly supervised classification methods that rely on little
or no training data. Such methods often rely on rules and pre-trained generic
models. More recently, pre-trained language models, and in particular large
language models, have shown superior performance in such settings. As a
result, we have seen a surge in the number of available models, each using
different architectures, parameters, pre-training corpora, and fine-tuning
strategies. Choosing the right model for a given task requires an evaluation
framework to measure the accuracy of the models on the end task.

Figure 1: Example of News Headlines and Event Classes in Our Benchmark

In this paper, we present an evaluation framework for unsupervised mapping of
news headlines to event classes in a knowledge graph. To the best of our
knowledge, this is the first benchmark dataset and evaluation framework for
this task. In what follows, we first present the task definition and use cases
we envision for the task. We then describe our methodology for creating the
benchmark dataset. Next, we present the results of our evaluation of a number
of methods belonging to two different kinds of unsupervised techniques. We
discuss key lessons learned and a number of avenues for future work. The
datasets used in our experiments as well as the evaluation framework are
publicly available Mbouadeu et al. (2023).

##  2 Task Definition and Use Cases

Our target task in this paper is as follows: Given a news headline and a set
of event classes from a knowledge graph, find the most relevant event class to
the news headline. The news headline is a short text (typically a sentence)
that indicates the content of a news article by providing a concise summary of
the article’s contents. The knowledge graph contains event-related classes.
Each class comes with one or more labels, a description of the class, and
possibly a class hierarchy and other attributes. Figure 1 shows examples of
news headlines, event classes, and their mappings. We refer to this task as
News Headline Event Mapping. Note that this task is different from the event
linking task defined by Yu et al. (2023) which takes an event mention (a
phrase) and a context as input, and finds a specific Wikipedia article as
output. Nevertheless, as described in Section 4.1, such methods can be used
for our task.

Figure 2 shows example use cases for news headline event mapping in the
context of a knowledge-based news event analysis solution Hassanzadeh et al.
(2022). In this context, news headlines from a variety of sources or a news
content aggregation service (e.g., EventRegistry Leban et al. (2014)) are
monitored in order to identify major news that could have an impact on a
users’ organization, on a certain region, or more generally on society. This
domain of interest is defined through a knowledge graph of events that
contains a rich source of knowledge about past events and event classes. Such
a source of knowledge can be gathered through automated knowledge extraction
methods Hassanzadeh et al. (2020); Heindorf et al. (2020) or be derived from
domain-specific or general-domain knowledge sources such as Wikidata Vrandečić
and Krötzsch (2014). The knowledge graph provides event classes along with
labels and descriptions to be used for news headline event mapping. The output
of headline event mapping is then used for an analysis of the potential causes
and effects of the identified event. The outcome can be used as a part of a
news monitoring solution to create alerts for the identified event or its
consequences so that it can assist with managing a potential risk or
opportunity. It can also provide the required knowledge for an analyst looking
at the implications of ongoing news for a business or organization. Finally,
it can be used as an input for scenario planning Sohrabi et al. (2019) or
event forecasting Muthiah et al. (2016); Radinsky et al. (2012).

Figure 2: News Headline Event Mapping in a Knowledge-Based Event Analysis
Solution Hassanzadeh et al. (2022)

##  3 Benchmark Dataset

To the best of our knowledge, there is no benchmark dataset for the task of
news headline event mapping. There are benchmarks on related tasks such as
entity linking van Erp et al. (2016) that include news headlines. However,
none of these benchmarks provide ground truth event class annotations. We
have, therefore, curated a new dataset designed for the news headline event
mapping task using Wikidata and Wikinews. First, we leveraged the links to
Wikinews articles in Wikidata to gather a collection of event-related
instances. To focus on event classes, we then filtered out instances that are
not subclasses of occurrence (Q1190554) as well as classes with very short
labels, as some non-event related entities are also linked to Wikinews.
Finally, these articles were reviewed manually to check whether they related
to news headlines and news events. This yielded 105 Wikinews headlines mapped
to Wikidata event classes. We manually added five headlines from other sources
for a final dataset of 110 mappings of headlines to Wikidata event classes.
The labels of all of the Wikidata classes included in our benchmark are shown
in Figure 3. The examples of Figure 1 were taken from the dataset.

Figure 3: News Event Classes in Our Benchmark

There are a number of other benchmark datasets in the literature for related
tasks. Closest to our task is that of zero-shot sentence classification. Yin
et al. (2019) present an excellent review of benchmarks for this task. Many
benchmarks for news headline classification and for zero-shot sentence
classification target binary classification (e.g., for emotions or sentiment
or clickbait detection), or a small number of topics. The closest to our
benchmark is the Yahoo! dataset Zhang et al. (2015), which consists of 10
topics. To our knowledge, there is no benchmark that targets the task of
assigning news headlines to event classes in a knowledge graph or a large
number of well-defined topics.

##  4 Evaluation

We use our benchmark and evaluation framework to evaluate the effectiveness of
a number of different kinds of methods in news headline event mapping. We
first describe the approaches and implementation details for each method. We
then present the results of the evaluation and a detailed discussion on key
lessons learned and directions for future work.

###  4.1 Methods

We experiment with news headline event mapping methods ranging from a simple
similarity-based baseline to adaptations of classic entity linking tools and
large generative language models.

####  4.1.1 Zero-Shot Classifiers

We evaluate two zero-shot text classification methods. One is a simple
baseline based on textual similarity, while another uses state-of-the-art pre-
trained language models for classification.

##### Similarity-Based Baseline

(Fuzzy) This method identifies a substring of a headline that is suggestive of
an event occurrence, and finds the most similar event class label in the
knowledge graph to that substring. The substring is found through a sliding
window of bigrams and trigrams of word tokens in the input, and matching them
using Levenshtein distance Chandrasekar et al. (2017) to our target event
class labels. The event class with the lowest distance is returned as the most
similar class to the headline.

##### Zero-Shot Text Classifier using Natrual Language Inference

(ZSTC) This classifier is a standard “MNLI” model: a pre-trained language
model fine-tuned on the multi-genre textual entailment corpus for the Natural
Language Inference (NLI) task from the RepEval workshop Williams et al.
(2018). Instances in the MNLI corpus are pairs of sentences with a label
indicating whether the first sentence Entails the second sentence, is
Contradicted by it, or is independent of it (“Neutral”). MNLI models can be
used for zero-shot text classification by supplying the text to be classified
as sentence1, and a textual representation of a target class as sentence2. For
our experiments, the textual representation of a class (sentence2) is simply
the English label of the class in Wikidata. Sentence1 is the headline to be
classified. The target class whose textual representation (label) has the
highest Entailment score is the predicted class for the text. Our zero-shot
text classifier uses the RoBERTa-large Liu et al. (2019) language model fine-
tuned on MNLI.

####  4.1.2 Classic Entity Linkers & Adaptations

We considered a number of state-of-the-art open-source entity linking (EL)
systems to adapt to include in our experiments. Most entity linking solutions
are trained to work only on named entities (e.g., people, locations,
organizations) and fail when it comes to events. We considered EL systems that
are more easily adaptable for mapping to event classes. The systems we
considered include BLINK Wu et al. (2020), OpenTapioca Delpeuch (2019), Falcon
Sakor et al. (2020), and Wikifier Brank et al. (2017). Out of these, our
adaptation of BLINK failed to perform well, and OpenTapioca required a
training corpus. Although training OpenTapioca using our dataset provided
promising results (another potential use case for our dataset), we excluded
the results in this paper to focus on fully unsupervised (zero-shot) methods.

##### Falcon 2.0

(Falcon EM) Falcon 2.0 Sakor et al. (2020) leverages NLP techniques to achieve
state-of-the-art entity linking performance on a number of EL datasets,
notably on question-structured prompts Sakor et al. (2020). Given a prompt, it
generates a list of entity surface forms, similar to event mentions. After
generating these surface forms or tokens, it selects candidate entities for
each of them by searching them in an information retrieval (IR) index (powered
by Elasticsearch) of a Wikidata data dump. We only included Wikidata concepts
that were recursively instances or subclasses of event classes in the dump to
tailor it to our task. In our evaluation, we used Falcon to match headlines to
Wikidata concept labels. If Falcon did not generate at least one candidate
concept, we successively stripped tokens from the right of the headline,
approximating more general phrases. we repeated the process until either a
candidate concept was found or the phrase became empty. The resulting
candidate concepts were then ranked using SPARQL ASK queries, measuring the
taxonomic distance between the candidate concepts and our chosen news event
classes. The class from our set of target event classes that was the shortest
distance from a Falcon-generated candidate concept was chosen as the predicted
class for the headline.

##### Wikifier

(Wikifier) Wikifier Brank et al. (2017) is a service for the task of
“wikification" – taking an input text and annotating phrases in the text with
Wikipedia URLs. Wikifier employs surface forms of hyperlinks in Wikipedia to
perform linking to Wikipedia entities. For example, the Wikipedia page for
earthquakes contains a link to the tsunami page. This suggests that earthquake
is related to tsunami. For any surface form throughout Wikipedia that is
present in the given text, Wikifier makes a candidate entity of the underlying
entity. A directed mention-concept graph is created, linking surface forms to
these candidate entities. Wikifier performs a global disambiguation based on
the distance between entities. Distance represents the number of hyperlink
hops required to get from one page to another. The smaller the distance, the
more related the entities are considered. The relatedness metrics are used to
score the candidate entities. Wikifier returns these candidate entities as
predictions along with their scores. We converted the Wikipedia hyperlinks to
Wikidata concepts with a simple lookup query. For our evaluation, we picked
the top prediction that was among one of our target event classes.

####  4.1.3 Large Generative Language Models

Another way to perform zero-shot classification is through the use of
generative large language models (LLMs) and prompts. There are a number of
LLMs available with different architectures, parameter sizes, and resource
requirements. For the results in this paper, we decided to pick just one of
the popular LLMs with reasonable resource requirements, namely GPT-J 6B Wang
and Komatsuzaki (2021), so that our experiments are reproducible without
requiring access to commercial APIs or expensive GPUs. We include two
different prompting strategies for the results in this paper. Experiments with
a wider variety of LLMs and more extensive prompt engineering are a subject
for future work.

##### GPT-J Event Mapping

(GPT-J EM) Our goal here is to form a prompt that yields the generation of the
relevant event class by the LLM. One way to create a prompt is to provide a
few examples (a “few-shot” strategy) of headline + delimiter + known event
class label, followed by the headline to be classified and the same delimiter,
and ask the model to generate completion text. Having experimented with a
number of prompting strategies, we decided to use a co-training approach Lang
et al. (2022).

Co-training works similarly to cross-validation, where each individual
headline is mapped with zero shots using GPT-J and then the best-performing
headlines are used to generate a few-shot prompt. The output of this method is
an event label that we then mapped to Wikidata.

##### GPT-J Event Mapping with Types

(GPT-J EMT) We continued our experiments with GPT-J by including all the event
classes in the prompt along with the pre-training. The set of labels from our
news event classes were listed separately and prefixed with “types:”. We then
added this list to the beginning of the prompt to signal the categories to be
picked from. We also prefixed each annotation in the pre-training examples
with “type:” to establish that association. Additionally, we implemented a
catch-all for non-event classifications. If a prediction didn’t match an event
class label, we performed textual similarity matching with our target event
labels to find the most similar event class to return as output.

###  4.2 Results

For our evaluation we ran each system from Section 4.1 on the headlines from
our news event corpus to generate the systems’ best predicted event classes.
We calculated accuracy of each system as the percentage of top-ranked
predictions matching the gold event class.

The results are shown in Table 1. In addition to the benchmark datasets, all
of our outputs as well as our evaluation script are available on our GitHub
repository Mbouadeu et al. (2023).

Table 1: Accuracy Results |  | Fuzzy
---
| ZSTC
---
Falcon EM | Wikifier | GPT-J EM |  | GPT-J EMT
---
Correct @1 | 22 | 23 | 33 | 49 | 65 | 74
Accuracy | 0.2 | 0.209 | 0.3 | 0.445 | 0.591 | 0.673

The zero-shot classifier methods (Fuzzy and ZSTC) performed comparably. They
both did well on headlines that have linguistic overlap with a target class
label. Fuzzy works when there is surface/lexical overlap, whereas ZSTC takes
advantage of semantic overlap. Examples of headlines having linguistic overlap
with target classes are: “Major explosions at UK oil depot”, “Mass shooting
takes place in New York City subway system”, and “Myanmar military vows to
abide by constitution amid coup fears”. The first two, for example, have
explosion and mass shooting target event classes, and labels for those classes
appear verbatim in the headlines.

Linguistic overlap can result in frequent false positives, particularly for
very general target classes. For example, for the headline “More than 80
people killed in Nice, France attack on Bastille Day”, both methods associated
“killed” with the killing event class and “attack” with the attack class.
Ideally, both classes would be included among the gold classes and a ranking
metric used to give credit to multiple (ranked) system predictions. For
simplicity, and for even comparison to systems without ranked/scored output,
we only report accuracy (correct @1).

Among the classic entity linking methods, Wikifier performed better than
Falcon EM. In general, it was able to map more challenging headlines having no
obvious linguistic overlap with class labels. For example, it was able to map
the headline “Russia withdraws from Chernobyl in Ukraine” to the war event
class.

The LLM-based methods also showed the ability to map news headlines to event
classes whose labels do not appear in the headline. Examples of such headlines
are: “Nine firefighters killed in South Carolina blaze” (event class fire),
and “Attack at Texas elementary school kills at least 19, including 18
children”. (event class school shooting). The second example is particularly
interesting because the LLM-based methods preferred the more specific school
shooting event class in spite of the headline’s overlap with the label of the
killing class. The LLM-based methods (GPT-J EM and GPT-J EMT) also showed a
more consistent ability to map news headlines to events with labels that are
generalizations of text appearing in headlines, such as violence and natural
disasters.

###  4.3 Lessons Learned and Future Work

##### An Ensemble Approach

Although the classifier and entity linking based methods did not perform as
well as the LLM-based methods, they complement each other. Combining their
coverage of successfully mapping headlines in the dataset yields 95% accuracy.
When comparing their coverage of the dataset, they generally succeed and fail
on different types of headlines. The classic entity linker adaptations do well
with headlines with single-worded event mentions that match directly to event
classes. LLM-based mappers do well with multi-worded event mentions that are
not necessarily substrings of the event class labels and those without any
clear event mentions as well. They are still able to make the association
between these more ambiguous mentions and the event entities, presumably from
their learning from large amounts of text. This is further supported by the
fact that of the 33% of headlines that the LLM-based mappers failed to
correctly map, 87% have a clear event mention that closely matches the labels
of their event classes. Nevertheless, there is still a noticeable amount of
overlap between the two types of methods, as shown in Figure 4. However, these
results do suggest that an ensemble approach that combines techniques used in
classic entity linking and leverages large language models, intentionally
deciding how and when to apply them, would improve performance on this task.

Figure 4: Overlap of Accurate Prediction Coverage of Entity Linking
Adaptations and LLM-based Methods

##### A Larger Dataset

Despite the relatively small size of the current version of our dataset, we
believe our results are informative, and highlight the strengths and
weaknesses of different classes of methods. We also believe the small size of
the data reflects well the real-world use case of building a generic and
adaptable event monitoring solution, where gathering ground truth data for
supervised solutions could be prohibitively expensive. Still, the methodology
we outlined in Section 3 can be extended to gather a larger and more diverse
collection of news headlines mapped to event classes. At the time of writing
this manuscript, we are applying a similar strategy to news headlines that are
referenced from within Wikipedia-related event articles to curate a second,
much larger version of our dataset.

##### More Experiments on LLMs

With the ever-growing number of publicly-available LLMs as well as commercial
APIs enabling access to such models and allowing a more extensive prompt
engineering effort, our dataset and its larger extensions can be used for a
study on various LLM-based news headline event mapping methods.

##  5 Conclusion

In this paper, we defined the task of news headline event mapping and outlined
a few use cases for the task in event monitoring, analysis, and forecasting
solutions. We presented an approach for creating a benchmark dataset, and used
it to create the first benchmark dataset for the evaluation of news headline
event mapping methods. We used the benchmark to evaluate different classes of
mapping methods, including a) zero-short classification based methods, b)
adaptations of classic entity linking methods, and c) methods based on large
generative language models. Our results provide interesting insights on the
strengths and weaknesses of each of the methods. We outlined several avenues
for future work, including our plan to extend the dataset, work on an ensemble
method, and further experiments on LLM-based methods. Our dataset, as well as
our evaluation script and outputs of the models, are publicly available on our
GitHub repository.

## References

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