Invariant measures on multimode quantum Gaussian states
Invariant measures on multimode quantum Gaussian states
复制标题
多模量子高斯态的不变测度
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
S. Pascazio
中科院分区：
文献类型：
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作者：
C. Lupo;S. Mancini;A. D. Pasquale;P. Facchi;G. Florio;S. Pascazio
由高斯酉变换群上的Haar测度导出了多模量子高斯态流形上的不变测度。为此，通过在两个不相交的子系统中引入系统的双分区，我们使用参数化来突出非局部自由度的作用-辛特征值-它表征了给定双分区上的量子纠缠。然后通过施加物理激励的能量约束来获得有限测度。通过对局部自由度的平均，我们最终推导出在量子光学和量子信息应用中特别感兴趣的某些情况下辛特征值的不变分布。
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 for applications in quantum optics and quantum information.