We present a new protocol and two lower bounds for quantum coin flipping. In our protocol, no dishonest party can achieve one outcome with probability more than 0.75. Then, we show that our protocol is optimal for a certain type of quantum protocols. For arbitrary quantum protocols, we show that if a protocol achieves a bias of at most $ε$, it must use at least $Ω(\log \log \frac{1}ε)$ rounds of communication. This implies that the parallel repetition fails for quantum coin flipping. (The bias of a protocol cannot be arbitrarily decreased by running several copies of it in parallel.)
We present a new protocol and two lower bounds for quantum coin flipping. In our protocol, no dishonest party can achieve one outcome with probability more than 0.75. Then, we show that our protocol is optimal for a certain type of quantum protocols. For arbitrary quantum protocols, we show that if a protocol achieves a bias of at most ε, it must use at least Ω(loglogε1) rounds of communication. This implies that the parallel repetition fails for quantum coin flipping. (The bias of a protocol cannot be arbitrarily decreased by running several copies of it in parallel.)
How can two parties with competing interests carry out a fair coin flip across a quantum communication channel? This problem (quantum weak coin-flipping) was formalized more than 15 years ago, and, despite some phenomenal theoretical progress, practical quantum coin-flipping protocols with vanishing bias have proved hard to find. In the current work we show that there is a reason that practical weak quantum coin-flipping is difficult: any quantum weak coin-flipping protocol with bias є must use at least exp( Ω (1/√є )) rounds of communication. This is a large improvement over the previous best known lower bound of Ω ( log log(1/є )) due to Ambainis from 2004. Our proof is based on a theoretical construction (the two-variable profile function) which may find further applications.
Coin flipping is a cryptographic primitive in which two distrustful parties wish to generate a random bit to choose between two alternatives. This task is impossible to realize when it relies solely on the asynchronous exchange of classical bits: one dishonest player has complete control over the final outcome. It is only when coin flipping is supplemented with quantum communication that this problem can be alleviated, although partial bias remains. Unfortunately, practical systems are subject to loss of quantum data, which allows a cheater to force a bias that is complete or arbitrarily close to complete in all previous protocols and implementations. Here we report on the first experimental demonstration of a quantum coin-flipping protocol for which loss cannot be exploited to cheat better. By eliminating the problem of loss, which is unavoidable in any realistic setting, quantum coin flipping takes a significant step towards real-world applications of quantum communication. When two spatially separated parties flip a coin, it is impossible to choose between two alternatives in an unbiased manner. This study presents a quantum coin-flipping protocol that overcomes this problem and ensures a dishonest party cannot bias the outcome completely.
We investigate coin-flipping protocols for multiple parties in a quantum broadcast setting: (1) we propose and motivate a definition for quantum broadcast. Our model of quantum broadcast channel is new. (2) We discovered that quantum broadcast is essentially a combination of pairwise quantum channels and a classical broadcast channel. This is a somewhat surprising conclusion, but helps us in both our lower and upper bounds. (3) We provide tight upper and lower bounds on the optimal bias /spl epsiv/ of a coin which can be flipped by k parties of which exactly g parties are honest: for any 1 /spl les/ g /spl les/ k, /spl epsiv/ = 1/2 - /spl Theta/ (g/k). Thus, as long as a constant fraction of the players are honest, they can prevent the coin from being fixed with at least a constant probability. This result stands in sharp contrast with the classical setting, where no non-trivial coin-flipping is possible when g /spl les/ k/2.
Coin flipping and bit commitment are two fundamental cryptographic primitives with numerous applications. Quantum information allows for such protocols in the information theoretic setting where no dishonest party can perfectly cheat. The previously best-known quantum coin flipping and bit commitment protocol by Ambainis achieved a cheating probability of at most 3/4 [A. Ambainis, Proceedings of the 30th Annual ACM Symposium on Theory of Computing, Washington, DC, IEEE Computer Society, 2001]. On the other hand, Kitaev showed that no quantum coin flipping or bit commitment protocol can have cheating probability less than 1/2 [A. Kitaev, Presentation at the 6th Workshop on Quantum Information Processing (QIP), 2003]. Closing these gaps has been one of the important open questions in quantum cryptography. In this paper, we resolve both questions. First, we present a quantum strong coin flipping protocol with cheating probability arbitrarily close to 1/2. More precisely, we show how to use any weak coin flipping protocol with cheating probability 1/2+ε in order to achieve a strong coin flipping protocol with cheating probability 1/2+O(ε). The optimal quantum strong coin flipping protocol follows from our construction and the optimal quantum weak coin flipping protocol described by [C. Mochon, arXiv:0711.4114, 2007]. Second, we provide the optimal bound for quantum bit commitment. On the one hand, we show a lower bound of approximately γ≈0.739, improving Kitaev's lower bound. On the other hand, we present an optimal quantum bit commitment protocol which has cheating probability arbitrarily close to γ. More precisely, we show how to use any weak coin flipping protocol with cheating probability 1/2+ε in order to achieve a quantum bit commitment protocol with cheating probability γ+O(ε). To obtain the final protocol, we then use the optimal quantum weak coin flipping protocol described by [C. Mochon, arXiv:0711.4114, 2007]. Unlike the previous protocol for coin flipping, our protocol uses quantum effects beyond the weak coin flip. To stress this fact, we additionally show that any classical bit commitment protocol with access to perfect weak (or strong) coin flipping has cheating probability at least 3/4.
In this paper, we focus on a special framework for quantum coin flipping protocols,_bit-commitment based protocols_, within which almost all known protocols fit. We show a lower bound of 1/16 for the bias in any such protocol. We also analyse a sequence of multi-round protocol that tries to overcome the drawbacks of the previously proposed protocols, in order to lower the bias. We show an intricate cheating strategy for this sequence, which leads to a bias of 1/4. This indicates that a bias of 1/4 might be optimal in such protocols, and also demonstrates that a cleverer proof technique may be required to show this optimality.