Key distillation from quantum channels using two-way communication protocols

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 BB84 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.Comment: 21 page

Security bound of two-bases quantum key-distribution protocols using qudits

We investigate the security bounds of quantum cryptographic protocols using $d$-level systems. In particular, we focus on schemes that use two mutually unbiased bases, thus extending the BB84 quantum key distribution scheme to higher dimensions. Under the assumption of general coherent attacks, we derive an analytic expression for the ultimate upper security bound of such quantum cryptography schemes. This bound is well below the predictions of optimal cloning machines. The possibility of extraction of a secret key beyond entanglement distillation is discussed. In the case of qutrits we argue that any eavesdropping strategy is equivalent to a symmetric one. For higher dimensions such an equivalence is generally no longer valid.Comment: 12 pages, 2 figures, to appear in Phys. Rev.

Security bounds in Quantum Cryptography using d-level systems

We analyze the security of quantum cryptography schemes for $d$-level systems using 2 or $d+1$ maximally conjugated bases, under individual eavesdropping attacks based on cloning machines and measurement after the basis reconciliation. We consider classical advantage distillation protocols, that allow to extract a key even in situations where the mutual information between the honest parties is smaller than the eavesdropper's information. In this scenario, advantage distillation protocols are shown to be as powerful as quantum distillation: key distillation is possible using classical techniques if and only if the corresponding state in the entanglement based protocol is distillable.Comment: 18 pages, 1 figure. Published versio

Security of Quantum Key Distribution with Entangled Qutrits

The study of quantum cryptography and quantum non-locality have traditionnally been based on two-level quantum systems (qubits). In this paper we consider a generalisation of Ekert's cryptographic protocol [Ekert] where qubits are replaced by qutrits. The security of this protocol is related to non-locality, in analogy with Ekert's protocol. In order to study its robustness against the optimal individual attacks, we derive the information gained by a potential eavesdropper applying a cloning-based attack.Comment: 9 pages original version: july 2002, replaced in january 2003 (reason: minor changes

Trusted Noise in Continuous-Variable Quantum Key Distribution: a Threat and a Defense

We address the role of the phase-insensitive trusted preparation and detection noise in the security of a continuous-variable quantum key distribution, considering the Gaussian protocols on the basis of coherent and squeezed states and studying them in the conditions of Gaussian lossy and noisy channels. The influence of such a noise on the security of Gaussian quantum cryptography can be crucial, even despite the fact that a noise is trusted, due to a strongly nonlinear behavior of the quantum entropies involved in the security analysis. We recapitulate the known effect of the preparation noise in both direct and reverse-reconciliation protocols, as well as the detection noise in the reverse-reconciliation scenario. As a new result, we show the negative role of the trusted detection noise in the direct-reconciliation scheme. We also describe the role of the trusted preparation or detection noise added at the reference side of the protocols in improving the robustness of the protocols to the channel noise, confirming the positive effect for the coherent-state reverse-reconciliation protocol. Finally, we address the combined effect of trusted noise added both in the source and the detector.Comment: 25 pages, 9 figure

Twisted Photons: New Quantum Perspectives in High Dimensions

Quantum information science and quantum information technology have seen a virtual explosion world-wide. It is all based on the observation that fundamental quantum phenomena on the individual particle or system-level lead to completely novel ways of encoding, processing and transmitting information. Quantum mechanics, a child of the first third of the 20th century, has found numerous realizations and technical applications, much more than was thought at the beginning. Decades later, it became possible to do experiments with individual quantum particles and quantum systems. This was due to technological progress, and for light in particular, the development of the laser. Hitherto, nearly all experiments and also nearly all realizations in the fields have been performed with qubits, which are two-level quantum systems. We suggest that this limitation is again mainly a technological one, because it is very difficult to create, manipulate and measure more complex quantum systems. Here, we provide a specific overview of some recent developments with higher-dimensional quantum systems. We mainly focus on Orbital Angular Momentum (OAM) states of photons and possible applications in quantum information protocols. Such states form discrete higher-dimensional quantum systems, also called qudits. Specifically, we will first address the question what kind of new fundamental properties exist and the quantum information applications which are opened up by such novel systems. Then we give an overview of recent developments in the field by discussing several notable experiments over the past 2-3 years. Finally, we conclude with several important open questions which will be interesting for investigations in the future.Comment: 15 pages, 7 figure

Quantum Cloning Machines and the Applications

No-cloning theorem is fundamental for quantum mechanics and for quantum information science that states an unknown quantum state cannot be cloned perfectly. However, we can try to clone a quantum state approximately with the optimal fidelity, or instead, we can try to clone it perfectly with the largest probability. Thus various quantum cloning machines have been designed for different quantum information protocols. Specifically, quantum cloning machines can be designed to analyze the security of quantum key distribution protocols such as BB84 protocol, six-state protocol, B92 protocol and their generalizations. Some well-known quantum cloning machines include universal quantum cloning machine, phase-covariant cloning machine, the asymmetric quantum cloning machine and the probabilistic quantum cloning machine etc. In the past years, much progress has been made in studying quantum cloning machines and their applications and implementations, both theoretically and experimentally. In this review, we will give a complete description of those important developments about quantum cloning and some related topics. On the other hand, this review is self-consistent, and in particular, we try to present some detailed formulations so that further study can be taken based on those results.Comment: 98 pages, 12 figures, 400+ references. Physics Reports (published online

Dense-coding quantum key distribution based on continuous-variable entanglement

We proposed a scheme of continuous-variable quantum key distribution, in which the bright Einstein-Podolsky-Rosen entangled optical beams are utilized. The source of the entangled beams is placed inside the receiving station, where half of the entangled beams are transmitted with round trip and the other half are retained by the receiver. The amplitude and phase signals modulated on the signal beam by the sender are simultaneously extracted by the authorized receiver with the scheme of the dense-coding correlation measurement for continuous quantum variables, thus the channel capacity is significantly improved. Two kinds of possible eavesdropping are discussed. The mutual information and the secret key rates are calculated and compared with those of unidirectional transmission schemes