TY - JOUR

T1 - Measurement-induced quantum walks

AU - Didi, A.

AU - Barkai, E.

N1 - Publisher Copyright:
© 2022 American Physical Society.

PY - 2022/5

Y1 - 2022/5

N2 - We investigate a tight-binding quantum walk on a graph. Repeated stroboscopic measurements of the position of the particle yield a measured "trajectory,"and a combination of classical and quantum mechanical properties for the walk are observed. We explore the effects of the measurements on the spreading of the packet on a one-dimensional line, showing that except for the Zeno limit, the system converges to Gaussian statistics similarly to a classical random walk. A large deviation analysis and an Edgeworth expansion yield quantum corrections to this normal behavior. We then explore the first passage time to a target state using a generating function method, yielding properties like the quantization of the mean first return time. In particular, we study the effects of certain sampling rates that cause remarkable changes in the behavior in the system, such as divergence of the mean detection time in finite systems and decomposition of the phase space into mutually exclusive regions, an effect that mimics ergodicity breaking, whose origin here is the destructive interference in quantum mechanics. For a quantum walk on a line, we show that in our system the first detection probability decays classically like (time)-3/2. This is dramatically different compared to local measurements, which yield a decay rate of (time)-3, indicating that the exponents of the first passage time depend on the type of measurements used.

AB - We investigate a tight-binding quantum walk on a graph. Repeated stroboscopic measurements of the position of the particle yield a measured "trajectory,"and a combination of classical and quantum mechanical properties for the walk are observed. We explore the effects of the measurements on the spreading of the packet on a one-dimensional line, showing that except for the Zeno limit, the system converges to Gaussian statistics similarly to a classical random walk. A large deviation analysis and an Edgeworth expansion yield quantum corrections to this normal behavior. We then explore the first passage time to a target state using a generating function method, yielding properties like the quantization of the mean first return time. In particular, we study the effects of certain sampling rates that cause remarkable changes in the behavior in the system, such as divergence of the mean detection time in finite systems and decomposition of the phase space into mutually exclusive regions, an effect that mimics ergodicity breaking, whose origin here is the destructive interference in quantum mechanics. For a quantum walk on a line, we show that in our system the first detection probability decays classically like (time)-3/2. This is dramatically different compared to local measurements, which yield a decay rate of (time)-3, indicating that the exponents of the first passage time depend on the type of measurements used.

UR - http://www.scopus.com/inward/record.url?scp=85130552062&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.105.054108

DO - 10.1103/PhysRevE.105.054108

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C2 - 35706264

AN - SCOPUS:85130552062

SN - 2470-0045

VL - 105

JO - Physical Review E

JF - Physical Review E

IS - 5

M1 - 054108

ER -