Invariant measures on multimode quantum Gaussian states

Details Invariant measures on multimode quantum Gaussian states Invariant measures on multimode quantum Gaussian states

2012-02-11

arxiv.org/abs/1202.2456v1

Physics

Quantum Physics

17 pages, comments are welcome

Scientific paper

We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint subsystems, we use a parameterization highlighting the role of nonlocal degrees of freedom -- the symplectic eigenvalues -- which characterize quantum entanglement across the given bipartition. A finite measure is then obtained by imposing a physically motivated energy constraint. By averaging over the local degrees of freedom we finally derive the invariant distribution of the symplectic eigenvalues in some cases of particular interest or applications in quantum optics and quantum information.

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