Bipartite separability of one parameter families of states using conditional quantum relative Tsallis entropy

Abstract

In any bipartition of a quantum state, it is proved that the negative values of the conditional version of sandwiched Tsallis relative entropy necessarily implies quantum entanglement. For any N, the separability ranges in the $1:N-1$ partition of symmetric one parameter families of noisy $N$-qubit W, GHZ, states are determined using the conditional quantum relative Tsallis entropy approach. The 1:N-1 separability range matches exactly with the range obtained through positive partial transpose criterion, for all N. The advantages of using non-commuting version of $q$-conditional relative Tsallis entropy is brought out through this and other one-parameter families of states.

11 pages, 3 figures; Accepted for publication in Physica A

References in corpus (4)

• Relating different quantum generalizations of the conditional Renyi entropy
• Entanglement sudden death in qubit-qutrit systems
• Generalized entropic criterion for separability
• Violation of majorization relations in entangled states and its detection by means of generalized entropic forms

Cited by in corpus (4)

• From Rényi Relative Entropic Generalization to Quantum Thermodynamical Universality
• Perturbative Thermodynamic Geometry of Nonextensive Ideal Classical, Bose and Fermi Gases
• Generalization of the possible algebraic basis of $q$-triplets
• Biseparability of noisy pseudopure, W and GHZ states using conditional quantum relative Tsallis entropy