Are Incoherent Operations Physically Consistent? -- A Critical Examination of Incoherent Operations

TL;DR

This paper critically examines the physical consistency of incoherent operations in quantum coherence resource theories, revealing limitations and proposing a new class with different operational properties.

Contribution

It establishes a criterion for physical consistency in resource theories, shows current basis-dependent theories fail this, and introduces dephasing-covariant incoherent operations.

Findings

Current basis-dependent coherence theories are physically inconsistent.

Physically consistent coherence theory has limited operational power.

Necessary and sufficient conditions for qubit state transformations are derived.

Abstract

Considerable work has recently been directed toward developing resource theories of quantum coherence. In most approaches, a state is said to possess quantum coherence if it is not diagonal in some specified basis. In this letter we establish a criterion of physical consistency for any resource theory in terms of physical implementation of the free operations, and we show that all currently proposed basis-dependent theories of coherence fail to satisfy this criterion. We further characterize the physically consistent resource theory of coherence and find its operational power to be quite limited. After relaxing the condition of physical consistency, we introduce the class of dephasing-covariant incoherent operations, present a number of new coherent monotones based on relative R\'{e}nyi entropies, and study incoherent state transformations under different operational classes. In particular, we derive necessary and sufficient conditions for qubit state transformations and show these conditions hold for all classes of incoherent operations.