On the experiment-friendly formulation of quantum backflow

Maximilien Barbier1,2 and Arseni Goussev3

1Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, D-01187 Dresden, Germany
2Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles (ULB), Code Postal 231, Campus Plaine, B-1050 Brussels, Belgium
3School of Mathematics and Physics, University of Portsmouth, Portsmouth PO1 3HF, United Kingdom

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In its standard formulation, quantum backflow is a classically impossible phenomenon in which a free quantum particle in a positive-momentum state exhibits a negative probability current. Recently, Miller et al. [Quantum 5, 379 (2021)] have put forward a new, "experiment-friendly" formulation of quantum backflow that aims at extending the notion of quantum backflow to situations in which the particle's state may have both positive and negative momenta. Here, we investigate how the experiment-friendly formulation of quantum backflow compares to the standard one when applied to a free particle in a positive-momentum state. We show that the two formulations are not always compatible. We further identify a parametric regime in which the two formulations appear to be in qualitative agreement with one another.

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[1] David Trillo, Thinh P. Le, and Miguel Navascués, "Quantum advantages for transportation tasks - projectiles, rockets and quantum backflow", npj Quantum Information 9 1, 69 (2023).

[2] Leonardo Di Bari, Valentin Daniel Paccoia, Orlando Panella, and Pinaki Roy, "Quantum backflow for a massless Dirac fermion on a ring", Physics Letters A 474, 128831 (2023).

[3] Dripto Biswas and Subir Ghosh, "Quantum backflow across a black hole horizon in a toy model approach", Physical Review D 104 10, 104061 (2021).

[4] A J Bracken and G F Melloy, "Comment on ‘Backflow in relativistic wave equations’", Journal of Physics A: Mathematical and Theoretical 56 13, 138002 (2023).

[5] Maximilien Barbier, Arseni Goussev, and Shashi C. L. Srivastava, "Unbounded quantum backflow in two dimensions", Physical Review A 107 3, 032204 (2023).

[6] Iwo Bialynicki-Birula, Zofia Bialynicka-Birula, and Szymon Augustynowicz, "Backflow in relativistic wave equations", Journal of Physics A: Mathematical and Theoretical 55 25, 255702 (2022).

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