Abstract In this paper, we discuss quantum uncertainty relations of Tsallis relative α entropy coherence for a single qubit system based on three mutually unbiased bases. For α ∈ 1 2 , 1 ∪ ( 1 , 2 ] , the upper and lower bounds of sums of coherence are obtained. However, the above results cannot be verified directly for any α ∈ 0 , 1 2 . Hence, we only consider the special case of α = 1 n + 1 , where n is a positive integer, and we obtain the upper and lower bounds. By comparing the upper and lower bounds, we find that the upper bound is equal to the lower bound for the special α = 1 2 , and the differences between the upper and the lower bounds will increase as α increases. Furthermore, we discuss the tendency of the sum of coherence, and find that it has the same tendency with respect to the different θ or φ, which is opposite to the uncertainty relations based on the Rényi entropy and Tsallis entropy.Abstract In this paper, we discuss quantum uncertainty relations of Tsallis relative α entropy coherence for a single qubit system based on three mutually unbiased bases. For α ∈ 1 2 , 1 ∪ ( 1 , 2 ] , the upper and lower bounds of sums of coherence are obtained. However, the above results cannot be verified directly for any α ∈ 0 , 1 2 . Hence, we only consider the special case of α = 1 n + 1 , where n is a positive integer, and we obtain the upper and lower bounds. By comparing the upper and lower bounds, we find that the upper bound is equal to the lower bound for the special α = 1 2 , and the differences between the upper and the lower bounds will increase as α increases. Furthermore, we discuss the tendency of the sum of coherence, and find that it has the same tendency with respect to the different θ or φ, which is opposite to the uncertainty relations based on the Rényi entropy and Tsallis entropy.

Communications in Theoretical PhysicsDec 13, 20212 citations

Tighter Weighted Relations of the Tsallis-q Entanglement

Ya-Juan Wu, Ke Wu

International Journal of Theoretical PhysicsNov 15, 20191 citation

Entanglement rates for Rényi, Tsallis, and other entropies

Anna Vershynina

We provide an upper bound on the maximal entropy rate at which the entropy of the expected density operator of a given ensemble of two states changes under nonlocal unitary evolution. A large class of entropy measures in considered, which includes Rényi and Tsallis entropies. The result is derived from a general bound on the trace-norm of a commutator, which can be expected to find other implementations. We apply this result to bound the maximal rate at which quantum dynamics can generate entanglement in a bipartite closed system with Rényi and Tsallis entanglement entropies taken as measures of entanglement in the system.We provide an upper bound on the maximal entropy rate at which the entropy of the expected density operator of a given ensemble of two states changes under nonlocal unitary evolution. A large class of entropy measures in considered, which includes Rényi and Tsallis entropies. The result is derived from a general bound on the trace-norm of a commutator, which can be expected to find other implementations. We apply this result to bound the maximal rate at which quantum dynamics can generate entanglement in a bipartite closed system with Rényi and Tsallis entanglement entropies taken as measures of entanglement in the system.

arXiv:1803.07117Journal of Mathematical PhysicsFeb 1, 201914 citations

The entanglement measure induced by Tsallis relative $\alpha$ entropyThe entanglement measure induced by Tsallis relative $$\alpha $$ entropy

Junqing Li, Shuo Dong, Wenjie Hou +1 more

PramanaApr 1, 20260 citations

On bounds of Tsallis relative entropy and an inequality for generalized skew information

Shigeru Furuichi

Quantum entropy and skew information play important roles in quantum information science. They are defined by the trace of the positive operators so that the trace inequalities often have important roles to develop the mathematical theory in quantum information science. In this paper, we study some properties for information quantities in quantum system through trace inequalities. Especially, we give upper bounds and lower bounds of Tsallis relative entropy, which is a one-parameter extension of the relative entropy in quantum system. In addition, we compare the known bounds and the new bounds, for both upper and lower bounds, respectively. We also give an inequality for generalized skew information by introducing a generalized correlation measure.Quantum entropy and skew information play important roles in quantum information science. They are defined by the trace of the positive operators so that the trace inequalities often have important roles to develop the mathematical theory in quantum information science. In this paper, we study some properties for information quantities in quantum system through trace inequalities. Especially, we give upper bounds and lower bounds of Tsallis relative entropy, which is a one-parameter extension of the relative entropy in quantum system. In addition, we compare the known bounds and the new bounds, for both upper and lower bounds, respectively. We also give an inequality for generalized skew information by introducing a generalized correlation measure.

arXiv:1008.3441Aug 20, 20101 citation

The entanglement measure induced by Tsallis relative

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entropy