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arXiv:2306.16756 · Physical Review A

Comment on “Multitime quantum communication: Interesting but not counterfactual”

Lev Vaidman A

Published Nov 8, 2023• 2 citations
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Abstract

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.

DOI
10.1103/physreva.108.056201

Related papers

Multitime quantum communication: Interesting but not counterfactual

Robert B. Griffiths

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.

arXiv:2301.01730•Physical Review A•Jun 28, 2023•4 citations

Reply to Comment on "Multitime Quantum Communication: Interesting But Not Counterfactual" by L. Vaidman

Robert B. Griffiths

This is a Reply to the Comment by Vaidman in arXiv:2306.16756 on the paper: R. B. Griffiths, Phys. Rev. A 107, 062219 (2023)

arXiv:2310.05968•Sep 23, 2023•0 citations

Comment on “Protocol for Direct Counterfactual Quantum Communication”

Lev Vaidman A

I argue that recent "Protocol for Direct Counterfactual Quantum Communication" by Salih et al. [PRL 110, 170502 (2013), arXiv:1206.2042] is counterfactual only for one type of the information bit.

arXiv:1304.6689•Physical Review Letters•May 23, 2014•64 citations

“Counterfactual” quantum protocols

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The counterfactuality of recently proposed protocols is analyzed. A definition of “counterfactuality” is offered and it is argued that an interaction-free measurement (IFM) of the presence of an opaque object can be named “counterfactual”, while proposed “counterfactual” measurements of the absence of such objects are not counterfactual. The quantum key distribution protocols which rely only on measurements of the presence of the object are counterfactual, but quantum direct communication protocols are not. Therefore, the name “counterfactual” is not appropriate for recent “counterfactual” protocols which transfer quantum states by quantum direct communication.

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Lev Vaidman A

The counterfactuality of recently proposed protocols is analyzed. A definition of `counterfactuality' is offered and it is argued that an interaction-free measurement of the presence of an opaque object can be named `counterfactual', while proposed "counterfactual" measurements of the absence of such objects are not counterfactual. The quantum key distribution protocols which rely only on measurements of the presence of the object are counterfactual, but quantum direct communication protocols are not. Therefore, the name `counterfactual' is not appropriate for recent "counterfactual" protocols which transfer quantum states by quantum direct communication.

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Reply to “Comment on ‘Multitime quantum communication: Interesting but not counterfactual' ”

Robert B. Griffiths

This is a response to comments and criticisms found in the preceding Comment [Phys. Rev. A 108, 056201 (2023)] by Vaidman on the paper in Phys. Rev. A 107, 062219 (2023).Received 27 September 2023Accepted 18 October 2023DOI:https://doi.org/10.1103/PhysRevA.108.056202©2023 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum communicationQuantum foundationsQuantum information theoryQuantum Information, Science & Technology

Physical Review A•Nov 8, 2023•0 citations
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.
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.
The counterfactuality of recently proposed protocols is analyzed. A definition of “counterfactuality” is offered and it is argued that an interaction-free measurement (IFM) of the presence of an opaque object can be named “counterfactual”, while proposed “counterfactual” measurements of the absence of such objects are not counterfactual. The quantum key distribution protocols which rely only on measurements of the presence of the object are counterfactual, but quantum direct communication protocols are not. Therefore, the name “counterfactual” is not appropriate for recent “counterfactual” protocols which transfer quantum states by quantum direct communication.
The counterfactuality of recently proposed protocols is analyzed. A definition of `counterfactuality' is offered and it is argued that an interaction-free measurement of the presence of an opaque object can be named `counterfactual', while proposed "counterfactual" measurements of the absence of such objects are not counterfactual. The quantum key distribution protocols which rely only on measurements of the presence of the object are counterfactual, but quantum direct communication protocols are not. Therefore, the name `counterfactual' is not appropriate for recent "counterfactual" protocols which transfer quantum states by quantum direct communication.