SEPARABILITY OF PURE N-QUBIT STATES:: TWO CHARACTERIZATIONS.

Given a pure state |ψ[sub N]>∈ℋ[sub N] of a quantum system composed of n qubits, where ℋ[sub N] is the Hilbert space of dimension N=2[sup n], this paper answers two questions: what conditions should the amplitudes in |ψ[sub N]> satisfy for this state to be separable (i) into a tensor product of n qubit states |ψ[sub 2]>[sub 0]⊗ |ψ[sub 2]>[sub 1] ⊗⋯⊗ |ψ[sub 2]>[sub n-1], and (ii), into a tensor product of two subsystems states |ψ[sub P]> ⊗ |ψ[sub Q]> with P=2[sup p] and Q=2[sup q] such that p+q=n? For both questions, necessary and sufficient conditions are proved, thus characterizing at the same time families of separable and entangled states of n qubit systems. A number of more refined questions about separability in n qubit systems can be studied on the basis of these results. [ABSTRACT FROM AUTHOR]