2019/12/11 by Anna Vershynina, Vershynina, Anna
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Information and Cryptography #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.1912.05426
openalex publication_date 2019/12/11 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
Several ways have been proposed in the literature to define a coherence\nmeasure based on Tsallis relative entropy. One of them is defined as a distance\nbetween a state and a set of incoherent states with Tsallis relative entropy\ntaken as a distance measure. Unfortunately, this measure does not satisfy the\nrequired strong monotonicity, but a modification of this coherence has been\nproposed that does. We introduce three new Tsallis coherence measures coming\nfrom a more general definition that also satisfy the strong monotonicity, and\ncompare all five definitions between each other. Using three coherence measures\nthat we discuss, one can also define a discord. Two of these have been used in\nthe literature, and another one is new. We also discuss two correlation\nmeasures based on Tsallis relative entropy. We provide explicit expressions for\nall three discord and two correlation measure on pure states. Lastly, we\nprovide tight upper and lower bounds on two discord and correlations measures\non any quantum state, with the condition for equality.\n