TY - JOUR

T1 - Randomly repeated measurements on quantum systems

T2 - Correlations and topological invariants of the quantum evolution

AU - Ziegler, K.

AU - Barkai, E.

AU - Kessler, D.

N1 - Publisher Copyright:
© 2021 IOP Publishing Ltd.

PY - 2021/10

Y1 - 2021/10

N2 - Randomly repeated measurements during the evolution of a closed quantum system create a sequence of probabilities for the first detection of a certain quantum state. The related discrete monitored evolution for the return of the quantum system to its initial state is investigated. We found that the mean number of measurements (MNM) until the first detection is an integer, namely the dimensionality of the accessible Hilbert space. Moreover, the mean first detected return (FDR) time is equal to the average time step between successive measurements times the MNM. Thus, the mean FDR time scales linearly with the dimensionality of the accessible Hilbert space. The main goal of this work is to explain the quantization of the mean return time in terms of a quantized Berry phase.

AB - Randomly repeated measurements during the evolution of a closed quantum system create a sequence of probabilities for the first detection of a certain quantum state. The related discrete monitored evolution for the return of the quantum system to its initial state is investigated. We found that the mean number of measurements (MNM) until the first detection is an integer, namely the dimensionality of the accessible Hilbert space. Moreover, the mean first detected return (FDR) time is equal to the average time step between successive measurements times the MNM. Thus, the mean FDR time scales linearly with the dimensionality of the accessible Hilbert space. The main goal of this work is to explain the quantization of the mean return time in terms of a quantized Berry phase.

KW - dynamical invariants

KW - monitored quantum evolution

KW - randomly repeated measurements

UR - http://www.scopus.com/inward/record.url?scp=85114819616&partnerID=8YFLogxK

U2 - 10.1088/1751-8121/ac095f

DO - 10.1088/1751-8121/ac095f

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SN - 1751-8113

VL - 54

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 39

M1 - 395302

ER -