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MiS Preprint

Operational advantage of basis-independent quantum coherence

Zhi-Hao Ma, Jian Cui, Zhu Cao, Shao-Ming Fei and Vlatko Vedral


In the quantitative theory of quantum coherence, the amount of coherence is defined as the distance between the given state to 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 been 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.

Jul 13, 2019
Jul 18, 2019

Related publications

2019 Repository Open Access
Zhi-Hao Ma, Jian Cui, Zhu Cao, Shao-Ming Fei, Vlatko Vedral, Tim Byrnes and Chandrashekar Radhakrishnan

Operational advantage of basis-independent quantum coherence

In: epl, 125 (2019) 5, p. 50005