Matrix permanent and quantum entanglement of permutation invariant states
arXiv:0905.0012 · doi:10.1063/1.3464263
Abstract
We point out that a geometric measure of quantum entanglement is related to the matrix permanent when restricted to permutation invariant states. This connection allows us to interpret the permanent as an angle between vectors. By employing a recently introduced permanent inequality by Carlen, Loss and Lieb, we can prove explicit formulas of the geometric measure for permutation invariant basis states in a simple way.
10 pages
References in corpus (7)
- The geometric measure of entanglement for symmetric states
- Entanglement of multiparty stabilizer, symmetric, and antisymmetric states
- The geometric measure of entanglement for a symmetric pure state with positive amplitudes
- Maximally entangled three-qubit states via geometric measure of entanglement
- Relative entropy of entanglement for certain multipartite mixed states
- Concentration of permanent estimators for certain large matrices
- Crystal Melting and Black Holes
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