Operational advantage of basis-independent quantum coherence

In the quantitative theory of quantum coherence, the amount of coherence is defined as the distance between the given state to the closest incoherent state. The set of incoherent states is conventionally defined as any state with a diagonal density matrix. One of the objections to this formulation i...

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Bibliographic Details
Published in:Europhysics letters 2019-03, Vol.125 (5), p.50005
Main Authors: Ma, Zhi-Hao, Cui, Jian, Cao, Zhu, Fei, Shao-Ming, Vedral, Vlatko, Byrnes, Tim, Radhakrishnan, Chandrashekar
Format: Article
Language:English
Subjects:
03.65.Ta
03.67.-a
Coherence
Information theory
Quantum phenomena
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Summary:In the quantitative theory of quantum coherence, the amount of coherence is defined as the distance between the given state to the closest incoherent state. The set of incoherent states is conventionally defined as any state with a diagonal density matrix. One of the objections to this formulation is that the incoherent states are intrinsically basis-dependent, which makes the amount of coherence also a basis-dependent quantity. Basis-independent measures have recently been proposed where the incoherent state is taken as the maximally mixed state. We show that this is the only possible choice of reference incoherent state, without modifying the original definition of coherence. We find a relation between the two formulations by defining a contribution to the coherence due to the basis choice. The hierarchical relationship between quantum coherence and the various quantum correlations is explored in detail. Finally, we illustrate some operational uses of the basis-independent quantum coherence in quantum information theory tasks.
ISSN:0295-5075
1286-4854
1286-4854
DOI:10.1209/0295-5075/125/50005