arXiv:1604.04596 · Physical Review A

Particle path through a nested Mach-Zehnder interferometer

Robert B. Griffiths

Published Sep 16, 2016• 79 citations

Abstract

Possible paths of a photon passing through a nested Mach-Zehnder interferometer on its way to a detector are analyzed using the consistent histories formulation of quantum mechanics, and confirmed using a set of weak measurements (but not weak values). The results disagree with an analysis by Vaidman [Phys. Rev. A 87, 052104 (2013)], and agree with a conclusion reached by Li et al. [Phys. Rev. A 88, 046102 (2013)]. However, the analysis casts serious doubt on the claim of Salih et al. (whose authorship includes Li et al.) [Phys. Rev. Lett. 110, 170502 (2013)] to have constructed a protocol for counterfactual communication: a channel which can transmit information even though it contains a negligible number of photons.

DOI: 10.1103/physreva.94.032115

Related papers

Comment on “Particle path through a nested Mach-Zehnder interferometer”

Hatim Salih

In a recent paper [Phys. Rev. A 94, 032115 (2016)], Griffiths questioned---based on an interesting consistent-histories (CH) argument---the counterfactuality, for one of the bit choices, of the protocol of Salih et al. for communicating without sending physical particles [Phys. Rev. Lett. 110, 170502 (2013)]. Here, we first show that for the Mach-Zehnder version used to explain our protocol, contrary to Griffiths's claim, no family of consistent histories exists where any history has the photon traveling through the communication channel, thus rendering the question of whether the photon was in the communication channel meaningless from a CH viewpoint. We then show that for the actual Michelson-type protocol, there is a consistent-histories family for each cycle that includes histories where the photon travels through the communication channel. We show that the probability of finding the photon in the communication channel at any time is zero---proving complete counterfactuality.

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Reply to “Comment on ‘Particle path through a nested Mach-Zehnder interferometer' ”

Robert B. Griffiths

While much of the technical analysis in the preceding Comment is correct, in the end it confirms the conclusion reached in my previous work [Phys. Rev. A 94, 032115 (2016)]: A consistent histories analysis provides no support for the claim of counterfactual quantum communication put forward by Salih et al. [Phys. Rev. Lett. 110, 170502 (2013)].

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Recently, A. Danan et al. [Phys. Rev. Lett. 111, 240402 (2013)] performed a much-discussed experiment in which which-way information was obtained from the light in a nested Mach-Zehnder interferometer by weak measurement. The presented analysis using the two-state vector formalism drew the conclusions that the photons followed disconnected paths. We analyze this experiment using standard quantum optical methods and arrive at analytical expressions that match the experimental results without the need for such disconnected photon paths. We also propose a simple amendment to the experiment capable of displaying new phenomena, highlighting the advantages of our description.

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Particle path(s) through a nested Mach-Zehnder interferometer: Reply to Griffiths

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Comment on “Particle path through a nested Mach-Zehnder interferometer”

Lev Vaidman A

Griffiths [Phys. Rev. A 94, 032115 (2016)] analyzed, in the framework of a consistent histories interpretation, the controversy regarding the approach to the past of a quantum particle introduced by Vaidman [Phys. Rev. A 87, 052104 (2013)]. I argue that Griffith's criticism of my approach using an analysis of experiments with weak probes is unfounded.

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