Measuring statistics-induced entanglement entropy with a Hong-Ou-Mandel interferometer Gu Zhang1 2Changki Hong3Tomer Alkalay3Vladimir Umansky3Moty Heiblum3Igor Gornyi2and Yuval Gefen4

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Measuring statistics-induced entanglement entropy with a Hong-Ou-Mandel interferometer

Gu Zhang,1, 2, ∗Changki Hong,3, ∗Tomer Alkalay,3, ∗Vladimir

Umansky,3Moty Heiblum,3, †Igor Gornyi,2, ‡and Yuval Gefen4, §

1Beijing Academy of Quantum Information Sciences, Beijing 100193, China

2Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany

3Braun Center for Submicron Research, Department of Condensed Matter Physics,

Weizmann Institute of Science, Rehovot 761001, Israel

4Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 761001, Israel

(Dated: December 27, 2023)

Despite its ubiquity in quantum computation and quantum information, a universally applicable deﬁnition

of quantum entanglement remains elusive. The challenge is further accentuated when entanglement is associ-

ated with other key themes, e.g., quantum interference and quantum statistics. Here, we introduce two novel

motifs that characterize the interplay of entanglement and quantum statistics: an ‘entanglement pointer’ and a

‘statistics-induced entanglement entropy’. The two provide a quantitative description of the statistics-induced

entanglement: (i) they are ﬁnite only in the presence of quantum entanglement underlined by quantum statis-

tics; (ii) their explicit form depends on the quantum statistics of the particles (e.g., fermions, bosons, anyons).

We have experimentally implemented these ideas by employing an electronic Hong-Ou-Mandel interferome-

ter fed by two highly diluted electron beams in an integer quantum Hall platform. Performing measurements

of auto-correlation and cross-correlation of current ﬂuctuations of the scattered beams (following ‘collisions’),

we quantify the statistics-induced entanglement by experimentally accessing the entanglement pointer and the

statistics-induced entanglement entropy. Our theoretical and experimental approaches pave the way to study

entanglement in various correlated platforms, e.g., those involving anyonic Abelian and non-Abelian states.

Introduction. A pillar of quantum mechanics – quantum

entanglement – prevents us from obtaining a full independent

knowledge of subsystem Aentangled with another subsystem

B. Indeed, the state of subsystem Amay be inﬂuenced or

even determined following a measurement of B, even when

both are distant apart. This feature, known as the non-locality

of quantum entanglement, is at the heart of the fast-developing

ﬁeld of quantum information processing (see, e.g., Refs. [1–

5]). An apt example is a system comprising two particles

with opposite internal magnetic moments (“spin up” and “spin

down”). Imagine we put one particle on Earth (subsystem A)

and the other on Mars (subsystem B). If measurement on A

reveals the particle is in the “up” state, this instantaneously

dictates that the Bparticle is “down”. Following Bell [6]

and CHSH [7] inequalities, measurements of the respective

spins in different directions may unambiguously demonstrate

the quantum nature of the entanglement of Aand B.

An essential way in which quantum entanglement reveals

itself is the entangled subsystem’s entropy. The entanglement

entropy (EE) of subsystem Acan be found when the complete

information of Bis discarded. This amounts to summing over

all possible states of B. Formally, the von Neumann EE is

deﬁned as Sent =−Tr(ρAln ρA), where ρA=TrB(ρAB)is

the reduced density matrix of Aafter tracing over the states of

B, where ρAB is the density matrix in the combined Hilbert

space A⊕B. When the subsystems share common entangled

pairs of particles, such pairs are effectively counted by the EE.

Another pillar of quantum mechanics is the quantum statis-

tics of indistinguishable particles, whose wavefunction might

acquire a non-trivial phase upon exchanging the particles’ po-

sitions (braiding). This phase is pertinent in classifying quasi-

particles as fermions, bosons, and, most interestingly, anyons.

Being instrumental in realizing platforms for quantum infor-

mation processing (see, e.g., Ref. [8]), it motivated several

insightful experiments [9–15] that intended to detect any-

onic statistics [16–23]. Among such experimental setups, the

Hong-Ou-Mandel (HOM) interferometer [24] was employed

as one of the simplest platforms to manifest bosonic [25],

fermionic (see, e.g., Refs. [26,27]), and anyonic (Laughlin

quasiparticles) [14,21,28] statistics. Despite their impor-

tance, the interplay of entanglement with quantum statistics

has hardly been studied, either theoretically or experimentally

(see, however, Refs. [27,29]).

In an attempt to address EE in the context of quantum trans-

port, it has been theoretically proposed [30] to focus on a sin-

gle quantum point contact (QPC) geometry (with partitioning

Tof the incident beam), which allows partial separation of

two subsystems (“arms”), Aand B. Following partial trac-

ing over states in one subsystem, the EE can, in principle, be

obtained indirectly via a weighted summation over even cu-

mulants of particle numbers extracted from the current-noise

measurements (see the discussion of noise cumulants in, e.g.,

Ref. [31]). However, even measurement of the fourth cumu-

lant is not straightforward [32] in mesoscopic conductors [33].

To our knowledge, no study of EE through measurements of

quantum transport has been reported. We note that the EE had

been measured in localized atomic systems (see Ref. [34] for

a review). In addition, the “impurity entropy” (not an EE), in-

duced by frustration at quantum criticality was most recently

reported in Refs. [35,36].

Perspective of our analysis. In the present study, we

fuse two foundational quantum-mechanical notions: quan-

tum statistics and entanglement, and propose the concept of

statistics-induced entanglement. We introduce two functions

quantifying entanglement arising from the quantum statistics

of indistinguishable particles: (i) the “entanglement pointer”

arXiv:2210.15520v3 [cond-mat.mes-hall] 25 Dec 2023

QPCA

QPCB

Figure 1. Schematics of the setup. (A) Schematics of the exper-

imental setup. (B) The corresponding theoretical schematics. The

HOM interferometer consists of two sources (SAand SB) and two

diluted middle arms (MA,MB) via transmission probabilities TA

and TB(with two QPC’s). The currents are measured at drains DA

and DB. For later convenience, we call the source arms after the

diluters as ˜

DAand ˜

DB. For simplicity, the two sources are equally

biased: VA=VB=Vbias. The red line separates the two “entan-

gled” subsystems, A(the two upper arms with labels “A”) and B

(the two lower arms with labels “B”). (C) Distribution functions of

the two middle arms (MAand MB) for non-interacting fermions

(fA,fB, respectively) at zero temperature (carrying shot noise). The

double-step distributions are modiﬁed when the ﬁlling factor is larger

than one, with an added interaction between the two modes on each

edge [Eq. (S34) of SI Section S2].

(EP, PE), and (ii) the statistics-induced entanglement entropy,

SEE (denoted as SSEE). Both are derived from correlations

of currents ﬂuctuations in an HOM conﬁguration, and are ex-

pressed in Eqs. (1)&(4). Importantly, these two functions

vanish for distinguishable particles, and are ﬁnite when indis-

tinguishable particles emitted from the two sources SAand

SBbecome entangled following “collisions”.

Typically entanglement is the outcome of Coulomb interac-

tion between distinct constituents of the system. Here, we fo-

cus on the entanglement being solely a manifestation of quan-

tum statistics. If one considers current-current correlators, this

contribution to the entanglement may be complemented (or

even fully masked) by the effect of Coulomb interactions be-

tween the colliding particles. Below we show, theoretically

and experimentally, that with our specially designed function,

SSEE, the leading contributions of the Coulomb interaction are

canceled, with the remaining terms dominated by quantum

statistics [cf. Eq. (3) and Eq. (S21) of Supplementary Infor-

mation (SI) Section S1].

We note that the acquisition of statistics-induced entangle-

ment is both instantaneous and non-local. It is acquired im-

mediately when two identical particles braid each other, even

at a distance. By these features it is universal. By contrast,

the Coulomb interaction contribution to the entanglement re-

quires the two particles to directly interact with each other,

and depends on the strength and duration of this interaction,

hence it is non-universal. This non-universal inﬂuence from

interaction becomes dominant in the measured noise (Figs. 4B

and 4C), but is negligible in our constructed EP, PE.

Turning now to the technicalities of our study, the theoret-

ical derivation of the explicit forms of the EP and SEE (see

Methods) employs, respectively, the Keldysh technique [31]

and an extended version of the approach of Ref. [30] [see

Eq. (8)]. The actual measurements were carried out in an

HOM conﬁguration [24], fabricated in a two-dimensional

electron gas (2DEG) tuned to the integer quantum Hall (IQH)

regime. Two highly diluted (via weak partitioning in two

outer QPCs) edge modes were let to “collide” at a center-QPC,

and current ﬂuctuations (shot noise) of two scattered diluted

beams (Fig. 1) were measured. While the deﬁnitions of the

EP and SEE are not restricted to a speciﬁc range of param-

eters, expressing SEE in terms of the measured EP is possi-

ble only within the limit of highly diluted impinging current

beams [Eq. (7)]. As will be shown, the theoretical prediction

agrees very well with the experimental data.

The model and the entanglement pointer (EP). Our HOM

interferometer consists of four arms, all in the IQH regime

(Fig. 1). Two sources SAand SBare biased equally at

VA=VB=Vbias, with sources currents weakly scattered

by two QPCs, each with dilution TAand TB, respectively.

The partitioned beams impinge on a central QPC (from mid-

dle arms MAand MBin Fig. 1) with transmission T[21].

The two transmitted electron beams are measured at drains

DAand DB.

With this setup, we deﬁne the ﬁrst entanglement-

quantiﬁcation function – EP, PE. It is expressed through the

cross-correlation of the two current ﬂuctuations, excluding the

statistics-irrelevant contribution,

PE(TA,TB, Vbias)≡ˆdt [⟨IA(t)IB(0)⟩irr |TA,TB,Vbias

−⟨IA(t)IB(0)⟩irr |0,TB,Vbias −⟨IA(t)IB(0)⟩irr |TA,0,Vbias ].

(1)

Here, IAand IBrefer to the current operators in the cor-

responding drains DAand DB(Fig. 1B), and “irr” refers to

the irreducible correlators (connected correlation function),

where the product of the averages is removed. Note that the

last two terms in Eq. (1) are each evaluated with only one

active source (i.e., either TAor TBis zero), and, thus do

not involve the two-particle scattering in the HOM conﬁgura-

tion [19,26,37]. This removal of last two terms has been car-

ried out in Refs. [37,38], however without referring to entan-

glement. Importantly, Eq. (1) yields zero for distinguishable,

non-interacting particles, since the ﬁrst term is then a super-

position of two independent single-source terms. By contrast,

the EP is ﬁnite and statistics-dependent for indistinguishable

particles.

For instance, for a double-step-like distribution of such par-

ticles (e.g., Fig. 1C for fermions), we obtain cross-correlations

(CC) of current operators,

fermions: ˆdt⟨IA(t)IB(0)⟩irrTA,TB,Vbias

−e3

hT(1 − T )(TA− TB)2+TATBPQPCVbias,

bosons: ˆdt⟨IA(t)IB(0)⟩irrTA,TB,Vbias

hT(1 − T )(TA− TB)2− TATBPQPCVbias.

(2)

Here PQPC describes an additional bunching (or anti-

bunching) probability induced by Coulomb interactions

within the central QPC (cf. SI Section S2). Note that for

equal diluters, TA=TB, the non-interacting part of the CC

vanishes, indicating that the nature of the CC is then solely

determined by interactions. This is however not so for the EP.

Indeed, with Eqs. (1) and (2), we obtain,

fermion EP: PE=(2 −PQPC)e3

hT(1 − T )TATBVbias,

boson EP: PE=(−2−PQPC)e3

hT(1 − T )TATBVbias.

(3)

In the presence of a weak inter-mode interaction among

particles within the middle arms MAand MB,PQPC is re-

placed with PQPC +Pfrac [see Methods and Eq. (S51) of SI

Section S2]. The term Pfrac refers to the inﬂuence of intra-

arm “charge fractionalization” that produces “particle-hole”

dipoles in the two interacting edge modes (Refs. [39,40]).

Crucially, the unavoidable Coulomb-interaction contribution

to the EP, parameterized by PQPC and Pfrac (introduced in

Supplementary Eqs. (S50) and (S51), respectively), appears

in terms that are quadratic in the beam dilution (TAand TB)

and hence is parametrically smaller than the linear (∼ TAPA

and ∼ TBPB) terms in the noise correlation functions [see

Eq. (13) in Materials and Methods]. It follows that the EP rids

of the undesired effect of Coulomb interactions, hence truly

reﬂecting the state’s statistical nature.

Entanglement entropy from statistics. The second entan-

glement quantiﬁer is the “statistics-induced entanglement en-

tropy” (SEE), which is deﬁned in a similar spirit to the EP (by

removing the statistics-irrelevant single-source contributions

to the EE),

SSEE(TA,TB)≡−[Sent(TA,TB)−Sent(TA,0)−Sent(0,TB)] .

(4)

To illustrate the relation between the SEE and Bell-pair en-

tanglement, we consider the case of two incoming fermions

(Fig. 2A). The pure two-particle state at the output of our de-

vice is represented as (see Fig. 2)

|Ψ⟩=|˜

ψ⟩+|ψ⟩.(5)

Here, |˜

ψ⟩≡|ψ2,0⟩+|ψ0,2⟩denotes a state where both par-

ticles end up in either subsystem A(2,0) or B(0,2) (Figs. 2B

and 2C, respectively). In either case, obeying Pauli’s block-

ade, two electrons must occupy the two arms of the same

subsystem: for example, ˜

DAand DAfor the state (2,0),

which can be written as (1,1,0,0) in the basis of drain arms

DA,DA,DB,˜

DB. Any coupling between the arms within one

subsystem cannot change the 1,1arrangement for subsystem

Ain |ψ2,0⟩. This implies that no quantum manipulations on

subsystem A, leading to Bell’s inequalities (Refs. [6,7]) are

possible with |˜

ψ⟩alone, i.e., without coupling the present

setup to extra channels. The same holds for subsystem B.

Nevertheless, |˜

ψ⟩is a non-product state with nonlocal [41,42]

entanglement: if the two particles are detected in subsystem

A, this automatically implies that no particles are to be de-

tected in subsystem B. In principle, Bell’s inequalities can

be tested with |˜

ψ⟩using modiﬁed devices akin to those pro-

posed for a similar bosonic state (a NOON state) in, e.g.,

Refs. [43,44] and Refs. [45,46], after the introduction of ex-

ternal states.

By contrast,

|ψ⟩=α| ↑A⟩| ↑B⟩+β| ↓A⟩| ↓B⟩ ≡ |ψ1,1⟩,(6)

represents an effective Bell pair (with amplitudes αand β),

where one particle leaves the device through subsystem A

and the other through B(hence |ψ1,1⟩, as opposed to |ψ2,0⟩

and |ψ0,2⟩, see Figs. 2D and 2E). Here, |↑A⟩,|↓A⟩are cer-

tain (mutually orthogonal) linear combinations of the states

|˜

DA⟩and |DA⟩;|↑B⟩,|↓B⟩are deﬁned similarly for subsys-

tem B[see Eq. (S67) of SI Section S3]. The quantum super-

position in Eq. (6) allows for rotating the “pseudospin” (i.e.,

rotation between orthonormal bases |↑A⟩and |↓A⟩) of sub-

system A, hence the measurement of pseudospins in a “trans-

verse direction” is possible, as required by Bell’s inequalities.

It is also worth noting that the states |↑A⟩,|↓A⟩are nonlocal:

each of them is constructed out of states in the arms associ-

ated with ˜

DAand DA, which are spatially separated by the

middle arm MAof length about 2µm in the real setup, see

Fig. 4A. The detailed forms of |˜

ψ⟩and |ψ⟩are manifestations

of quantum statistics, which underlines the statistics-induced

entanglement, captured by the function SSEE.

Technically, the building blocks of SEE, Sent (Eq. (4)) can

be obtained [30,47,48] by calculating the “generating func-

tion” χ(λ)≡Pqexp(iλq)Pqof the full counting statistics

(FCS) [31] (see Methods). Here Pqrefers to the probability to

D E

| 2,0i

| 0,2i

Figure 2. Two components |˜

ψ⟩and |ψ⟩, of two-particle wave-

functions, shown in the schematics of Fig. 1B. (A) Pre-collision

conﬁgurations. Two particles (red and blue pulses) are injected

from SAand SB, respectively. Hereafter, post-scattering quasi-

particles comprise contributions from both incident particles (blue

and red). (B) and (C): Constituents of the state |˜

ψ⟩=|ψ2,0⟩+

|ψ0,2⟩. (D) and (E): Constituents of the “Bell pair” state |ψ⟩=

α|↑A⟩|↑B⟩+β|↓A⟩|↓B⟩, Eq. (6). In comparison to |˜

ψ⟩conﬁgura-

tions, particle states of |ψ⟩conﬁgurations are entangled, both within

(indicated by dashed ellipses) and between (indicated by the red-blue

mixed pulses) subsystems.

transport charge qbetween the subsystems Aand Bover the

measurement time. In a steady state, SSEE is proportional to

the dwell time τ(see SI Section S5), which corresponds to the

shortest travel time from the central QPC to an external drain.

This should be replaced by the coherence time, τφ, if the latter

is shorter than the dwell time. The EE grows linearly with the

coherent arm’s length (beyond this coherence length the parti-

cles become dephased, hence disentangled). In the following

analysis we neglect externally-induced dephasing along the

arms, as the dephasing length in this type of IQH devices is

known to be longer than the arm’s length.

While the function SSEE is in principle measurable, it

becomes readily accessible in the strongly diluted limit

TA,TB≪1. In this limit, SSEE is approximately equal to a

function ˜

SSEE, which is proportional to the EP of free fermions

and bosons (see Methods):

SSEE TA,TB≪1

−−−−−−→ − 1

2e2PEln(TATBT2)τ≡˜

SSEE.(7)

Note the statistics-sensitive factor, PE. Since the non-

interacting (purely statistical) contribution to PE(cf. Eq. (3))

for bosons is opposite in sign to its fermionic counterpart, so

is the corresponding ˜

SSEE.

Importantly, addressing SEE (compared to Sent) has two

obvious upsides. First, extracting PEvia current cross-

correlation measurements, this quantity is easy to obtain in the

strongly diluted particle beam limit. Second, it allows us to rid

of most of the undesired effects of Coulomb interactions, and

clearly single out quantum statistics contributions. To validate

TA=TB=0.01

TA=TB=0.2

TA=TB=0.01

TA=TB=0.2

A B

C D

0.0 0.2 0.4 0.6 0.8 1.0

0.00

0.05

0.10

0.15

0.0 0.2 0.4 0.6 0.8 1.0

-0.15

-0.10

-0.05

0.00

0.0 0.2 0.4 0.6 0.8 1.0

-8

-6

-4

-2

Figure 3. Comparison between theoretical values of SSEE and

SSEE.Free fermions [panels (A) and (B)] and free bosons [panels

of Twhen TA=TB= 0.01 in (A) and (C). When TA=TB= 0.2

[(B) and (D)], a ﬁnite but small difference begins to show up be-

tween them. The bias used Vbias = 20.7µV. We take the dwell time

τdwell = 0.01ns (see SI Section S5 for the evaluation of τdwell).

Eq. (7) we compare SSEE [calculated according to Eq. (S21) of

SI Section S1] and ˜

SSEE for free fermions (Figs. 3A&3B) and

free bosons (Figs. 3C&3D). We next compare out theoretical

predictions with experiment.

Experimental results. The experimental structure was fab-

ricated in uniformly doped GaAs/AlGaAs heterostructure,

with an electron density of 9.2 ×1010 cm−2and 4.2 K dark

mobility 3.9 ×106cm2V−1s−1. The 2DEG is located 125nm

below the surface. Measurements were conducted at an elec-

tron temperature ∼14mK. The structure is shown in Fig. 1A

(schematically) and in Fig. 4A (electron micrograph). Two

QPCs are used to dilute the two electron beams, which “col-

lided” at the central QPC located 2µm away. Two ampliﬁers,

each with an LC circuit tuned to 730 KHz (with bandwidth 44

KHz) measuring the charge ﬂuctuations, are placed at a large

distance (around 100µm) from the 2D Hall bar. The outer-

most edge mode of ﬁlling factor ν= 3 of the IQH was diluted

by the two external QPCs.

Cross-correlation of the current ﬂuctuations of the reﬂected

diluted beams from the central QPC (T= 0.53), with TA=

TB= 0.2, is plotted in Fig. 4B. The corresponding single

source CC, with TA= 0.2 & TB= 0, is plotted in Fig. 4C.

Though the data is rather scattered, the agreement with the

theoretically expected CC is reasonable. For both cases,

the measured data displays a clear deviation from the non-

interacting curve: an evidence of strong interaction inﬂuence.

Importantly, for the equal-source situation (TA=TB= 0.2,

Fig. 4B), the CC is entirely produced by interactions within a

single source [see SI Eq. (S48)], indicating the inadequacy of

CC to quantify entanglement.

The measured data, with the applied source voltage larger

than the electron’s temperature (eV > kBT) was used to

calculate the EP (Fig. 4D) and the SEE (Fig. 4E), and then

compared with the expected EP and SEE. The measurement

results conformed with the theoretical prediction of the EP.

More data for ν= 3 and ν= 1 situations is provided in SI

Sections S8 and S9, respectively.

0 5 10 15

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0 5 10 15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0 5 10 15 20

-0.15

-0.10

-0.05

0.00

0.05

CC (105e3V/~)

Vbias(µV)

Non-interacting ﬁt

Interacting ﬁt

Double-source

TA=TB=0.2

Single-source

CC (105e3V/~)

Vbias(µV)

Non-interacting ﬁt

Interacting ﬁt

TA=0.2,TB=0

EP (105e3V/~)

Vbias(µV)

TA=TB=0.2

Vbias(µV)

TA=TB=0.2

0 5 10 15 20

-0.05

0.00

0.05

0.10

0.15

Figure 4. Experimental setup and experiment-theory comparisons. (A) SEM (scanning electron microscope) micrograph of the central

part of the fabricated sample. Subsystems Aand B(cf. Fig. 1B) are highlighted by shaded blue and shaded red areas, respectively. Transport

directions of edge states in the arms associated with the sources SA,B and drains DA,B ,˜

DA,B , as well as in the diluted “middle arms” MA,B ,

are indicated by dashed black arrows. (B), (C) Double-source and single-source cross-correlations (CCs), respectively [see Eq. (S48) of the

SI for expressions that include interaction contributions]. In both cases, theoretical curves with interaction taken into account (blue curves)

agree better with the experimental data (black dots). (D), (E) Measured data for the EP and SEE. Panel (D) compares the measured EP (black

dots) with theoretical curves: including interaction contributions (blue) and non-interacting particles (red). Although the interaction strength

is the same as in (B) and (C), the difference between the theoretically calculated values of the EP with and without interaction contribution is

much smaller than for the cross-current correlations, panels B and C. This demonstrates that the expression for the EP subtracts the interaction

contribution to leading order. Panel (E): Comparison between the experimentally measured data (black dots) and the theoretical dependence

of SSEE on the source current (here τdwell = 0.01ns as in Fig. 4). Experimental data points are obtained in two steps (see SI Section S1D for

details): (i) we evaluate ˜

SSEE (using Eq. (7)) with the measured EP from panel (D), and, (ii) relying on the fact that at the experimental value

T= 0.53 the ratio SSEE/˜

SSEE ≈1.22 in Fig. 4B, we use this ratio to scale the measured ˜

SSEE to reconstruct SSEE. Both the interacting (blue)

and non-interacting (red) theoretical curves for SSEE agree remarkably well with the experimental data.

As discussed above, the current ﬂuctuations are also in-

ﬂuenced by two sources of Coulomb interactions: (i) inter-

mode interaction at the same edge, and (ii) interaction within

the central QPC in the process of the two-particle scattering

(Figs. 4B&4C). However, the inﬂuence of these interactions

on the EP and SEE is negligible in our setup, which is in great

contrast to, e.g., Refs. [49,50], where entanglement is purely

interaction-induced; see also Refs. [51,52], as Figs. 4D&4E

demonstrate (see also SI Section S2). Thus, the measured cur-

rent noise indeed yields the information on statistics-induced

entanglement.

Summary and outlook. Entanglement and exchange statis-

tics are two cornerstones of the quantum realm. Swapping

quantum particles affects the many-body wavefunction by

introducing a statistical phase, even if the particles do not

interact directly. We have shown that quantum statistics

induces genuine entanglement of indistinguishable particles,

and developed theoretical and experimental tools to unam-

biguously quantify this effect. Our success in ridding of

the contribution of the local Coulomb interaction, facilitates

a manifestation of the foundational property of quantum

mechanics – nonlocality. It also presents the prospects of gen-

eralizing our protocol to a broad range of correlated systems,

including those hosting anyons (Abelian and non-Abelian,

see e.g., SI Section S7), and exotic composite particles (e.g.

“neutralons” at the edge of topological insulators [53,54]).

Our protocol may also be generalized to include setups

based on more complex edge structures, and platforms where

the quasi-particles involved are spinful. Another intriguing

direction is to explore the interplay of statistic-induced en-

tanglement and quantum interference (e.g., similar structures

considered in SI Section S8).

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Measuringstatistics-inducedentanglemententropywithaHong-Ou-MandelinterferometerGuZhang,1,2,∗ChangkiHong,3,∗TomerAlkalay,3,∗VladimirUmansky,3MotyHeiblum,3,†IgorGornyi,2,‡andYuvalGefen4,§1BeijingAcademyofQuantumInformationSciences,Beijing100193,China2InstituteforQuantumMaterialsandTechnologies,Karlsru...

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Measuring statistics-induced entanglement entropy with a Hong-Ou-Mandel interferometer Gu Zhang1 2Changki Hong3Tomer Alkalay3Vladimir Umansky3Moty Heiblum3Igor Gornyi2and Yuval Gefen4

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