Theoretical Statistics and Mathematics Unit, ISI Delhi

Exchangeable, stationary and entangled chains of Gaussian states

by K. R. Parthasarathy and Ritabrata Sengupta

We explore conditions on the covariance matrices of a
consistent chain of mean zero finite mode Gaussian states in
order that the chain may be exchangeable or stationary. For
an exchangeable chain our conditions are necessary and
sufficient. Every stationary Gaussian chain admits an
asymptotic entropy rate. Whereas an exchangeable chain
admits a simple expression for its entropy rate, in our
examples of stationary chains the same admits an integral
formula based on the asymptotic eigenvalue distribution for
Toeplitz matrices. An example of a stationary entangled
Gaussian chain is given.

isid/ms/2015/06 [fulltext]

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