Direct counterfactual quantum communication protocol beyond single photon source

Li, Zhenghong; Feng, Shang-Yue; Al-Amri, M.; Zubairy, M. Suhail

doi:10.48550/arxiv.2202.03935

Cited by 1 publication

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“…The original SLAZ proposal has motivated a large number of papers; see the extensive bibliographies in [3,4]. Merely trying to summarize them, much less provide a detailed review, lies outside the scope of the present paper.…”

Section: Discussionmentioning

confidence: 99%

“…Significant extensions of the original SLAZ scheme by the last three members of the original collaboration include: the use of a phase change rather than absorption to transmit the λ = 1 bit [7]; a scheme to transmit quantum states by multiple iterations of the original SLAZ scheme [8]; using many photons in place of a single photon to transmit a classical bit [4]. These and others are certainly interesting ideas from the perspective of transmitting quantum information, and worth further exploration.…”

Section: Discussionmentioning

confidence: 99%

“…5, of the present paper contains a few remarks about how its results apply to some of these publications, but a review, much less a detailed discussion, lies far outside its scope. The interested reader is referred to the extensive bibliographies found in [3,4].…”

Section: Introductionmentioning

confidence: 99%

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Multitime Quantum Communication: Interesting But Not Counterfactual

Griffiths¹

2023

Preprint

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A protocol for transmission of information between two parties introduced by Salih et al., Phys. Rev. Lett. 110 (2013) 170502 (hereafter SLAZ), 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 SLAZ protocol. 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.

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Section: Discussionmentioning

confidence: 99%