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arXiv:1504.05551

Quantum bit commitment using Wheeler's delayed choice experiment

Chi-Yee Cheung

Published Apr 21, 2015• 0 citations
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Abstract

We construct a quantum bit commitment scheme using a double-slit setup similar to Wheeler's delayed choice experiment. Bob sends photons toward the double-slit, and Alice commits by determining either the slit from which each photon emerges (for $b=0$), or its landing position on a screen (for $b=1$). Since the photon's wave front expands at the speed of light, Alice cannot delay the detection indefinitely, or it would very soon be out of her control no matter how much resources she has.

DOI
10.48550/arxiv.1504.05551

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We construct a quantum bit commitment scheme using a double-slit setup similar to Wheeler's delayed choice experiment. Bob sends photons toward the double-slit, and Alice commits by determining either the slit from which each photon emerges (for b=0b=0b=0), or its landing position on a screen (for b=1b=1b=1). Since the photon's wave front expands at the speed of light, Alice cannot delay the detection indefinitely, or it would very soon be out of her control no matter how much resources she has.
Delaying Quantum Choice Photons can display wavelike or particle-like behavior, depending on the experimental technique used to measure them. Understanding this duality lies at the heart of quantum mechanics. In two reports, Peruzzo et al. (p. 634 ) and Kaiser et al. (p. 637 ; see the Perspective on both papers by Lloyd ) perform an entangled version of John Wheeler's delayed-choice gedanken experiment, in which the choice of detection can be changed after a photon passes through a double-slit to avoid the measurement process affecting the state of the photon. The original proposal allowed the wave and particle nature of light to be interchanged after the light had entered the interferometer. By contrast in this study, entanglement allowed the wave and particle nature to be interchanged after the light was detected and revealed the quantum nature of the photon, for example, it displays wave- and particle-like behavior simultaneously.
Using a neutron double-slit setup, we construct a quantum bit commitment scheme in which time development of quantum states plays an essential role. Our scheme evades the widely accepted no-go theorem by the fact that it is neither possible to stop the time evolution of spreading wave packets, nor is it possible to evolve them backward in time. Moreover, for unstable particles such as neutrons, one cannot delay detecting their positions indefinitely, or they would disintegrate spontaneously and escape detection. We find that using non-stationary states instead of stationary ones, unconditionally secure quantum bit commitment is possible.
This paper proposes a cheat-sensitive quantum bit commitment scheme based on single photons, in which Alice commits a bit to Bob. Here, Bob's probability of success at cheating as obtains the committed bit before the opening phase becomes close to (just like performing a guess) as the number of single photons used is increased. And if Alice alters her committed bit after the commitment phase, her cheating will be detected with a probability that becomes close to 1 as the number of single photons used is increased. The scheme is easy to realize with present day technology.
Based on the basic version of the Double-slit experiment, a coherent light source, such as a laser beam, illuminates a plate pierced by two parallel slits, and the light passing through the slits is observed on a screen behind the plate.The wave nature of light causes the light waves passing through the two slits to interfere, producing bright and dark bands on the screen — a result that would not be expected if light consisted of classical particles. Our new variant is as below: We shut one of the two parallel slits once the light passed the slits. Or we keep the two slits shutting and opening randomly in high speed. We believe this variant experiment could lead to a farther fundamental understanding of the Quantum Mechanics.
This experiment was conceived of as a method of transmitting information from inside a black hole to the outside. As it turns out, it doesn't work in the form described (and possibly not in any form), but the way in which Nature prevents quantum-mechanical effects from transmitting usable information using quantum correlations is illuminating. In the process, one can learn some quantum theory, as well as quantum optics. The proposed scheme uses a double-slit experiment, in the manner of the Delayed Choice set up (see Kim et. al.), where the region where the interference takes place (between "signal" photons) is spatially separated from the region where the Delayed Choice (with "idler" photons) is made. Indeed, this Double-Delayed Choice, which is this thought experiment, has one of the idler photons slip inside the event horizon and serves as the method to attempt to communicate from the inside to the outside.