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arXiv:1707.09483 · Scientific Reports

Nonlocal Position Changes of a Photon Revealed by Quantum Routers

Avshalom C. Elitzur, Eliahu Cohen, Ryo Okamoto, Shigeki Takeuchi

Published May 10, 2018• 14 citations
arXivHTMLPDF

Abstract

Abstract Since its publication, Aharonov and Vaidman’s three-box paradox has undergone three major advances: i). A non-counterfactual scheme by the same authors in 2003 with strong rather than weak measurements for verifying the particle’s subtle presence in two boxes. ii) A realization of the latter by Okamoto and Takeuchi in 2016. iii) A dynamic version by Aharonov et al. in 2017, with disappearance and reappearance of the particle. We now combine these advances together. Using photonic quantum routers the particle acts like a quantum “shutter.” It is initially split between Boxes A, B and C, the latter located far away from the former two. The shutter particle’s whereabouts can then be followed by a probe photon, split in both space and time and reflected by the shutter in its varying locations. Measuring the former is expected to reveal the following time-evolution: The shutter particle was, with certainty, in boxes A+C at t1, then only in C at t2, and finally in B+C at t3. Another branch of the split probe photon can show that boxes A+B were empty at t2. A Bell-like theorem applied to this experiment challenges any alternative interpretation that avoids disappearance-reappearance in favor of local hidden variables.

DOI
10.1038/s41598-018-26018-y

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Abstract Since its publication, Aharonov and Vaidman’s three-box paradox has undergone three major advances: i). A non-counterfactual scheme by the same authors in 2003 with strong rather than weak measurements for verifying the particle’s subtle presence in two boxes. ii) A realization of the latter by Okamoto and Takeuchi in 2016. iii) A dynamic version by Aharonov et al. in 2017, with disappearance and reappearance of the particle. We now combine these advances together. Using photonic quantum routers the particle acts like a quantum “shutter.” It is initially split between Boxes A, B and C, the latter located far away from the former two. The shutter particle’s whereabouts can then be followed by a probe photon, split in both space and time and reflected by the shutter in its varying locations. Measuring the former is expected to reveal the following time-evolution: The shutter particle was, with certainty, in boxes A+C at t1, then only in C at t2, and finally in B+C at t3. Another branch of the split probe photon can show that boxes A+B were empty at t2. A Bell-like theorem applied to this experiment challenges any alternative interpretation that avoids disappearance-reappearance in favor of local hidden variables.
What is the true meaning of quantum superposition? Can a particle genuinely reside in several places simultaneously? These questions lie at the heart of this paper which presents an updated survey of some important stages in the evolution of the three-boxes paradox, as well as novel conclusions drawn from it. We begin with the original thought experiment of Aharonov and Vaidman, and proceed to its non-counterfactual version. The latter was recently realized by Okamoto and Takeuchi using a quantum router. We then outline a dynamic version of this experiment, where a particle is shown to "disappear" and "re-appear" during the time evolution of the system. This surprising prediction based on self-cancellation of weak values is directly related to our notion of Quantum Oblivion. Finally, we present the non-counterfactual version of this disappearing-reappearing experiment. Within the near future, this last version of the experiment is likely to be realized in the lab, proving the existence of exotic hitherto unknown forms of superposition. With the aid of Bell's theorem, we prove the inherent nonlocality and nontemporality underlying such pre- and post-selected systems, rendering anomalous weak values ontologically real.
The interference between two paths of a single photon at a double slit is widely considered to be the most paradoxical result of quantum theory. Here is a new interesting question to the phenomenon: can a single shutter simultaneously close two slits by effectively being in a superposition of different locations? Aharonov and Vaidman have shown that it is indeed possible to construct a quantum shutter that can close two slits and reflect a probe photon perfectly when its initial and final states are appropriately selected. Here we report the experimental demonstration of their proposal overcoming the difficulty to realize a 'quantum shutter' by employing photonic quantum routers. The reflectance ratio of 0.61 ± 0.027 surpasses the classical limit with 4.1 standard deviation, shedding new light on the unusual physical properties of quantum operations. This experimental demonstration, where the strong measurement and non-local superposition seem co-existing, provides an alternative to weak measurements as a way to explore the nature of quantum physics.
Summary form only given. The interference between two paths of a single photon at a double slit is widely considered to be the most paradoxical result of quantum theory. Here is a new interesting question to the phenomenon: Can a single shutter simultaneously close two slits by effectively being in a superposition of different locations? Aharonov and Vaidman have shown that it is indeed possible to construct a quantum shutter that can close two slits and reflect a probe photon perfectly when its initial and final states are appropriately selected [1]. Here we report the experimental demonstration of their proposal overcoming the difficulty to realize a quantum shutter' by employing photonic quantum routers [2]. The reflectance ratio of 0.61 ± 0.027 surpasses the classical limit with 4.1 standard deviation, shedding new light on the unusual physical properties of quantum operations. This experimental demonstration, where the strong measurement and non-local superposition seem co-existing, provides an alternative to weak measurements as a way to explore the nature of quantum physics.
A novel prediction is derived by the Two-State-Vector-Formalism (TSVF) for a particle superposed over three boxes. Under appropriate pre- and post-selections, and with tunneling enabled between two of the boxes, it is possible to derive not only one, but three predictions for three different times within the intermediate interval. These predictions are moreover contradictory. The particle (when looked for using a projective measurement) seems to disappear from the first box where it would have been previously found with certainty, appearing instead within the third box, to which no tunneling is possible, and later re-appearing within the second. It turns out that local measurement (i.e. opening one of the boxes) fails to indicate the particle's presence, but subtler measurements performed on the two boxes together reveal the particle's nonlocal modular momentum spatially separated from its mass. Another advance of this setting is that, unlike other predictions of the TSVF that rely on weak and/or counterfactual measurements, the present one uses actual projective measurements. This outcome is then corroborated by adding weak measurements and the Aharonov-Bohm effect. The results strengthen the recently suggested time-symmetric Heisenberg ontology based on nonlocal deterministic operators. They can be also tested using the newly developed quantum router.
The “N‐box experiment” is a much‐discussed thought experiment in quantum mechanics. It is claimed by some authors that a single particle prepared in a superposition of N+1 box locations and which is subject to a final “post‐selection” measurement corresponding to a different superposition can be said to have occupied “with certainty” N boxes during the intervening time. However, others have argued that under closer inspection, this surprising claim fails to hold. Aharonov and Vaidman have continued their advocacy of the claim in question by proposing a variation on the N‐box experiment, in which the boxes are replaced by shutters and the pre‐ and post‐selected particle is entangled with a photon. These authors argue that the resulting “N‐shutter experiment” strengthens their original claim regarding the N‐box experiment. It is argued in this article that the apparently surprising features of this variation are no more robust than those of the N‐box experiment and that it is not accurate to say that the particle is “with certainty” in all N shutters at any given time.Shutters, Boxes, but No Paradoxes: Time Symmetry Puzzles in Quantum TheoryAll authorsRuth E. Kastner https://doi.org/10.1080/02698590412331289279Published online:14 October 2010 Figure 1 Hilbert Space of the Shutter Particle. Display full size Figure 1 Hilbert Space of the Shutter Particle.
The quantum three-box paradox considers a ball prepared in a superposition of being in any one of three boxes. Bob makes measurements by opening either box 1 or box 2. After performing some unitary operations (shuffling), Alice can infer with certainty that the ball was detected by Bob, regardless of which box he opened, if she detects the ball after opening box 3. The paradox is that the ball would have been found with certainty by Bob in either box if that box had been opened. Resolutions of the paradox include that Bob’s measurement cannot be made non-invasively or else that realism cannot be assumed at the quantum level. Here, we strengthen the case for the former argument by constructing macroscopic versions of the paradox. Macroscopic realism implies that the ball is in one of the boxes prior to Bob or Alice opening any boxes. We demonstrate the consistency of the paradox with macroscopic realism, if carefully defined (as weak macroscopic realism, wMR) to apply to the system at the times prior to Alice or Bob opening any boxes but after the unitary operations associated with preparation or shuffling. By solving for the dynamics of the unitary operations and comparing with mixed states, we demonstrate agreement between the predictions of wMR and quantum mechanics: the paradox only manifests if Alice’s shuffling combines both local operations (on box 3) and nonlocal operations, on the other boxes. Following previous work, the macroscopic paradox is shown to correspond to a violation of a Leggett–Garg inequality, which implies failure of non-invasive measurability if wMR holds.