Unitary local invariance

Details Unitary local invariance Unitary local invariance

2005-02-03

arxiv.org/abs/quant-ph/0502025v2

Int. J. Quant. Inf. 3, 655 (2005).

Physics

Quantum Physics

Revised version. Accepted for publication Int. J. Quant. Inf

Scientific paper

We address unitary local (UL) invariance of bipartite pure states. Given a bipartite state $|\Psi>>=\sum_{ij} \psi_{ij}\: |i>_1\otimes |j>_2$ the complete characterization of the class of local unitaries $U_1\otimes U_2$ for which $U_1\otimes U_2 |\Psi>>=|\Psi>>$ is obtained.The two relevant parameters are the rank of the matrix $\Psi$, $[\Psi]_{ij}=\psi_{ij}$, and the number of its equal singular values, {\em i.e.} the degeneracy of the eigenvalues of the partial traces of $|\Psi>>$.

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