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arXiv:quant-ph/9910034 · Journal of Experimental and Theoretical Physics Letters

Relativistic quantum coin tossing

S. N. Molotkov, S. S. Nazin

Published Nov 1, 1999• 0 citations
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Abstract

A relativistic quantum exchange protocol enabling “coin tossing at a distance” between two participants is proposed. The exchange protocol is based on the fact that to distinguish a pair of orthogonal states with certainty in relativistic quantum mechanics requires a finite time that depends on the structure of the states themselves.
DOI
10.1134/1.568249

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The relativistic quantum protocols realizing the bit commitment and distant coin tossing schemes are proposed. The protocols are based on the fact that the non-stationary orthogonal extended quantum states cannot be reliably distinguished if they are not fully accessible for the measurement. As the states propagate from the domain controlled by one of the user to the domain accessible for the measurements performed by the other user, they become reliably distinguishable for the second user. Important for the protocol are both the quantum nature of the states and the existence of a finite maximum speed of the signal propagation imposed by the special relativity. PACS numbers: 89.70.+c, 03.65.-w 1
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.
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In coin tossing two remote participants want to share a uniformly distributed random bit. At the least in the quantum version, each participant test whether or not the other has attempted to create a bias on this bit. It is requested that, for b = 0,1, the probability that Alice gets bit b and pass the test is smaller than 1/2 whatever she does, and similarly for Bob. If the bound 1/2 holds perfectly against any of the two participants, the task realised is called an exact coin tossing. If the bound is actually 1/2+ξ1/2 + \xi1/2+ξ where the bias ξ\xiξ vanishes when a security parameter m defined by the protocol increases, the task realised is a (non exact) coin tossing. It is found here that exact coin tossing is impossible. At the same time, an unconditionally secure quantum protocol that realises a (non exact) coin tossing is proposed. The protocol executes m biased quantum coin tossing procedures at the same time. It executes the first round in each of these m procedures sequentially, then the second rounds are executed, and so on until the end of the n procedures. Each procedure requires 4n particles where n∈O(lg⁡m)n \in O(\lg m)n∈O(lgm). The final bit x is the parity of the m random bits. The information about each of these m bits is announced a little bit at a time which implies that the principle used against bit commitment does not apply. The bias on x is smaller than 1/m1/m1/m. The result is discussed in the light of the impossibility result for exact coin tossing.
In this Letter we present the first implementation of a quantum coin-tossing protocol. This protocol belongs to a class of "two-party" cryptographic problems, where the communication partners distrust each other. As with a number of such two-party protocols, the best implementation of the quantum coin tossing requires qutrits, resulting in a higher security than using qubits. In this way, we have also performed the first complete quantum communication protocol with qutrits. In our experiment the two partners succeeded to remotely toss a row of coins using photons entangled in the orbital angular momentum. We also show the experimental bounds of a possible cheater and the ways of detecting him.
In this letter we present the first implementation of a quantum coin tossing protocol.This protocol belongs to a class of "two-party" cryptographic problems, where the communication partners distrust each other.As with a number of such two-party protocols, the best implementation of the quantum coin tossing requires qutrits.In this way, we have also performed the first complete quantum communication protocol with qutrits.In our experiment the two partners succeeded to remotely toss a row of coins using photons entangled in the orbital angular momentum.We also show the experimental bounds of a possible cheater and the ways of detecting him.