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Nature Communications

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

Gu Zhang, Changki Hong, Tomer Alkalay, V. Umansky, Moty Heiblum, I. V. Gornyi, Yuval Gefen

Published Apr 23, 2024• 8 citations
Publisher

Abstract

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 associated 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 statistics and (ii) their explicit form depends on the quantum statistics of the particles (e.g., fermions, bosons, and anyons). We have experimentally implemented these ideas by employing an electronic Hong-Ou-Mandel interferometer 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.

DOI
10.1038/s41467-024-47335-z

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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 associated 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 statistics and (ii) their explicit form depends on the quantum statistics of the particles (e.g., fermions, bosons, and anyons). We have experimentally implemented these ideas by employing an electronic Hong-Ou-Mandel interferometer 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.
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 associated 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 statistics; (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 interferometer 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.
Hong-Ou-Mandel interferometry allows one to detect the presence of entanglement in two-photon input states. The same result holds for two-particle input states which obey fermionic statistics. In the latter case, however, antibouncing introduces qualitative differences in the interferometer response. This effect is analyzed in a gedanken experiment where the particles entering the interferometer are assumed to belong to a one-parameter family of quons which continuously interpolate between the bosonic and fermionic statistics.
characteristic of exotic quantum phases of matter. However, its experimental verication is an outstanding challenge in condensed matter physics. Within small quantum information processing units, entanglement may be detected via resource-intensive state tomography or class-specic entanglement witnesses. Here, we demonstrate a novel approach to the measurement of entanglement entropy of any bosonic system, using a quantum gas microscope with tailored potential landscapes. We extend the concept of Hong-Ou-Mandel interference from two particles to many-body states. Interfering two copies of identically prepared states measures the quantum mechanical purity of the system and its subsystems, placing bounds on the entanglement entropy. We apply this technique to observe the entanglement dynamics in a few-particle quench of a bosonic system. Our protocol may be applied to any many-body state and provides a new platform for the characterization of strongly correlated states in optical
Collision of quantum particles remains an effective way of probing their mutual statistics. Colliders based on quantum point contacts in quantum Hall edge states have been successfully used to probe the statistics of the underlying quantum particles. Notwithstanding the extensive theoretical work focusing on pointlike colliders, when it comes to experiment, the colliders are rarely pointlike objects and can support a resonant level or multiple tunneling points. We present a study of a paradigmatic extended (non-point-like) fermionic collider (and an extension to bosonic colliders). As with particle interferometers, in an extended collider there is an infinite number of trajectories for any single- or multiparticle event. Self-interference of the former can lead to an apparent bunching of fermions when we compare the cross-current correlator with a classical benchmark representing two colliding beams. In view of this apparent bunching behavior of fermions, we identify an experimentally accessible current correlator, which reveals the true mutual statistics of fermions.
The role of anyonic statistics stands as a cornerstone in the landscape of topological quantum techniques. While recent years have brought forth encouraging and persuasive strides in detecting anyons, a significant facet remains unexplored, especially in view of connecting anyonic physics to quantum information platforms-whether and how entanglement can be generated by anyonic braiding. Here, we demonstrate that even when two anyonic subsystems (represented by anyonic beams) are connected only by electron tunneling, entanglement between them, manifesting fractional statistics, is generated. To demonstrate this physics, we rely on a platform where fractional quantum Hall edges are bridged by a quantum point contact that allows only transmission of fermions (so-called Andreev-like tunneling). This invokes the physics of two-beam collisions in an anyonic Hong-Ou-Mandel collider, accompanied by a process that we dub anyon-quasihole braiding. We define an entanglement pointer-a current-noise-based function tailored to quantify entanglement associated with quasiparticle fractional statistics. Our work, which exposes, both in theory and in experiment, entanglement associated with anyonic statistics and braiding, prospectively paves the way to the exploration of entanglement induced by non-Abelian statistics.
We investigate the two-photon scattering properties of a Jaynes-Cummings (JC) nonlinearity consisting of a two-level system (qubit) interacting with a single-mode cavity, which is coupled to two waveguides, each containing a single incident photon wave packet initially. In this scattering setup, we study the interplay between the Hong-Ou-Mandel (HOM) effect arising due to quantum interference and effective photon-photon interactions induced by the presence of the qubit. We calculate the two-photon scattering matrix of this system analytically and identify signatures of interference and interaction in the second-order auto- and cross-correlation functions of the scattered photons. In the dispersive regime, when qubit and cavity are far detuned from each other, we find that the JC nonlinearity can be used as an almost linear, in situ tunable beam splitter giving rise to ideal Hong-Ou-Mandel interference, generating a highly path-entangled two-photon NOON state of the scattered photons. The latter manifests itself in strongly suppressed waveguide cross-correlations and Poissonian photon number statistics in each waveguide. If the two-level system and the cavity are on resonance, the JC nonlinearity strongly modifies the ideal HOM conditions leading to a smaller degree of path entanglement and sub-Poissonian photon number statistics. In the latter regime, we find that photon blockade is associated with bunched autocorrelations in both waveguides, while a two-polariton resonance can lead to bunched as well as antibunched correlations.