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Physical Review A

Comment on “Wigner rotations and an apparent paradox in relativistic quantum information”

Marco O. Lanzagorta, Tanner Crowder

Published Aug 10, 2017• 6 citations
Publisher

Abstract

We show that the paradox published by Saldanha and Vedral [Phys. Rev. A 87, 042102 (2013)] is based on an improper interpretation of the localization probability density and a miscalculation of the wave functions. This Comment shows that there is no paradox as stated.
DOI
10.1103/physreva.96.026101

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Reply to Comment on "Wigner rotations and an apparent paradox in relativistic quantum information"

Pablo L. Saldanha, Vlatko Vedral

As Lanzagorta and Crowder have shown in their Comment [Phys. Rev. A 96, 026101 (2017)], the linear application of the Wigner rotations to the quantum state of two massive relativistic particles does not entail the instantaneous transmission of information as we concluded in our paper [Phys. Rev. A 87, 042102 (2013)]. But in the new version of our paper in arXiv [arXiv:1303.4367v2] we show (and solve) another paradox that is generated by the linear application of the Wigner rotations to a system with a single relativistic particle. So the conclusion of our paper that we cannot in general linearly apply the Wigner rotations to the quantum state of a relativistic particle without considering the appropriate physical interpretation is still valid, although the paradox presented in that paper is inappropriate.

arXiv:1708.09007•Aug 29, 2017•0 citations

Wigner rotations and an apparent paradox in relativistic quantum information

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It is shown that a general model for particle detection in combination with a linear application of the Wigner rotations, which correspond to momentum-dependent changes of the particle spin under Lorentz transformations, to the state of a massive relativistic particle in a superposition of two counterpropagating momentum states leads to a paradox. The paradox entails the instantaneous transmission of information between two spatially separated parties. A solution to the paradox is given when the physical construction of the corresponding state is taken into account, suggesting that we cannot in general linearly apply the Wigner rotations to a quantum state without considering the appropriate physical interpretation.

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Physical interpretation of the Wigner rotations and its implications for relativistic quantum information

Pablo L. Saldanha, Vlatko Vedral

We present a new treatment for the spin of a massive relativistic particle in the context of quantum information based on a physical interpretation of the Wigner rotations, obtaining different results in relation to previous works. We are led to the conclusion that it is not possible to define a reduced density matrix for the particle spin and that the Pauli–Lubanski (or similar) spin operators are not suitable for describing measurements where the spin couples to an electromagnetic field in the measuring apparatus. These conclusions contradict the assumptions made by most of the previous papers on the subject. We also propose an experimental test of our formulation.

arXiv:1111.7145•New Journal of Physics•Feb 20, 2012•50 citations
As Lanzagorta and Crowder have shown in their Comment [Phys. Rev. A 96, 026101 (2017)], the linear application of the Wigner rotations to the quantum state of two massive relativistic particles does not entail the instantaneous transmission of information as we concluded in our paper [Phys. Rev. A 87, 042102 (2013)]. But in the new version of our paper in arXiv [arXiv:1303.4367v2] we show (and solve) another paradox that is generated by the linear application of the Wigner rotations to a system with a single relativistic particle. So the conclusion of our paper that we cannot in general linearly apply the Wigner rotations to the quantum state of a relativistic particle without considering the appropriate physical interpretation is still valid, although the paradox presented in that paper is inappropriate.
It is shown that a general model for particle detection in combination with a linear application of the Wigner rotations, which correspond to momentum-dependent changes of the particle spin under Lorentz transformations, to the state of a massive relativistic particle in a superposition of two counterpropagating momentum states leads to a paradox. The paradox entails the instantaneous transmission of information between two spatially separated parties. A solution to the paradox is given when the physical construction of the corresponding state is taken into account, suggesting that we cannot in general linearly apply the Wigner rotations to a quantum state without considering the appropriate physical interpretation.
In their paper (arXiv:2402.09879), Aredes and Saldanha analyze several paradoxes related to weak values and present a "general argument" that aims to show that "realistic interpretations ...of weak values lead to inconsistencies". Although we agree with the identified inconsistencies for the specific weak values analyzed there, in this Comment we demonstrate that the origin of these inconsistencies is not their general argument, which is formally incorrect. We use Bohmian mechanics as a counterexample to confirm that their conclusions are not valid for all weak values and quantum theories. In particular, we show that weak values postselected in position can in fact be interpreted within Bohmian mechanics as properties of quantum systems, detached from any measuring devices, in a consistent and meaningful way.
Von Zuben [J. Math. Phys. 41, 6093 (2000)] proposed a resolution to spatial localization problems related to Hegerfeldt’s paradox. To do so, he applied Dirac’s formalism to a free spinless massive particle to introduce a new perspective in which this paradox could be interpreted as an apparent phenomenon. However, although being a physically interesting proposal, here we show that its main result was obtained using an incomplete basis for the physical Hilbert space, the correction of which invalidates the proposed resolution.
We present a new treatment for the spin of a massive relativistic particle in the context of quantum information based on a physical interpretation of the Wigner rotations, obtaining different results in relation to previous works. We are led to the conclusion that it is not possible to define a reduced density matrix for the particle spin and that the Pauli–Lubanski (or similar) spin operators are not suitable for describing measurements where the spin couples to an electromagnetic field in the measuring apparatus. These conclusions contradict the assumptions made by most of the previous papers on the subject. We also propose an experimental test of our formulation.