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arXiv:2011.11667 · Physical Review Letters

What Is Nonlocal in Counterfactual Quantum Communication?

Yakir Aharonov, Daniel Rohrlich

Published Dec 21, 2020• 22 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.125.260401

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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 classical theories of communication rely on the assumption that there has to be a flow of particles from Bob to Alice in order for him to send a message to her. We develop a quantum protocol that allows Alice to perceive Bob's message ``counterfactually''; that is, without Alice receiving any particles that have interacted with Bob. By utilizing a setup built on results from interaction-free measurements, we outline a communication protocol whereby the information travels in the opposite direction of the emitted particles. In comparison to previous attempts on such protocols, this one is such that a weak measurement at the message source would not leave a weak trace that could be detected by Alice's receiver. While some interaction-free schemes require a large number of carefully aligned beam splitters, our protocol is realizable with two or more beam splitters. We demonstrate this protocol by numerically solving the time-dependent Schr\"odinger equation for a Hamiltonian that implements this quantum counterfactual phenomenon.
It has been conjectured that counterfactual communication is impossible, even for post-selected quantum particles. We strongly challenge this by proposing precisely such a counterfactual scheme where-unambiguously-none of Alice's photons that correctly contribute to her information about Bob's message have been to Bob. We demonstrate counterfactuality experimentally by means of weak measurements, and conceptually using consistent histories-thus simultaneously satisfying both criteria without loopholes. Importantly, the fidelity of Alice learning Bob's bit can be made arbitrarily close to unity.
It has been conjectured that counterfactual communication is impossible, even for post-selected quantum particles. We strongly challenge this by proposing precisely such a counterfactual scheme where—unambiguously—none of Alice’s photons that correctly contribute to her information about Bob’s message have been to Bob. We demonstrate counterfactuality experimentally by means of weak measurements, and conceptually using consistent histories—thus simultaneously satisfying both criteria without loopholes. Importantly, the fidelity of Alice learning Bob’s bit can be made arbitrarily close to unity.
It has been conjectured that counterfactual communication is impossible, even for post-selected quantum particles. We strongly challenge this by proposing exactly such a counterfactual scheme where---unambiguously---none of Alice's photons that contribute to the message from Bob have been to Bob. We demonstrate counterfactuality experimentally by means of weak measurements, as well as conceptually using consistent histories---thus simultaneously closing both loopholes. Importantly, the fidelity of Alice learning Bob's bit can be made arbitrarily close to unity.