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Extremality of Gaussian Quantum States

2006; American Physical Society; Volume: 96; Issue: 8 Linguagem: Inglês

10.1103/physrevlett.96.080502

1092-0145

Michael M. Wolf, G. Giedke, J. I. Cirac,

Quantum Computing Algorithms and Architecture

We investigate Gaussian quantum states in view of their exceptional role within the space of all continuous variables states. A general method for deriving extremality results is provided and applied to entanglement measures, secret key distillation and the classical capacity of bosonic quantum channels. We prove that for every given covariance matrix the distillable secret key rate and the entanglement, if measured appropriately, are minimized by Gaussian states. This result leads to a clearer picture of the validity of frequently made Gaussian approximations. Moreover, it implies that Gaussian encodings are optimal for the transmission of classical information through bosonic channels, if the capacity is additive.