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

TL;DR

This paper introduces new measures for quantifying entanglement induced by quantum statistics and demonstrates their experimental measurement using a Hong-Ou-Mandel interferometer with electrons in a quantum Hall system.

Contribution

It proposes the concepts of an 'entanglement pointer' and 'statistics-induced entanglement entropy' and experimentally measures them in an electronic interferometer setup.

Findings

Quantitative description of statistics-induced entanglement.

Experimental measurement of entanglement pointer and entropy.

Potential application to anyonic and non-Abelian states.

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; (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.