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

C. L. Liu

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.

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

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.
Paper Structure (5 sections, 18 equations, 1 figure, 1 table)

This paper contains 5 sections, 18 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Resource theory of coherence
  3. Increasing $C_m(\rho)$ by using IOs
  4. Coherence monotones and state transformations
  5. Conclusions

Figures (1)

  • Figure 1: Schematic of the inclusion relations among the sets of coherence monotones under different classes of free operations. Here, $\mathcal{M}_{\mathcal{F}}$ denotes the set of coherence monotones under a given class $\mathcal{F}$ of free operations.