Bounds on positive operator-valued measure based coherence of superposition

• URL: http://arxiv.org/abs/2305.06705v1
• Date: Thu, 11 May 2023 10:31:04 GMT
• Title: Bounds on positive operator-valued measure based coherence of superposition
• Authors: Meng-Li Guo, Jin-Min Liang, Bo Li, Shao-Ming Fei, and Zhi-Xi Wang
• Abstract summary: POVM-based coherence measures have been proposed with respect to the relative entropy of coherence. We derive analytically the lower and upper bounds on these POVM-based coherence of an arbitrary given superposed pure state. Our results can be used to estimate range of quantum coherence of superposed states.
• Score: 4.536603451832357
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum coherence is a fundamental feature of quantum physics and plays a significant role in quantum information processing. By generalizing the resource theory of coherence from von Neumann measurements to positive operator-valued measures (POVMs), POVM-based coherence measures have been proposed with respect to the relative entropy of coherence, the $l_1$ norm of coherence, the robustness of coherence and the Tsallis relative entropy of coherence. We derive analytically the lower and upper bounds on these POVM-based coherence of an arbitrary given superposed pure state in terms of the POVM-based coherence of the states in superposition. Our results can be used to estimate range of quantum coherence of superposed states. Detailed examples are presented to verify our analytical bounds.

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