Stochastic local operations and classical communication equations and classification of even nn qubits

preprint2011arXivOpen access

Abstract

For any even nn qubits we establish four SLOCC equations and construct four SLOCC polynomials (not complete) of degree 2n/22^{n/2}, which can be exploited for SLOCC classification (not complete) of any even nn qubits. In light of the SLOCC equations, we propose several different genuine entangled states of even nn qubits and show that they are inequivalent to the ∣GHZ>|GHZ>, ∣W>|W>, or ∣l,n>|l,n> (the symmetric Dicke states with ll excitations) under SLOCC via the vanishing or not of the polynomials. The absolute values of the polynomials can be considered as entanglement measures.

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