Pair-Wise Classifications of Patterns in a Two-Qubits System

Manu Pratap Singh, Kishori Radhey, B. S. Rajput

Manu Pratap Singh, B. S. Rajput

Philippe Jorrand, Mehdi Mhalla

A state ψ = α/00] + β/01] + γ/10] +δ/11] of a system of two qubits is separable if the equality among pair-wise products αδ = βγ holds. This paper generalize this form of condition for distinguishing among separable and entangled states of systems of n qubits. Given a pure state /ψN] of a quantum system composed of n qubits, where N = 2n, this paper defines minimal sets of equalities among pair-wise products of amplitudes of /ψN] for characterizing two forms of separability of /ψN]: (i) into a tensor product of n qubit states /ψ2]0 x/ψ2]1 x...x/ψ2]n-1, and (ii), into a tensor product of 2 subsystems states /ψp]x/ψQ] with P=2p and Q=2q such that p+q=n.

Cao Min, Zhu Shi-Qun

The pair-wise thermal entanglement in a four-qubit Heisenberg XXZ chain is investigated to study the role of anisotropy when an external magnetic field is included. It is found that pair-wise entanglement is absent between nearest- and next-nearest neighbouring qubits with anisotropic parameter Δ⩽−1. For two nearest-neighbouring qubits, increasing the parameter can not only induce the entanglement, but also extend the entanglement region in terms of magnetic field B and temperature T . For two next-nearest-neighbouring qubits, increasing anisotropic parameter can shift the location of the entanglement and control the extent of the entanglement in terms of magnetic field at a finite temperature.

Carlos Sabín, Guillermo García Alcaine