Minimal sets of conditions for distinguishing among separable and entangled states of multiqubit systems

Abstract

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.