Evolution prediction from tomography

  • Jason M. Dominy
  • Lorenzo Campos Venuti
  • Alireza Shabani
  • Daniel A. Lidar


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 \(0<\tau _{1}<\dots <\tau _{M}\) with \(M\ge 1\). 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.


Quantum process tomography Prediction Unitary evolution Completely positive maps 



This research was supported by the ARO MURI Grant W911NF-11-1-0268.


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© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of ChemistryUniversity of Southern CaliforniaLos AngelesUSA
  2. 2.Department of Electrical EngineeringUniversity of Southern CaliforniaLos AngelesUSA
  3. 3.Department of PhysicsUniversity of Southern CaliforniaLos AngelesUSA
  4. 4.Center for Quantum Information Science and TechnologyUniversity of Southern CaliforniaLos AngelesUSA
  5. 5.Department of ChemistryUniversity of CaliforniaBerkeleyUSA
  6. 6.Department of Applied Mathematics & StatisticsUniversity of CaliforniaSanta CruzUSA

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