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EPJ Web of Conferences

Locality and nonlocality in the interaction-free measurement

Daniel Rohrlich, Yakir Aharonov, Tomer Landsberger

Published Jan 1, 2018• 4 citations
Publisher

Abstract

We present a paradox involving a particle and a mirror. They exchange a nonlocal quantity, modular angular momentum Lz mod 2ћ, but there seems to be no local interaction between them that allows such an exchange. We demonstrate that the particle and mirror do interact locally via a weak local current 〈Lz mod 2ћ〉w. In this sense, we transform the “interaction-free measurement” of Elitzur and Vaidman, in which two local quantities (the positions of a photon and a bomb in the two arms of a Mach-Zehnder interferometer) interact nonlocally, into a thought experiment in which two nonlocal quantities (the weak modular angular momentum of the particle and of the mirror) interact locally.

DOI
10.1051/epjconf/201818202105

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We present a paradox involving a particle and a mirror. They exchange a nonlocal quantity, modular angular momentum Lz mod 2ћ, but there seems to be no local interaction between them that allows such an exchange. We demonstrate that the particle and mirror do interact locally via a weak local current 〈Lz mod 2ћ〉w. In this sense, we transform the “interaction-free measurement” of Elitzur and Vaidman, in which two local quantities (the positions of a photon and a bomb in the two arms of a Mach-Zehnder interferometer) interact nonlocally, into a thought experiment in which two nonlocal quantities (the weak modular angular momentum of the particle and of the mirror) interact locally.
We revisit the "counterfactual quantum communication" of Salih et al. [1], who claim that an observer "Bob" can send one bit of information to a second observer "Alice" without any physical particle traveling between them. We show that a locally conserved, massless current-specifically, a current of modular angular momentum, L_{z} mod 2ℏ-carries the one bit of information. We integrate the flux of L_{z} mod 2ℏ from Bob to Alice and show that it equals one of the two eigenvalues of L_{z} mod 2ℏ, either 0 or ℏ, thus precisely accounting for the one bit of information he sends her. We previously [2] obtained this result using weak values of L_{z} mod ℏ; here we do not use weak values.
The gedanken experiment of Elitzur and Vaidman showing wave-particle duality was realized as a demonstration at a scientific exposition. Presence or absence of a mirror in one arm of an interferometer was measured while detecting one photon at a time. A reasonable fraction of events was ‘‘interaction-free,’’ which means that the conclusion that there was a mirror in the beam could be drawn from the signal of a photon that had not interacted with the mirror. The demonstration was found to be thought-provoking.
Recently, it has been pointed out that it is possible to make a quantum-mechanical interaction-free measurement (IFM), in which the existence of an object in a given region of space may be determined seemingly without interacting with it.1,2 In the embodiment first proposed by Elitzur and Vaidman,3 a standard Michelson interferometer is aligned so that incident single photons (obtained in our experiment by using parametric downconversion; see Fig. 1) must exit by the same port in which they entered, in the absence of any object within the interferometer. The presence of an object (e.g., the mirror leading to detector DB) in one of the arms completely changes the possible outcomes because the constructive interference is interrupted. Now it is possible that the photon will exit from the other exit port, to detector DIfm. By detecting the photon in this case, one can claim with certainty that an object was within the interferometer, even though the photon could not have interacted with it. If the beam splitter has a very low reflectivity, then the fraction of IFMs approaches 1/2.
I shall discuss two recently suggested quantum experiments. These experiments lead to paradoxical situations. I will argue that in the framework of a particular Many Worlds Interpretation of quantum theory the paradoxes do not arise. The first experiment is the “interaction-free measurement” (Elitzur and Vaidman 1993). The experimental group at Innsbruck headed by Prof. Zeilinger is working now on its realization. Before describing the experiment let me discuss a general question: “How do we know that there is an object in a region of space?” The simplest case is when the object itself causes some physical changes outside the region: i) The object is charged, so there is a field outside. We can measure this field. ii) The object yields a potential outside. Aharonov and Bohm have taught us that potential even without field leads to a measurable effect. iii) The objects radiates photons or other particles.
Although regarded today as an important resource in quantum information, nonlocality has yielded over the years many conceptual conundrums. Among the latter are nonlocal aspects of single particles which have been of major interest. In this paper, the nonlocality of single quanta is proved using a delayed choice modification of the complex-valued weak values in a square nested Mach--Zehnder interferometer with spatially separated measuring devices. We show that local hidden variables models may use hidden signaling and a list of contextual instructions to replicate quantum probabilities and the mean pointer shifts corresponding to the measured real part of weak values, but in doing so necessarily fail to reproduce the quantum variance of pointer shifts. Our analysis also demonstrates that the recently proposed weak values of quantum histories are inherently nonlocal physical quantities due to their dependence on the total Feynman sum that yields the complex-valued quantum probability amplitude for the studied quantum transition.
Straightforward novel methods for stabilizing, tuning, and controlling a twin Mach-Zehnder interferometer for the purpose of observing a subtle dynamical quantum nonlocality effect in a recent optical experiment are presented and discussed. Weak measurements were required for observing a subtle quantum dynamical nonlocality effect that reveals itself in a change of a weak value. Consequently, emphasis is placed upon describing the approaches to apparatus stabilization and interaction strength control between photons and the apparatus. The details discussed in this paper should be of general interest to experimentalists engaging in weak measurement and weak value research.