Incoherent Operations Enable State Transformations Impossible under Dephasing-covariant Incoherent Operations

TL;DR

This paper demonstrates that incoherent operations can perform state transformations impossible under dephasing-covariant incoherent operations, resolving a key open problem and highlighting limitations of existing monotones.

Contribution

It shows that IOs can achieve certain state transformations beyond DIO capabilities and reveals the insufficiency of current monotones to fully characterize DIO convertibility.

Findings

IOs enable transformations forbidden under DIOs

No single IO monotone characterizes all state convertibility

Common monotones for IOs and DIOs are insufficient for DIOs

Abstract

We show that incoherent operations (IOs) can achieve the state transformations that are forbidden under dephasing-covariant incoherent operations (DIOs), thereby resolving the open problem posed by Chitambar and Gour [Phys. Rev. Lett. 117, 030401 (2016)]. We further demonstrate that no set of IO monotones suffices to characterize state convertibility under strictly incoherent operations (SIOs), and that monotones common to IOs and DIOs are insufficient to characterize convertibility under DIOs.