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arXiv:quant-ph/9911055

Unconditionally Secure Relativistic Quantum Bit Commitment

S. N. Molotkov, S. S. Nazin

Published Nov 12, 1999• 1 citation
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Abstract

A new relativistic quantum protocol is proposed allowing to implement the bit commitment scheme. The protocol is based on the idea that in the relativistic case the field propagation to the region of space accessible to measurement requires, contrary to the non-relativistic case, a finite non-zero time which depends on the structure of the particular state of the field. In principle, the secret bit can be stored for arbitrarily long time with the probability arbitrarily close to unit.

DOI
10.48550/arxiv.quant-ph/9911055

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A new relativistic quantum protocol is proposed allowing to implement the bit commitment scheme. The protocol is based on the idea that in the relativistic case the field propagation to the region of space accessible to measurement requires, contrary to the non-relativistic case, a finite non-zero time which depends on the structure of the particular state of the field. In principle, the secret bit can be stored for arbitrarily long time with the probability arbitrarily close to unit.
A relativistic quantum exchange protocol making it possible to implement a bit commitment scheme is realized. The protocol is based on the idea that in the relativistic case the propagation of a field into a region of space accessible for measurement requires, in contrast to the nonrelativistic case, a finite time that depends on the structure of the states. The protocol requires one classical and several quantum communication channels. It turns out that it is possible in principle to preserve the secret bit for as long a period of time desired and with probability as close to 1 as desired.
Currently, it is believed in the literature that unconditionally secure bit commitment is impossible in non-relativistic quantum cryptography while only a weaker notion of bit commitment with finite commitment time is achievable in relativistic quantum setting. Moreover, relativistic classical bit commitment protocols allow arbitrary long commitment time but such protocols are not practically feasible; either because of multiple rounds of communication that result in exponential increase in communication complexity or due to asymptotic nature of security argument. The impossibility of practically feasible standard bit commitment leaves an obvious skepticism on the completeness of Hilbert space quantum cryptography and its claims of unconditional security. Contrary to the previously proposed results, we demonstrate here that an information-theoretic standard bit commitment scheme can be devised by using rules of purely non-relativistic quantum mechanics only; neither additional resources from theory of relativity nor multiple rounds of communications are required. The proposed bit commitment scheme can be applied efficiently with existing quantum technologies without long term quantum memory; quantum entanglement is required only for time t+δ where t is the communication time between the committer and receiver while δ << t is the processing time at laboratory.
New relativistic quantum protocols realizing the bit commitment and coin tossing schemes are proposed. The protocols are based on the idea that spatially extended nonstationary orthogonal quantum states inaccessible for measurement cannot be unambiguously distinguished. As the states are transmitted from the region controlled by one party to the region accessible for measurement by the other party, the states become reliably distinguishable when accessed as a whole. Essential points of the protocol are both the quantum character of states and the existence of an ultimate signal propagation speed dictated by special relativity.
Quantum physics allows for unconditionally secure communication between parties that trust each other. However, when the parties do not trust each other such as in the bit commitment scenario, quantum physics is not enough to guarantee security unless extra assumptions are made. Unconditionally secure bit commitment only becomes feasible when quantum physics is combined with relativistic causality constraints. Here we experimentally implement a quantum bit commitment protocol with relativistic constraints that offers unconditional security. The commitment is made through quantum measurements in two quantum key distribution systems in which the results are transmitted via free-space optical communication to two agents separated with more than 20 km. The security of the protocol relies on the properties of quantum information and relativity theory. In each run of the experiment, a bit is successfully committed with less than 5.68×10(-2) cheating probability. This demonstrates the experimental feasibility of quantum communication with relativistic constraints.
Bit commitment is a fundamental cryptographic primitive in which Alice wishes to commit a secret bit to Bob. Perfectly secure bit commitment between two mistrustful parties is impossible through an asynchronous exchange of quantum information. Perfect security is, however, possible when Alice and Bob each split into several agents exchanging classical information at times and locations suitably chosen to satisfy specific relativistic constraints. In this Letter we first revisit a previously proposed scheme [C. Crépeau et al., Lect. Notes Comput. Sci. 7073, 407 (2011)] that realizes bit commitment using only classical communication. We prove that the protocol is secure against quantum adversaries for a duration limited by the light-speed communication time between the locations of the agents. We then propose a novel multiround scheme based on finite-field arithmetic that extends the commitment time beyond this limit, and we prove its security against classical attacks. Finally, we present an implementation of these protocols using dedicated hardware and we demonstrate a 2 ms-long bit commitment over a distance of 131 km. By positioning the agents on antipodal points on the surface of Earth, the commitment time could possibly be extended to 212 ms.