TY - JOUR

T1 - Poisson stochastic master equation unravelings and the measurement problem

T2 - A quantum stochastic calculus perspective

AU - Keys, Dustin

AU - Wehr, Jan

N1 - Funding Information:
The authors were partially supported by the National Science Foundation, Grant No. DMS 1615045. D.K. gratefully acknowledges Michael Tabor Fellowship from the Program of Applied Mathematics, University of Arizona. Both authors would like to thank the Institute of Photonic Science, Castelldefels (Spain), and Maciej Lewenstein for their hospitality.
Publisher Copyright:
© 2020 Author(s).

PY - 2020/3/1

Y1 - 2020/3/1

N2 - This paper studies a class of quantum stochastic differential equations, modeling an interaction of a system with its environment in the quantum noise approximation. The space representing quantum noise is the symmetric Fock space over L2R+. Using the isomorphism of this space with the space of square-integrable functionals of the Poisson process, the equations can be represented as classical stochastic differential equations, driven by Poisson processes. This leads to a discontinuous dynamical state reduction which we compare to the Ghirardi - Rimini-Weber model. A purely quantum object, the norm process, is found, which plays the role of an observer {in the sense of Everett [H. Everett III, Rev. Mod. Phys. 29(3), 454 (1957)]}, encoding all events occurring in the system space. An algorithm introduced by Dalibard et al. [Phys. Rev. Lett. 68(5), 580 (1992)] to numerically solve quantum master equations is interpreted in the context of unraveling, and the trajectories of expected values of system observables are calculated.

AB - This paper studies a class of quantum stochastic differential equations, modeling an interaction of a system with its environment in the quantum noise approximation. The space representing quantum noise is the symmetric Fock space over L2R+. Using the isomorphism of this space with the space of square-integrable functionals of the Poisson process, the equations can be represented as classical stochastic differential equations, driven by Poisson processes. This leads to a discontinuous dynamical state reduction which we compare to the Ghirardi - Rimini-Weber model. A purely quantum object, the norm process, is found, which plays the role of an observer {in the sense of Everett [H. Everett III, Rev. Mod. Phys. 29(3), 454 (1957)]}, encoding all events occurring in the system space. An algorithm introduced by Dalibard et al. [Phys. Rev. Lett. 68(5), 580 (1992)] to numerically solve quantum master equations is interpreted in the context of unraveling, and the trajectories of expected values of system observables are calculated.

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U2 - 10.1063/1.5133974

DO - 10.1063/1.5133974

M3 - Article

AN - SCOPUS:85081238791

VL - 61

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 3

M1 - 032101

ER -