Geometry of quantum inference

SL Braunstein, A Mann, M Revzen

Research output: Contribution to conferencePaperpeer-review


The Kullback information - a quantity taken from classical information theory - is the `'relative'' information (negative entropy) of one statistical distribution with respect to another. Put differently, it is the negative entropy in the presence of prior information. Classically, the global minimum of the Kullback information can often be found by solving a set of local problems, which amounts to setting up a trajectory to the optimal (most likely) distribution. Here we are interested in trying to generalize `'thermodynamic'' reasoning by accounting for our bias towards an a priori quantum state of the system. In this general problem there is no closed-form expression for the quantum Kullback information. The known expectation values are incorporated in the form of constraints that, in general, may not commute with the a priori state. The quantum mechanical version of these trajectories, which we derive here, yields a close approximation to the global optimum of the quantum Kullback information according to numerical experiments.
Original languageUndefined/Unknown
Publication statusPublished - 1996

Bibliographical note

International Symposium on the Dilemma of Einstein, Podolsky and Rosen, in Honour of Nathan Rosen, HAIFA, ISRAEL, MAR, 1995

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