Collective phases of identical particles interfering on linear multiports

TL;DR

This paper introduces collective geometric phases for identical particles in linear multiports, revealing new multi-particle interference phenomena governed by collective phases, with implications for quantum information processing.

Contribution

It defines collective geometric phases for bosons and fermions, demonstrating genuine N-particle interference that cannot be reduced to lower-order correlations.

Findings

Genuine N-particle interference is governed by collective phases.

Deterministic distinguishability enables N-particle interference.

Collective phases are not detectable by second-order correlation criteria.

Abstract

We introduce collective geometric phases of bosons and fermions interfering on a linear unitary multiport, where each phase depends on the internal states of identical particles (i.e., not affected by the multiport) and corresponds to a cycle of the symmetric group. We show that quantum interference of $N$ particles in generic pure internal states, i.e., with no pair being orthogonal, is governed by $(N-1)(N-2)/2$ independent triad phases (each involving only three particles). The deterministic distinguishability, preventing quantum interference with two or three particles, allows for the genuine $(N\ge 4)$-particle phase (interference) on a multiport: setting each particle to be deterministically distinguishable from all others except two by their internal states allows for a novel (circle-dance) interference of $N\ge 4$ particles governed by a collective $N$-particle phase, while simultaneously preventing the $R$-particle interference for $3\le R\le N-1$. The genuine $N$-particle interference manifests the $N$th order quantum correlations between identical particles at a multiport output, it does not appear in the marginal probability for a subset of the particles, e.g., it cannot be detected if at least one of the particles is lost. This means that the collective phases are not detectable by the usual "quantumness" criteria based on the second-order quantum correlations. The results can be useful for quantum computation, quantum information, and other quantum technologies with single photons. \end{abstract}