The Average Quantum Coherence of Pure State Decomposition
- URL: http://arxiv.org/abs/2105.02382v1
- Date: Thu, 6 May 2021 00:43:03 GMT
- Title: The Average Quantum Coherence of Pure State Decomposition
- Authors: Ming-Jing Zhao, Teng Ma, and Rajesh Pereira
- Abstract summary: We study the average quantum coherence over the pure state decompositions of a mixed quantum state.
For any given qubit state, the optimal pure state decomposition achieving the maximal average quantum coherence is shown.
The results presented in this paper are universal and suitable for all coherence measures.
- Score: 1.758380079660726
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We study the average quantum coherence over the pure state decompositions of
a mixed quantum state. An upper bound of the average quantum coherence is
provided and sufficient conditions for the saturation of the upper bound are
shown. These sufficient conditions always hold for two and three dimensional
systems. This provides a tool to estimate the average coherence experimentally
by measuring only the diagonal elements, which remarkably requires less
measurements compared with state tomography. We then describe the pure state
decompositions of qubit state in Bloch sphere geometrically. For any given
qubit state, the optimal pure state decomposition achieving the maximal average
quantum coherence as well as three other pure state decompositions are shown in
the Bloch sphere. The order relations among their average quantum coherence are
invariant for any coherence measure. The results presented in this paper are
universal and suitable for all coherence measures.
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