TY - GEN
T1 - From the Heisenberg to the Schrödinger Picture
T2 - 60th IEEE Conference on Decision and Control, CDC 2021
AU - Nurdin, Hendra I.
AU - Gough, John
N1 - Funding Information:
H. I. Nurdin is with the School of Electrical Engineering and Telecommunications, UNSW Australia, Sydney NSW 2052, Australia (email: [email protected]) J. Gough is with the Department of Physics, Aberystwyth University, Ceredigion, SY23 3BZ, Wales, UK (email: [email protected]). JG acknowledges funding under ANR grant (ANR-19-CE48-0003)
Publisher Copyright:
© 2021 IEEE.
PY - 2021
Y1 - 2021
N2 - A general theory of quantum stochastic processes was formulated by Accardi, Frigerio and Lewis in 1982 within the operator-algebraic framework of quantum probability theory, as a non-commutative extension of the Kolmogorovian classical stochastic processes. More recently, studies on non-Markovian quantum processes have led to the discrete-time process tensor formalism in the Schrödinger picture to describe the outcomes of sequential interventions on open quantum systems. However, there has been no treatment of the relationship of the process tensor formalism to the quantum probabilistic theory of quantum stochastic processes. This paper gives an exposition of quantum stochastic processes and the process tensor and the relationship between them. In particular, it is shown how the latter emerges from the former via extended correlation kernels incorporating ancillas.
AB - A general theory of quantum stochastic processes was formulated by Accardi, Frigerio and Lewis in 1982 within the operator-algebraic framework of quantum probability theory, as a non-commutative extension of the Kolmogorovian classical stochastic processes. More recently, studies on non-Markovian quantum processes have led to the discrete-time process tensor formalism in the Schrödinger picture to describe the outcomes of sequential interventions on open quantum systems. However, there has been no treatment of the relationship of the process tensor formalism to the quantum probabilistic theory of quantum stochastic processes. This paper gives an exposition of quantum stochastic processes and the process tensor and the relationship between them. In particular, it is shown how the latter emerges from the former via extended correlation kernels incorporating ancillas.
UR - http://www.scopus.com/inward/record.url?scp=85126027900&partnerID=8YFLogxK
U2 - 10.1109/CDC45484.2021.9683765
DO - 10.1109/CDC45484.2021.9683765
M3 - Conference Proceeding (Non-Journal item)
AN - SCOPUS:85126027900
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 4164
EP - 4169
BT - 60th IEEE Conference on Decision and Control, CDC 2021
PB - IEEE Press
Y2 - 13 December 2021 through 17 December 2021
ER -