Minimal Rényi–Ingarden–Urbanik Entropy of Multipartite Quantum States

Entropy

Marco Enríquez¹  Zbigniew Puchaᐪ³  Karol Życzkowski²  Demosthenes Ellinas⁴  Giorgio Kaniadakis⁴  Jiannis Pachos⁴ 

[1] Departamento de Física, Cinvestav, AP 14-740, Mexico DF 07000, Mexico; E-Mail:;Smoluchowski Institute of Physics, Jagiellonian University, ul. Reymonta 4, Kraków PL-30-059, Poland;Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, Bałtycka 5, Gliwice 44-100, Poland; E-Mail:;Departamento de Física, Cinvestav, AP 14-740, Mexico DF 07000, Mexico; E-Mail

关键词: quantum entanglement;    Rényi–Ingarden–Urbanik entropy;    three-tangle;    hyperdeterminants;    random states;   

DOI  :  10.3390/e17075063

来源: mdpi

【 摘 要 】

We study the entanglement of a pure state of a composite quantum system consisting of several subsystems with d levels each. It can be described by the Rényi–Ingarden–Urbanik entropy S_q of a decomposition of the state in a product basis, minimized over all local unitary transformations. In the case q = 0, this quantity becomes a function of the rank of the tensor representing the state, while in the limit q → ∞, the entropy becomes related to the overlap with the closest separable state and the geometric measure of entanglement. For any bipartite system, the entropy S₁ coincides with the standard entanglement entropy. We analyze the distribution of the minimal entropy for random states of three- and four-qubit systems. In the former case, the distribution of the three-tangle is studied and some of its moments are evaluated, while in the latter case, we analyze the distribution of the hyperdeterminant. The behavior of the maximum overlap of a three-qudit system with the closest separable state is also investigated in the asymptotic limit.

【 授权许可】

CC BY   
© 2015 by the authors; licensee MDPI, Basel, Switzerland