Journal
QUANTUM INFORMATION PROCESSING
Volume 20, Issue 2, Pages -Publisher
SPRINGER
DOI: 10.1007/s11128-021-03017-z
Keywords
Quantum coherence; Complementarity relations; Uncertainty relations; Mutually unbiased bases; Quantum state discrimination
Funding
- NSFC [11761073, 11675113, 12075159]
- Beijing Municipal Commission of Education [KZ201810028042]
- Beijing Natural Science Foundation [Z190005]
- Academy for Multidisciplinary Studies, Capital Normal University
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, China [SIQSE202001]
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The study focuses on the complementarity and uncertainty relations of coherence under mutually unbiased bases using skew information. It also derives the complementarity relation for geometric measure of coherence based on the coherence via skew information. As applications, two tighter upper bounds are presented for minimum error probabilities in discriminating a set of pure states with least square measurement, improving upon previous results.
The complementarity (upper bound) and uncertainty relations (lower bound) of the coherence via skew information under mutually unbiased bases (MUBs) are studied. The complementarity relation for the geometric measure of coherence is also obtained based on the relation between the coherence via skew information and the geometric measure of coherence. As applications, two tighter upper bounds are presented on the minimum error probabilities that discriminate a set of pure states with the least square measurement, which improve the results of Xiong et al. (Phys Rev A 98:032324, 2018).
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