Jon Tyson, Institute for Quantum Computing (IQC)
Abstract
I will derive provably-tight two-sided estimates of the reversibility of an
arbitrary quantum channel in terms of entanglement fidelity and on the
conditional min-entropy of an arbitrary bipartite mixed quantum state. Channel reversals have been studied by a number of research groups under the banner of "Approximate quantum error recovery."
I also derive an approximate error recovery map. This map is a
quadratically weighted version of the channel reversal which Barnum
and Knill (2002) constructed by generalizing the ad-hoc "pretty good"
measurement. Our recovery map is an extension of Holevo's quadratically-
weighted asymptotically optimal measurement, which was discussed last
Monday.
The natural notion of a directional iterate for channel reversals
corresponds naturally to an interative computational scheme introduced
by Reimpell and Werner (2005). In particular, their monotonicity theorem
follows in greater generality as by the trivial geometric properties of
directional iterates.
A reference for this talk is J. Math. Phys 51, 092204 (2010).