Uncertainty relation between detection probability and energy fluctuations

Abstract

A classical random walker starting on a node of a finite graph will always reach any other node since the search is ergodic, namely it is fully exploring space, hence the arrival probability is unity. For quantum walks, destructive interference may induce effectively non-ergodic features in such search processes. Under repeated projective local measurements, made on a target state, the final detection of the system is not guaranteed since the Hilbert space is split into a bright subspace and an orthogonal dark one. Using this we find an uncertainty relation for the deviations of the detection probability from its classical counterpart, in terms of the energy fluctuations.

arXiv comment12 pages, special issue Axiomatic Approaches to Quantum Mechanics, 4 figures

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Cited by in corpus (6)

• Quantum unitary evolution interspersed with repeated non-unitary interactions at random times: The method of stochastic Liouville equation, and two examples of interactions in the context of a tight-binding chain
• Restart uncertainty relation for monitored quantum dynamics
• Measurement induced quantum walks
• Quantum random walk and tight-binding model subject to projective measurements at random times
• Resonances of recurrence time of monitored quantum walks
• Interaction-induced transition in quantum many-body detection probability