Coherence measures with respect to general quantum measurements

Jianwei Xu, Lian-He Shao, and Shao-Ming Fei

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Submission date: 22. Jun. 2020
Pages: 13
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Abstract:
Quantum coherence with respect to orthonormal bases has been studied extensively in the past few years. Recently, Bischof, et al. [Phys. Rev. Lett. 123, 110402 (2019)] generalized it to the case of general positive operator-valued measure (POVM) measurements. Such POVM-based coherence, including the block coherence as special cases, have significant operational interpretations in quantifying the advantage of quantum states in quantum information processing. In this work we first establish an alternative framework for quantifying the block coherence and provide several block coherence measures. We then present several coherence measures with respect to POVM measurements, and prove a conjecture on the l₁-norm related POVM coherence measure.