Uncertainty relations for unified (α,β)-relative entropy of coherence under mutually unbiased equiangular tight frames

2025/06/11 by Cheng, Baolong, Zhaoqi Wu, Wu, Zhaoqi
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Connexins and lens biology #FOS: Physical sciences #Mathematical Analysis and Transform Methods #Quantum Physics (quant-ph) #Statistical Mechanics and Entropy

paper · doi:10.48550/arxiv.2506.09779

openalex publication_date 2025/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Uncertainty relations based on quantum coherence is an important problem in quantum information science. We discuss uncertainty relations for averaged unified (α,β)-relative entropy of coherence under mutually unbiased equiangular tight frames, and derive an interesting result for different parameters. As consequences, we obtain corresponding results under mutually unbiased bases, equiangular tight frames or based on Tsallis α- relative entropies and Rényi-α relative entropies. We illustrate the derived inequalities by explicit examples in two dimensional spaces, showing that the lower bounds can be regarded as good approximations to averaged coherence quantifiers under certain circumstances.

Citations

• Characterization of Generalized Alpha-Beta Divergence and Associated Entropy Measures
• Uncertainty relations in terms of generalized entropies derived from information diagrams
• Mutually Unbiased Equiangular Tight Frames
• Quantum cryptography: Public key distribution and coin tossing
• Grassmannian Frames with Applications to Coding and Communication

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