Quantum Coin Flipping Research Articles

Quantum game— “PQ” problem

This paper reviews the coin flipping problem of “PQ” in a classical two-player game, and shows that when one player adopts quantum strategy, he can beat his classical opponent and gain higher returns. By using quantitative means, the whole “PQ” problem is put under a more general and fair condition, and it is generalized and studied again from many aspects and angles. Finally, we obtain some more essential and important conclusions, and explain the conclusions and its practical significance through some practical examples. At the same time, this paper gives the definition of imperfect fair game and the definition of perfect fair game, revises the quantum coin flipping game to make the game fair, and studies a multi-round version of quantum coin flipping. Some basic conclusions of fair quantum game are obtained, and the meaning of perfectly fair game is explained in practice.

Unconditionally secure quantum coin flipping

Quantum coin flipping (QCF) is an essential primitive for quantum cryptography. Unconditionally secure strong QCF with an arbitrarily small bias was widely believed to be impossible. But basing on a problem which cannot be solved without quantum algorithm, here we propose such a QCF protocol, and show how it manages to evade all existing no-go proofs on QCF.

Quantum Game—Research on “PQ” Problem

This paper reviews the coin flipping problem of PQ in a classical two-player game, and shows that when one player adopts quantum strategy, he can beat his classical opponent and gain higher returns. By means of quantitative means, the whole PQ problem is put in a more general and fair condition, and it is generalized and studied again from many aspects and angles. Finally, we get some more essential and important conclusions, and through some examples to explain the conclusions and its practical significances. At the same time, this paper gives the definitions of imperfect fair games and perfect fair games, revises the quantum coin flipping game to make the game fair, and studies a multi-round version of quantum coin flipping. Some basic conclusions of fair quantum game are obtained, and the meaning of perfectly fair game is explained in practice.

Quantum Protocol for Decision Making and Verifying Truthfulness among N-quantum Parties: Solution and Extension of the Quantum Coin Flipping Game

Quantum Protocol for Decision Making and Verifying Truthfulness among N-quantum Parties: Solution and Extension of the Quantum Coin Flipping Game

Quantum coin flipping, qubit measurement, and generalized Fibonacci numbers

The problem of Hadamard quantum coin measurement in $n$ trials, with arbitrary number of repeated consecutive last states is formulated in terms of Fibonacci sequences for duplicated states, Tribonacci numbers for triplicated states and $N$-Bonacci numbers for arbitrary $N$-plicated states. The probability formulas for arbitrary position of repeated states are derived in terms of Lucas and Fibonacci numbers. For generic qubit coin, the formulas are expressed by Fibonacci and more general, $N$-Bonacci polynomials in qubit probabilities. The generating function for probabilities, the Golden Ratio limit of these probabilities and Shannon entropy for corresponding states are determined. By generalized Born rule and universality of $n$-qubit measurement gate, we formulate problem in terms of generic $n$-qubit states and construct projection operators in Hilbert space, constrained on the Fibonacci tree of the states. The results are generalized to qutrit and qudit coins, described by generalized Fibonacci-$N$-Bonacci sequences.

Arbitrary Finite Dimensional Generalization of Quantum Coin-Flipping Game

Two players of coin-flipping game randomly choose one of two strategies, flipping over or not. Meyer quantized states of the game to be described instead by density matrices of the two-dimensional Hilbert space. In order to obtain and unify generation of the two players coin-flipping game with more than two strategies, we renew the need for equivalently describing Meyer’s PQ coin-flipping game by representing player’s strategies as elements of permutation groups. Expanding the dimension of quantum vector to arbitrary N-dimension in the coin-flipping game model, we generalize Meyer’s PQ coin-flipping game to PQ arbitrary finite strategies game. Owing to the quantum Fourier transform, quantum contrivance of Q has a winning strategy in PQ coin-flipping game with arbitrary finite strategies. Even though the player Q has a small probability of winning his opponent in the classical PQ coin-flipping game with arbitrary finite strategies, he can win his opponent who uses classical mixed strategies by his quantum strategies. Furthermore, we realize the winning quantum strategies of quantum player Q of PQ coin-flipping game with arbitrary finite strategies in macro world.

Physical Limitations of Quantum Cryptographic Primitives or Optimal Bounds for Quantum Coin Flipping and Bit Commitment

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 $30$th 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 $1/\sqrt{2}$ [A. Kitaev, Presentation at the $6$th 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 $1/\sqrt{2}$. More precisely, we show how to ...

Biased decoy-state measurement-device-independent quantum key distribution with finite resources

So far, most of existed single-shot quantum coin flipping(QCF) protocols failed in a noisy quantum channel. Here, we present a nested-structured framework that makes it possible to achieve partially noise-tolerant QCF, due to that there is a trade-off between the security and the justice correctness. It is showed that noise-tolerant single-shot QCF protocols can be produced by filling the presented framework up with existed or even future protocols. We also proved a lower bound of 0.25, with which a cheating Alice or Bob could bias the outcome.

Experimental plug and play quantum coin flipping.

Performing complex cryptographic tasks will be an essential element in future quantum communication networks. These tasks are based on a handful of fundamental primitives, such as coin flipping, where two distrustful parties wish to agree on a randomly generated bit. Although it is known that quantum versions of these primitives can offer information-theoretic security advantages with respect to classical protocols, a demonstration of such an advantage in a practical communication scenario has remained elusive. Here we experimentally implement a quantum coin flipping protocol that performs strictly better than classically possible over a distance suitable for communication over metropolitan area optical networks. The implementation is based on a practical plug and play system, developed by significantly enhancing a commercial quantum key distribution device. Moreover, we provide combined quantum coin flipping protocols that are almost perfectly secure against bounded adversaries. Our results offer a useful toolbox for future secure quantum communications.

Semi-loss-tolerant strong quantum coin-flipping protocol using quantum non-demolition measurement

In this paper, we present a semi-loss-tolerant strong quantum coin-flipping (QCF) protocol with the best bias of 0.3536. Our manuscript applies Quantum non-demolition (QND) measurement to quantum coin-flipping protocol. Furthermore, a single photon as a single qubit is used to avoid the difficult implementation of EPR resources. We also analyze the security of our protocol obtaining the best result among all coin-flipping protocols considering loss. A semi-loss-tolerant Quantum Dice Rolling (QDR) protocol is first proposed, and the security of corresponding three-party QDR is analyzed to better demonstrate the security of our QCF.

Loss-and-Noise Tolerant Single-Shot Quantum Coin Flipping

To make quantum coin flipping protocols more practical, we propose a new method that makes single-shot quantum coin flipping (SS-QCF) protocols tolerant of loss and noise. First, we present a new SS-QCF protocol which is a modification version of the previous one by Berlín et al.[ Phys. Rev. A Vol. 80 (2009), p. 062321]. Next, we prove that our protocol performs well against loss and noise. It shows that the presented protocol is able to be applied in real-world channels.

Single-Photon Multiparty Quantum Cryptographic Protocols With Collective Detection

In order to reduce the requirements on quantum devices, Shih proposed two three-party quantum key distribution (QKD) protocols . However, Gao presented a simple and effective attack strategy (i.e., dense-coding attack) upon the two protocols . In this paper, we make a deep analysis on the reason why Shih three-party QKD protocols are not secure. Meanwhile, we improve the three-party QKD protocols so that they can resist the Gao attack. On this basis, we present a formalism of single-photon multiparty quantum cryptographic protocol with collective detection. In this formalism, single photons are employed and all participants, except one whom we call as the center, only need to have the ability to perform single qubit unitary operations. Considering the expensive quantum devices, this formalism is low-priced which means it is easy to realize. Further more, this formalism can be widely used in various quantum cryptographic protocols, such as quantum secret sharing, quantum coin flipping, and quantum secure direct communication.

Experimental loss-tolerant quantum coin flipping.

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.

Fully Distrustful Quantum Bit Commitment and Coin Flipping

In the distrustful quantum cryptography model the parties have conflicting interests and do not trust one another. Nevertheless, they trust the quantum devices in their labs. The aim of the device-independent approach to cryptography is to do away with the latter assumption, and, consequently, significantly increase security. It is an open question whether the scope of this approach also extends to protocols in the distrustful cryptography model, thereby rendering them "fully" distrustful. In this Letter, we show that for bit commitment-one of the most basic primitives within the model-the answer is positive. We present a device-independent (imperfect) bit-commitment protocol, where Alice's and Bob's cheating probabilities are ≃0.854 and 3/4, which we then use to construct a device-independent coin flipping protocol with bias ≲0.336.

Quantum dice rolling: a multi-outcome generalization of quantum coin flipping

The problem of quantum dice rolling (DR)—a generalization of the problem of quantum coin flipping (CF) to more than two outcomes and parties—is studied in both its weak and strong variants. We prove by construction that quantum mechanics allows for (i) weak N-sided DR admitting arbitrarily small bias for any N and (ii) two-party strong N-sided DR saturating Kitaev's bound for any N. To derive (ii) we also prove by construction that quantum mechanics allows for (iii) strong imbalanced CF saturating Kitaev's bound for any degree of imbalance. Furthermore, as a corollary of (ii) we introduce a family of optimal 2m-party strong nm-sided DR protocols for any pair m and n.

Fair loss-tolerant quantum coin flipping

Coin flipping is a cryptographic primitive in which two spatially separated players, who in principle do not trust each other, wish to establish a common random bit. If we limit ourselves to classical communication, this task requires either assumptions on the computational power of the players or it requires them to send messages to each other with sufficient simultaneity to force their complete independence. Without such assumptions, all classical protocols are so that one dishonest player has complete control over the outcome. If we use quantum communication, on the other hand, protocols have been introduced that limit the maximal bias that dishonest players can produce. However, those protocols would be very difficult to implement in practice because they are susceptible to realistic losses on the quantum channel between the players or in their quantum memory and measurement apparatus. In this paper, we introduce a novel quantum protocol and we prove that it is completely impervious to loss. The protocol is fair in the sense that either player has the same probability of success in cheating attempts at biasing the outcome of the coin flip. We also give explicit and optimal cheating strategies for both players.

Dilemma that Cannot Be Resolved by Biased Quantum Coin Flipping

We show that a biased quantum coin flip (QCF) cannot provide the performance of a black-boxed biased coin flip, if it satisfies some fidelity conditions. Although such a QCF satisfies the security conditions of a biased coin flip, it does not realize the ideal functionality and, therefore, does not satisfy the demands for universally composable security. Moreover, through a comparison within a small restricted bias range, we show that an arbitrary QCF is distinguishable from a black-boxed coin flip unless it is unbiased on both sides of parties against insensitive cheating. We also point out the difficulty in developing cheat-sensitive quantum bit commitment in terms of the uncomposability of a QCF.

Serial composition of quantum coin flipping and bounds on cheat detection for bit commitment

Quantum protocols for coin flipping can be composed in series in such a way that a cheating party gains no extra advantage from using entanglement between different rounds. This composition principle applies to coin-flipping protocols with cheat sensitivity as well, and is used to derive two results: There are no quantum strong coin-flipping protocols with cheat sensitivity that is linear in the bias (or bit-commitment protocols with linear cheat detection) because these can be composed to produce strong coin flipping with arbitrarily small bias. On the other hand, it appears that quadratic cheat detection cannot be composed in series to obtain even weak coin flipping with arbitrarily small bias.

A new protocol and lower bounds for quantum coin flipping

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 out protocol is optimal among 3-round protocols of a certain form. 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 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.)

Bit-commitment-based quantum coin flipping

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.