Dephasing-Covariant Operations Enable Asymptotic Reversibility of Quantum Resources

TL;DR

This paper demonstrates that dephasing-covariant operations enable asymptotic reversibility in quantum resource theories of coherence and entanglement, allowing state interconversion without maximal resource non-generating operations.

Contribution

It shows that dephasing-covariant operations achieve asymptotic reversibility in coherence and entanglement resource theories, a novel result in quantum resource manipulation.

Findings

Any two states are asymptotically interconvertible under dephasing-covariant operations in coherence.

Dephasing-covariant operations prohibit increase of all Renyi b5-entropies of entanglement.

Asymptotic reversibility is possible between maximally correlated mixed states, even multipartite.

Abstract

We study the power of dephasing-covariant operations in the resource theories of coherence and entanglement. These are quantum operations whose actions commute with a projective measurement. In the resource theory of coherence, we find that any two states are asymptotically interconvertible under dephasing-covariant operations. This provides a rare example of a resource theory in which asymptotic reversibility can be attained without needing the maximal set of resource non-generating operations. When extended to the resource theory of entanglement, the resultant operations share similarities with LOCC, such as prohibiting the increase of all R\'enyi $\alpha$-entropies of entanglement under pure state transformations. However, we show these operations are still strong enough to enable asymptotic reversibility between any two maximally correlated mixed states, even in the multipartite setting.