Information geometry of Gaussian channels

Details Information geometry of Gaussian channels Information geometry of Gaussian channels

2009-11-08

arxiv.org/abs/0911.1558v2

Phys. Rev. A 81, 062326 (2010)

Physics

Quantum Physics

19 pages, 4 figures

Scientific paper

10.1103/PhysRevA.81.062326

We define a local Riemannian metric tensor in the manifold of Gaussian channels and the distance that it induces. We adopt an information-geometric approach and define a metric derived from the Bures-Fisher metric for quantum states. The resulting metric inherits several desirable properties from the Bures-Fisher metric and is operationally motivated from distinguishability considerations: It serves as an upper bound to the attainable quantum Fisher information for the channel parameters using Gaussian states, under generic constraints on the physically available resources. Our approach naturally includes the use of entangled Gaussian probe states. We prove that the metric enjoys some desirable properties like stability and covariance. As a byproduct, we also obtain some general results in Gaussian channel estimation that are the continuous-variable analogs of previously known results in finite dimensions. We prove that optimal probe states are always pure and bounded in the number of ancillary modes, even in the presence of constraints on the reduced state input in the channel. This has experimental and computational implications: It limits the complexity of optimal experimental setups for channel estimation and reduces the computational requirements for the evaluation of the metric: Indeed, we construct a converging algorithm for its computation. We provide explicit formulae for computing the multiparametric quantum Fisher information for dissipative channels probed with arbitrary Gaussian states, and provide the optimal observables for the estimation of the channel parameters (e.g. bath couplings, squeezing, and temperature).

Affiliated with

Also associated with

No associations

Rating

Information geometry of Gaussian channels does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Information geometry of Gaussian channels, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Information geometry of Gaussian channels will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-659610