Estimating coherence with respect to general quantum measurements

• URL: http://arxiv.org/abs/2109.14323v1
• Date: Wed, 29 Sep 2021 10:19:23 GMT
• Title: Estimating coherence with respect to general quantum measurements
• Abstract summary: 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 $ have been obtained.
• Score: 4.707579791895607
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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