Distinguishability Transitions in Non-Unitary Boson Sampling Dynamics

TL;DR

This paper explores how parity-time symmetry breaking in non-unitary boson sampling affects boson distinguishability, revealing transitions that enable classical simulation and differ from unitary quantum dynamics.

Contribution

It uncovers distinguishability transitions in non-unitary boson dynamics driven by $ ext{PT}$ symmetry breaking, highlighting new regimes for classical simulation and understanding of non-Hermitian quantum systems.

Findings

$ ext{PT}$ symmetry breaking enhances regions of boson distinguishability.

Transitions affect the efficiency of classical algorithms for sampling.

Distinguishability transitions differ from those in unitary quantum systems.

Abstract

We discover novel transitions characterized by distinguishability of bosons in non-unitary dynamics with parity-time ($\mathcal{PT}$) symmetry. We show that $\mathcal{PT}$ symmetry breaking, a unique transition in non-Hermitian open systems, enhances regions in which bosons can be regarded as distinguishable. This means that classical computers can sample the boson distributions efficiently in these regions by sampling the distribution of distinguishable particles. In a $\mathcal{PT}$-symmetric phase, we find one dynamical transition upon which the distribution of bosons deviates from that of distinguishable particles, when bosons are initially put at distant sites. If the system enters a $\mathcal{PT}$-broken phase, the threshold time for the transition is suddenly prolonged, since dynamics of each boson is diffusive (ballistic) in the $\mathcal{PT}$-broken ($\mathcal{PT}$-symmetric) phase. Furthermore, the $\mathcal{PT}$-broken phase also exhibits a notable dynamical transition on a longer time scale, at which the bosons again become distinguishable. This transition, and hence the classical easiness of sampling bosons in long times, are true for generic postselected non-unitary quantum dynamics, while it is absent in unitary dynamics of isolated quantum systems. $\mathcal{PT}$ symmetry breaking can also be characterized by the efficiency of a classical algorithm based on the rank of matrices, which can (cannot) efficiently compute the photon distribution in the long-time regime of the $\mathcal{PT}$-broken ($\mathcal{PT}$-symmetric) phase.