We identify those properties of a quantum channel that are relevant for cryptography. We focus on general key distribution protocols that use prepare and measure schemes and the existing classical reconciliation techniques, as these are the protocols feasible with current technology. Given a channel, we derive an easily computable necessary condition of security for such protocols. In spite of its simplicity, this condition is shown to be tight for the Bennett-Brassard 1984 and six-state protocols. We show that the condition becomes also sufficient in the event of a so-called collective attack.
We identify those properties of a quantum channel that are relevant for cryptography. We focus on general key distribution protocols that use prepare and measure schemes and the existing classical reconciliation techniques, as these are the protocols feasible with current technology. Given a channel, we derive an easily computable necessary condition of security for such protocols. In spite of its simplicity, this condition is shown to be tight for the Bennett-Brassard 1984 and six-state protocols. We show that the condition becomes also sufficient in the event of a so-called collective attack.
We provide a general formalism to characterize the cryptographic properties of quantum channels in the realistic scenario where the two honest parties employ prepare and measure protocols and the known two-way communication reconciliation techniques. We obtain a necessary and sufficient condition to distill a secret key using this type of schemes for Pauli qubit channels and generalized Pauli channels in higher dimension. Our results can be applied to standard protocols such as Bennett-Brassard 1984 or six-state, giving a critical error rate of 20% and 27.6%, respectively. We explore several possibilities to enlarge these bounds, without any improvement. These results suggest that there may exist weakly entangling channels useless for key distribution using prepare and measure schemes.
Communications in secrecy are often required in many commercial and military applications. Unfortunately, many cryptographic schemes in use today such as public-key cryptography based on the RSA algorithm would be broken with either unanticipated advances in hardware and algorithm or the advent of quantum computers. Quantum cryptography, on the other hand, has been proven secure even against the most general attack allowed by the laws of physics and is a promising technology poised for widespread adoption in realistic cryptographic applications. Quantum cryptography allows two parties to expand on a secret key that they have previously shared. Various quantum cryptographic protocols have been proposed to perform this task. In this paper, we survey some popular quantum cryptographic protocols (including the famous Bennett-Brassard 1984 protocol) and discuss their security. Specifically, we consider their security in two cases: the ideal case where a perfect single-photon source is used and the practical case where a realistic laser source is used. We compare the protocols and find that the efficient six-state protocol outperforms the others both in the tolerable quantum bit error rate and in the key generation rate when a realistic laser source is used.
We present a technique for proving the security of quantum-key-distribution (QKD) protocols. It is based on direct information-theoretic arguments and thus also applies if no equivalent entanglement purification scheme can be found. Using this technique, we investigate a general class of QKD protocols with one-way classical post-processing. We show that, in order to analyze the full security of these protocols, it suffices to consider collective attacks. Indeed, we give new lower and upper bounds on the secret-key rate which only involve entropies of two-qubit density operators and which are thus easy to compute. As an illustration of our results, we analyze the Bennett-Brassard 1984, the six-state, and the Bennett 1992 protocols with one-way error correction and privacy amplification. Surprisingly, the performance of these protocols is increased if one of the parties adds noise to the measurement data before the error correction. In particular, this additional noise makes the protocols more robust against noise in the quantum channel.
In this work we present a security analysis for quantum key distribution, establishing a rigorous tradeoff between various protocol and security parameters for a class of entanglement-based and prepare-and-measure protocols. The goal of this paper is twofold: 1) to review and clarify the stateof-the-art security analysis based on entropic uncertainty relations, and 2) to provide an accessible resource for researchers interested in a security analysis of quantum cryptographic protocols that takes into account finite resource effects. For this purpose we collect and clarify several arguments spread in the literature on the subject with the goal of making this treatment largely self-contained. More precisely, we focus on a class of prepare-and-measure protocols based on the Bennett-Brassard (BB84) protocol as well as a class of entanglement-based protocols similar to the Bennett-Brassard-Mermin (BBM92) protocol. We carefully formalize the different steps in these protocols, including randomization, measurement, parameter estimation, error correction and privacy amplification, allowing us to be mathematically precise throughout the security analysis. We start from an operational definition of what it means for a quantum key distribution protocol to be secure and derive simple conditions that serve as sufficient condition for secrecy and correctness. We then derive and eventually discuss tradeoff relations between the block length of the classical computation, the noise tolerance, the secret key length and the security parameters for our protocols. Our results significantly improve upon previously reported tradeoffs.
Quantum cryptography is one of the most important quantum information applications. The present thesis covers several topics on quantum cryptography, such as the security analysis of quantum channels for key distribution protocols and the study of quantum cloning. First, we introduce a general formalism to characterize the cryptographic properties of quantum channels in the realistic scenario where the two honest parties employ prepare and measure protocols and the known two-way communication reconciliation techniques. We derive a necessary and sufficient condition to distill a secret key using this type of schemes for arbitrary bipartite quantum systems of finite dimension. The obtained results suggest that there may exist weakly entangling channels useless for key distribution using prepare and measure schemes. Next, we consider Gaussian states and Gaussian operations for cryptographic tasks and derive a new security condition. As it happens for quantum systems of finite dimension, our results suggest that there may also exist weakly entangled Gaussian states useless for key distribution, using Gaussian operations. Finally, we study the connection between cloning and state estimation. It was a long-standing problem to show whether state estimation becomes equivalent to quantum cloning in the asymptotic limit of an infinite number of clones. The equivalence is proven here using two known results in quantum information theory, the monogamy of quantum states and the properties of entanglement-breaking channels.
In the 1980s it was first realized that quantum–mechanical phenomena can be exploited directly for the manipulation, storage and transmission of information. The discovery of quantum algorithms for prime factorization [18] and unstructured search [7], which outperformed the best classical algorithms for these tasks significantly, opened up new vistas for computer science and gave an initial thrust to the emerging field of quantum computation. To implement a quantum algorithm, however, a large scale quantum computer is necessary and such a device has yet to be built. Research in quantum information, on the other hand, has shown that quantum effects can be harnessed to provide efficient and highly secure communication channels, which can be built using current technology. Entangled quantum states, superpositions and quantum measurement are among the characteristics of the subatomic world which nature puts at our disposal; these and related phenomena enable the development of novel techniques for computation and communication with no rival in classical computing and communication theory. The focus in this paper is on communication protocols involving the use of such phenomena. Quantum protocols have particularly important applications in cryptography. Several quantum protocols have been proposed for cryptographic tasks such as oblivious transfer, bit commitment and key distribution [8,13]. The BB84 protocol for quantum key distribution [2,14], which allows two users to establish a common secret key using a single quantum channel, has been shown to be unconditionally secure against all attacks [11]. Other quantum protocols include procedures for