Incoherent Gaussian equivalence of $m-$mode Gaussian states

TL;DR

This paper establishes the conditions under which multimode Gaussian states are equivalent under incoherent Gaussian operations, linking coherence freezing to entropy measures and providing insights into noise resilience in quantum systems.

Contribution

It derives necessary and sufficient conditions for Gaussian state equivalence under incoherent operations and connects coherence freezing with entropy-based measures.

Findings

Gaussian states are incoherent equivalent iff related by incoherent unitaries

Incoherent equivalence is tied to frozen coherence in Gaussian states

Relative entropy measure of coherence remains frozen under certain conditions

Abstract

Necessary and sufficient conditions for arbitrary multimode (pure or mixed) Gaussian states to be equivalent under incoherent Gaussian operations are derived. We show that two Gaussian states are incoherent equivalence if and only if they are related by incoherent unitaries. This builds the counterpart of the celebrated result that two pure entangled states are equivalent under LOCC if and only if they are related by local unitaries. Furthermore, incoherent equivalence of Gaussian states is equivalent to frozen coherence [Phys. Rev. Lett. \textbf{114}, 210401 (2015)]. Basing this as foundation, we find all measures of coherence are frozen for an initial Gaussian state under strongly incoherent Gaussian operations if and only if the relative entropy measure of coherence is frozen for the state. This gives an entropy-based dynamical condition in which the coherence of an open quantum system is totally unaffected by noise.