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arXiv:2303.08962

Counterportation and the two-state vector formalism

Justin Dressel, Reznik, Gregory, Lev Vaidman A

Published Mar 15, 2023• 0 citations
arXivHTMLPDF

Abstract

Hatim Salih discovered a method for transferring a quantum state with no particles present in the transmission channel, which he named counterportation. Recently [H. Salih, Quantum Sci. Technol. 8, 025016 (2023)], he presented a feasible procedure for its implementation. The modification of the protocol by Aharonov and Vaidman, adopted by Salih, justifies the claim that no photons were present in the transmission channel during counterportation. We argue, however, that there is an error in this paper. The analysis of a simplified protocol, which questions the validity of the two-state vector formalism description of the photon presence in the communication channel, is incorrect.

DOI
10.48550/arxiv.2303.08962

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In a recent paper, Griffiths [Phys. Rev. A 107, 062219 (2023)] analyzed a protocol for transmission of information between two parties introduced by Salih et al. [Phys. Rev. Lett. 110, 170502 (2013)]. There is a considerable controversy about the counterfactuality of this protocol, and Griffiths suggested to resolve it by introducing a new measure of channel usage, which he called ``Cost.'' I argue that this measure is not appropriate because the original interaction-free measurement protocol which triggered the definition of the concept of counterfactuality is not counterfactual according to this measure.

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Hatim Salih discovered a method for transferring a quantum state with no particles present in the transmission channel, which he named counterportation. Recently [H. Salih, Quantum Sci. Technol. 8, 025016 (2023)], he presented a feasible procedure for its implementation. The modification of the protocol by Aharonov and Vaidman, adopted by Salih, justifies the claim that no photons were present in the transmission channel during counterportation. We argue, however, that there is an error in this paper. The analysis of a simplified protocol, which questions the validity of the two-state vector formalism description of the photon presence in the communication channel, is incorrect.
Abstract Hatim Salih discovered a method for transferring a quantum state with no particles present in the transmission channel, which he named counterportation. Recently (Salih 2023 Quantum Sci. Technol. 8 025016), he presented a feasible procedure for its implementation. The modification of the protocol by Aharonov and Vaidman, adopted by Salih, justifies the claim that no photons were present in the transmission channel during counterportation. We argue, however, that there is an error in this paper. The analysis of a simplified protocol, which questions the validity of the two-state vector formalism description of the photon presence in the communication channel, is incorrect.
Counterfactual communication, i.e., a communication without particles traveling in the transmission channel, is a bizarre quantum effect. Starting from interaction-free measurements many protocols achieving various tasks from counterfactual cryptography to counterfactual transfer of quantum states were proposed and implemented in experiments. However, the meaning of conterfactuality in various protocols remains a controversial topic. A simple error-free counterfactual protocol is proposed. This protocol and its modification are used as a test bed for analysis of the meaning of counterfactuality to clarify the counterfactuality status of various counterfactual proposals.
The possibility to communicate between spatially separated regions, without even a single photon passing between the two parties, is an amazing quantum phenomenon. The possibility of transmitting one value of a bit in such a way, the interaction-free measurement, has been known for quarter of a century. The protocols of full communication, including transmitting unknown quantum states, were proposed only a few years ago, but it was shown that in all these protocols the particle was leaving a weak trace in the transmission channel, the trace being larger than the trace left by a single particle passing through the channel. This made the claim of counterfactuality of these protocols at best controversial. However, a simple modification of these recent protocols eliminates the trace in the transmission channel, making all these protocols counterfactual.
A protocol for transmission of information between two parties introduced by Salih et al. [Phys. Rev. Lett. 110, 170502 (2013)] involves sending quantum amplitude back and forth through a quantum channel in a series of steps, rather than simply sending a signal in one direction. The authors claimed that their protocol was ``counterfactual'' in the sense that while a quantum channel is needed to connect the parties, its actual usage becomes vanishingly small in the asymptotic limit as the number of steps tends to infinity. Here we show that this claim is incorrect because it uses probabilistic reasoning that is not valid at intermediate times in the presence of quantum interference. When ill-defined probabilities are replaced with a well-defined measure of channel usage, here called ``Cost,'' equal to the absolute square of the amplitude sent through the channel, the total Cost does not go to zero in the asymptotic limit of a large number of steps, but is bounded below by a rigorous inequality. A detailed analysis shows that this bound is satisfied in the protocol of Salih et al. [Phys. Rev. Lett. 110, 170502 (2013)]. The analysis leading to the bound uses the fact that the Gram matrix formed by inner products of a collection of pure quantum states is additive over Hilbert subspaces and invariant under unitary time transformations. Its off-diagonal elements, which in general are not positive, play a significant role in the formal argument as well as providing a somewhat strange way of visualizing the transfer of information.
In a recent paper, Griffiths [Phys. Rev. A 107, 062219 (2023)] analyzed a protocol for transmission of information between two parties introduced by Salih et al. [Phys. Rev. Lett. 110, 170502 (2013)]. There is a considerable controversy about the counterfactuality of this protocol, and Griffiths suggested to resolve it by introducing a new measure of channel usage, which he called ``Cost.'' I argue that this measure is not appropriate because the original interaction-free measurement protocol which triggered the definition of the concept of counterfactuality is not counterfactual according to this measure.