Department of Mathematics

Probability

  •  Lubashan Pathirana Karunarathna, MSU
  •  Limiting Theorems for Compositions of Stationary and Ergodic Random Maps With Applications in Quantum Processes
  •  11/09/2022
  •  3:00 PM - 3:50 PM
  •  C405 Wells Hall
  •  Dapeng Zhan (zhan@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 sequence 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. These results do not require the sequences of quantum operations that describe the quantum process to be trace non-increasing and hence can be applied to a larger class of compositions of random positive maps. 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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