Probability backflow for correlated quantum states

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.

Times of arrival and gauge invariance

“…From the preceding Bohmian derivation, one also expects that ΠQF would not be a generally valid arrival-time distribution. In particular, it is reasonable only as long as (2.25) holds, which is equivalent to the current positivity (or ‘no backflow’) condition [49,50]: normal∀t>0 and normal∀x∈Q,1emJfalse(x,tfalse)⋅ds≥0. Even though (2.26) can be violated in principle, see [75–78], stable backflow situations are, as it happens, very difficult to set up experimentally. This is because, on the one hand, the flux density of freely evolving wave functions becomes approximately radial at large distances from the support of the initial wave function ψ 0 [49,50]: Jfalse(x,tfalse)≈boldxt4|ψ~0(xt)|2, granting (2.26) for just about any surface Q placed in the far-field (as is typical of scattering experiments).…”

“…Even though (2.26) can be violated in principle, see [75][76][77][78], stable backflow situations are, as it happens, very difficult to set up experimentally. This is because, on the one hand, the flux density of freely evolving wave functions becomes approximately radial at large distances from the support of the initial wave function ψ 0 [49,50]:…”

Experiment-friendly formulation of quantum backflow

“…The phenomenon was extended into phase space in Ref. [14] and systems suitable for observing QB in an experiment were discussed in Refs. [27,15].…”

On the experiment-friendly formulation of quantum backflow

“…[4,9,17]. QB is also known to bear close relation to the arrival-time problem [2,3,[18][19][20][21][22][23][24][25] and some nonclassical aspects of the flow of probability in quantum systems [7,[26][27][28][29].…”

“…The numerical method is based on the approach originally presented in Ref [1],. and has been further discussed in Section IIIB of Ref [29]. and the appendix of Ref [12]…”