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arXiv · 2109.14323

Estimating coherence with respect to general quantum measurements

Jianwei Xu·Lin Zhang·Shao-Ming Fei
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Abstract

The conventional coherence is defined with respect to a fixed orthonormal basis, i.e., to a von Neumann measurement. Recently, generalized quantum coherence with respect to general positive operator-valued measurements (POVMs) has been presented. Several well-defined coherence measures, such as the relative entropy of coherence $C_{r}$, the $l_{1}$ norm of coherence $C_{l_{1}}$ and the coherence $C_{T,\alpha }$ based on Tsallis relative entropy with respect to general POVMs have been obtained. In this work, we investigate the properties of $C_{r}$, $l_{1}$ and $C_{T,\alpha }$. We estimate the upper bounds of $C_{l_{1}}$; we show that the minimal error probability of the least square measurement state discrimination is given by $C_{T,1/2}$; we derive the uncertainty relations given by $C_{r}$, and calculate the average values of $C_{r}$, $C_{T,\alpha }$ and $C_{l_{1}}$ over random pure quantum states. All these results include the corresponding results of the conventional coherence as special cases.

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Jianwei Xu, Lin Zhang, Shao-Ming Fei. 2021-09-29. Estimating coherence with respect to general quantum measurements. https://doi.org/10.1007/s11128-021-03393-6

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