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.
 J. Kijowski ``On the time operator in quantum mechanics and the Heisenberg uncertainty relation for energy and time'' Reports Math. Phys. 6, 361 (1974).
 J. M. Yearsley, J. J. Halliwell, R. Hartshorn, and A. Whitby, ``Analytical examples, measurement models, and classical limit of quantum backflow'' Phys. Rev. A 86, 042116 (2012).
 J. J. Halliwell, E. Gillman, O. Lennon, M. Patel, and I. Ramirez, ``Quantum backflow states from eigenstates of the regularized current operator'' J. Phys. A: Math. Theor. 46, 475303 (2013).
 G. F. Melloyand A. J. Bracken ``The velocity of probability transport in quantum mechanics'' Ann. Phys. (Leipzig) 7, 726 (1998).
 P. Strange ``Large quantum probability backflow and the azimuthal angle-angular momentum uncertainty relation for an electron in a constant magnetic field'' Eur. J. Phys. 33, 1147 (2012).
 M. V. Berry ``Quantum backflow, negative kinetic energy, and optical retro-propagation'' J. Phys. A: Math. Theor. 43, 415302 (2010).
 J. G. Muga, J. P. Palao, and C. R. Leavens, ``Arrival time distributions and perfect absorption in classical and quantum mechanics'' Phys. Lett. A 253, 21 (1999).
 J. J. Halliwell, H. Beck, B. K. B. Lee, and S. O'Brien, ``Quasiprobability for the arrival-time problem with links to backflow and the Leggett-Garg inequalities'' Phys. Rev. A 99, 012124 (2019).
 A. Goussev ``Equivalence between quantum backflow and classically forbidden probability flow in a diffraction-in-time problem'' Phys. Rev. A 99, 043626 (2019).
 A. Goussev ``Probability backflow for correlated quantum states'' Phys. Rev. Research 2, 033206 (2020).
 M. Palmero, E. Torrontegui, J. G. Muga, and M. Modugno, ``Detecting quantum backflow by the density of a Bose-Einstein condensate'' Phys. Rev. A 87, 053618 (2013).
 Sh. Mardonov, M. Palmero, M. Modugno, E. Ya. Sherman, and J. G. Muga, ``Interference of spin-orbit-coupled Bose-Einstein condensates'' EPL (Europhysics Lett.) 106, 60004 (2014).
 L. Cohen ``The Weyl Operator and its Generalization'' Birkhäuser (2013).
 W. Appel ``Mathématiques pour la physique et les physiciens, 4è Ed.'' H & K Eds (2008).
 M. de Gosson ``Symplectic Geometry and Quantum Mechanics'' Birkhäuser (2006).
 K. Gottfriedand T.-M. Yan ``Quantum Mechanics: Fundamentals (2nd Edition)'' Springer (2003).
 S. Harocheand J.-M. Raimond ``Exploring the Quantum: Atoms, Cavities and Photons'' Oxford Univ. Press (2006).
 W.-W. Pan, X.-Y. Xu, Y. Kedem, Q.-Q. Wang, Z. Chen, M. Jan, K. Sun, J.-S. Xu, Y.-J. Han, C.-F. Li, and G.-C. Guo, ``Direct Measurement of a Nonlocal Entangled Quantum State'' Phys. Rev. Lett. 123, 150402 (2019).
 S. Zhang, Y. Zhou, Y. Mei, K. Liao, Y.-L. Wen, J. Li, X.-D. Zhang, S. Du, H. Yan, and S.-L. Zhu, ``$\delta$-Quench Measurement of a Pure Quantum-State Wave Function'' Phys. Rev. Lett. 123, 190402 (2019).
 S. N. Sahoo, S. Chakraborti, A. K. Pati, and U. Sinha, ``Quantum State Interferography'' Phys. Rev. Lett. 125, 123601 (2020).
 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).
 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).
 Dripto Biswas and Subir Ghosh, "Quantum backflow across a black hole horizon in a toy model approach", Physical Review D 104 10, 104061 (2021).
 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).
 Maximilien Barbier, Arseni Goussev, and Shashi C. L. Srivastava, "Unbounded quantum backflow in two dimensions", Physical Review A 107 3, 032204 (2023).
 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).
 S. V. Mousavi and S. Miret-Artés, "Different routes to the classical limit of backflow", Journal of Physics A Mathematical General 55 47, 475302 (2022).
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