Many-body quantum interference on hypercubes

TL;DR

This paper explores how symmetries in hypercube graphs influence many-body quantum interference, leading to predictable suppression of certain quantum states, with implications for quantum information processing.

Contribution

It analytically characterizes suppression laws in hypercube graphs with arbitrary subgraphs, linking initial state symmetries to the suppression of final states in many-particle quantum systems.

Findings

Initial states invariant under hypercube symmetries cause many suppressed final states.

Suppression conditions depend solely on initial symmetries.

Fraction of suppressed states relates to the number of independent symmetries.

Abstract

Beyond the regime of distinguishable particles, many-body quantum interferences influence quantum transport in an intricate manner. However, symmetries of the single-particle transformation matrix alleviate this complexity and even allow the analytic formulation of suppression laws, which predict final states to occur with a vanishing probability due to total destructive interference. Here we investigate the symmetries of hypercube graphs and their generalizations with arbitrary identical subgraphs on all vertices. We find that initial many-particle states, which are invariant under self-inverse symmetries of the hypercube, lead to a large number of suppressed final states. The condition for suppression is determined solely by the initial symmetry, while the fraction of suppressed states is given by the number of independent symmetries of the initial state. Our findings reveal new insights into particle statistics for ensembles of indistinguishable bosons and fermions and may represent a first step towards many-particle quantum protocols in higher-dimensional structures.