Evolution prediction from tomography

Evolution prediction from tomography Quantum process tomography provides a means of measuring the evolution operator for a system at a fixed measurement time t. The problem of using that tomographic snapshot to predict the evolution operator at other times is generally ill-posed since there are, in general, infinitely many distinct and compatible solutions. We describe the prediction, in some “maximal ignorance” sense, of the evolution of a quantum system based on knowledge only of the evolution operator for finitely many times $$0<\tau _{1}<\dots <\tau _{M}$$ 0 < τ 1 < ⋯ < τ M with $$M\ge 1$$ M ≥ 1 . To resolve the ill-posedness problem, we construct this prediction as the result of an average over some unknown (and unknowable) variables. The resulting prediction provides a description of the observer’s state of knowledge of the system’s evolution at times away from the measurement times. Even if the original evolution is unitary, the predicted evolution is described by a non-unitary, completely positive map. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals
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Publisher
Springer US
Copyright
Copyright © 2017 by Springer Science+Business Media New York
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-017-1524-z
Publisher site
See Article on Publisher Site

Abstract

Quantum process tomography provides a means of measuring the evolution operator for a system at a fixed measurement time t. The problem of using that tomographic snapshot to predict the evolution operator at other times is generally ill-posed since there are, in general, infinitely many distinct and compatible solutions. We describe the prediction, in some “maximal ignorance” sense, of the evolution of a quantum system based on knowledge only of the evolution operator for finitely many times $$0<\tau _{1}<\dots <\tau _{M}$$ 0 < τ 1 < ⋯ < τ M with $$M\ge 1$$ M ≥ 1 . To resolve the ill-posedness problem, we construct this prediction as the result of an average over some unknown (and unknowable) variables. The resulting prediction provides a description of the observer’s state of knowledge of the system’s evolution at times away from the measurement times. Even if the original evolution is unitary, the predicted evolution is described by a non-unitary, completely positive map.

Journal

Quantum Information ProcessingSpringer Journals

Published: Feb 4, 2017

References

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