Measurement induced quantum walks

Abstract

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 which cause remarkable change in the behavior in the system, like divergence of the mean detection time in finite systems and a 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 $(\text{time}{)}^{-3/2}$, this is dramatically different compared to local measurements which yield a decay rate of $(\text{time}{)}^{-3}$, indicating that the exponents of the first passage time depends on the type of measurements used.

arXiv comment22 pages, 18 figures

References in corpus (30)

• Measurement-Induced Phase Transitions in the Dynamics of Entanglement
• Realization of quantum walks with negligible decoherence in waveguide lattices
• Persistence and First-Passage Properties in Non-equilibrium Systems
• Continuous-Time Quantum Walks: Models for Coherent Transport on Complex Networks
• Decoherence in quantum walks - a review
• The quantum to classical transition for random walks
• Quantum random walks with decoherent coins
• Hitting time for quantum walks on the hypercube
• Quantum Many-Body Scars in Optical Lattices
• Decoherence in the quantum walk on the line
• Recurrence for discrete time unitary evolutions
• Detection of a quantum particle on a lattice under repeated projective measurements
• Quantum walks: the first detected passage time problem
• Quantum walks on quotient graphs
• First detected arrival of a quantum walker on an infinite line
• Hitting time for the continuous quantum walk
• Interlacing Relaxation and First-Passage Phenomena in Reversible Discrete and Continuous Space Markovian Dynamics
• Probing Measurement Induced Effects in Quantum Walks via Recurrence
• Large fluctuations of the first detected quantum return time
• Quantumness in decoherent quantum walk using measurement-induced disturbance
• Dark states of quantum search cause imperfect detection
• Quantum walks: the first detected transition time
• Measurements in the Lévy quantum walk
• Quantum random walks on the $N$-cycle subject to decoherence on the coin degree of freedom
• Uncertainty and symmetry bounds for the quantum total detection probability
• Beyond Zeno: Approaching Infinite Temperature upon Repeated Measurements
• Classical-like behavior in quantum walks with inhomogeneous, time-dependent coin operators
• To Measure, or Not to Measure, That is the Question
• Uncertainty relation between detection probability and energy fluctuations
• Quantization of the mean decay time for non-Hermitian quantum systems

Cited by in corpus (13)

• Topological Speed Limit
• Measurements on an Anderson Chain
• Measurement induced quantum walks on an IBM Quantum Computer
• Restart uncertainty relation for monitored quantum dynamics
• Resonances of recurrence time of monitored quantum walks
• Causality, localization, and universality of monitored quantum walks with long-range hopping
• Discrete-time Semiclassical Szegedy Quantum Walks
• Measurement Induced Chirality II: Diffusion and Disorder
• Observation of partial and infinite-temperature thermalization induced by repeated measurements on a quantum hardware
• Performance advantage of protective quantum measurements
• Accelerated first detection in discrete-time quantum walks using sharp restarts
• On Hitting Times for General Quantum Markov Processes
• Monte Carlo particle transport on quantum computers