Abstract
In its original formulation, quantum backflow (QB) is an interference effect that manifests itself as a negative probability transfer for free-particle states comprised of plane waves with only positive momenta. Quantum reentry (QR) is another interference effect in which a wave packet expanding from a spatial region of its initial confinement partially returns to the region in the absence of any external forces. Here we show that both QB and QR are special cases of a more general classically-forbidden probability flow for quantum states with certain position-momentum correlations. We further demonstrate that it is possible to construct correlated quantum states for which the amount of probability transferred in the "wrong" (classically impossible) direction exceeds the least upper bound on the corresponding probability transfer in the QB and QR problems, known as the Bracken-Melloy constant.
Highlights
Quantum backflow (QB) is a quantum-mechanical interference effect with no counterpart in classical mechanics
We have shown that both QB and Quantum reentry (QR) effects manifest themselves as right-to-left probability transfer for initial states with linear position-momentum correlations, for which the measurement of p − kx, with k 0, is guaranteed to yield a positive result
We extend our study to states with nonlinear positionmomentum correlations, for which the outcome of measuring S(p) − xis certain to be positive
Summary
Quantum backflow (QB) is a quantum-mechanical interference effect with no counterpart in classical mechanics. Analyzed by Bracken and Melloy [3] They showed that the supremum of the right-to-left probability transfer—sup (τ, T ) where the supremum is taken over all normalizable states comprised of plane waves with positive momenta—coincides with the supremum λsup of the eigenvalue spectrum in the following integral eigenproblem:. The situation is different in quantum mechanics: there exist states, initially localized in the x < 0 region, for which (τ, T ) is positive This is the manifestation of the QR effect. The least upper bound on the QR probability appears to equal the Bracken-Melloy constant, λsup [24] This suggests the existence of a deep connection between QB and QR. We show that the least upper bound on the classically forbidden probability transfer in this generalized backflow problem exceeds the Bracken-Melloy constant.
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