Department of Mathematics

Mathematical Physics and Operator Algebras

  •  Lubashan Pathirana, MSU
  •  Limiting Theorems for Discrete and Continuous Parameter Stationary and Ergodic Quantum Processes.
  •  10/18/2022
  •  11:00 AM - 12:00 PM
  •  C304 Wells Hall
  •  Jeffrey Hudson Schenker (schenke6@msu.edu)

A discrete parameter quantum process is represented by a sequence of quantum operations, which are completely positive maps that are trace non-increasing. Given a stationary and ergodic sequences of such maps, an ergodic theorem describing convergence to equilibrium for a general class of such processes was recently obtained by Movassagh and Schenker. Under irreducibility conditions we obtain a law of large numbers that describes the asymptotic behavior of the processes involving the Lyapunov exponent. Furthermore, a central limit type theorem is obtained under mixing conditions. In the continuous time parameter, a quantum process is represented by a double-indexed family of positive map valued random variables. For a stationary and ergodic family of such maps, we extend the results by Movassagh and Schenker to the continuous case.

 

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Michigan State University
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