Marcos Curty

Entanglement as a Precondition for Secure Quantum Key Distribution

We demonstrate that a necessary precondition for an unconditionally secure quantum key distribution is that both sender and receiver can use the available measurement results to prove the presence of entanglement in a quantum state that is effectively distributed between them. One can thus systematically search for entanglement using the class of entanglement witness operators that can be constructed from the observed data. We apply such analysis to two well-known quantum key distribution protocols, namely, the 4-state protocol and the 6-state protocol. As a special case, we show that, for some asymmetric error patterns, the presence of entanglement can be proven even for error rates above 25% (4-state protocol) and 33% (6-state protocol).

Experimentally realizable quantum comparison of coherent states and its applications

When comparing quantum states to each other, it is possible to obtain an unambiguous answer, indicating that the states are definitely different, already after a single measurement. In this paper we investigate comparison of coherent states, which is the simplest example of quantum state comparison for continuous variables. The method we present has a high success probability, and is experimentally feasible to realize as the only required components are beam splitters and photon detectors. An easily realizable method for quantum state comparison could be important for real applications. As examples of such applications we present a lock and key scheme and a simple scheme for quantum public key distribution.

Complete hierarchies of efficient approximations to problems in entanglement theory

We investigate several problems in entanglement theory from the perspective of convex optimization. This list of problems comprises (A) the decision whether a state is multi-party entangled, (B) the minimization of expectation values of entanglement witnesses with respect to pure product states, (C) the closely related evaluation of the geometric measure of entanglement to quantify pure multi-party entanglement, (D) the test whether states are multi-party entangled on the basis of witnesses based on second moments and on the basis of linear entropic criteria, and (E) the evaluation of instances of maximal output purities of quantum channels. We show that these problems can be formulated as certain optimization problems: as polynomially constrained problems employing polynomials of degree three or less. We then apply very recently established known methods from the theory of semi-definite relaxations to the formulated optimization problems. By this construction we arrive at a hierarchy of efficiently solvable approximations to the solution, approximating the exact solution as closely as desired, in a way that is asymptotically complete. For example, this results in a hierarchy of novel, efficiently decidable sufficient criteria for multi-particle entanglement, such that every entangled state will necessarily be detected in some step of the hierarchy. Finally, we present numerical examples to demonstrate the practical accessibility of this approach.

Detecting two-party quantum correlations in quantum-key-distribution protocols

A necessary precondition for secure quantum key distribution is that sender and receiver can prove the presence of entanglement in a quantum state that is effectively distributed between them. In order to deliver this entanglement proof one can use the class of entanglement witness (EW) operators that can be constructed from the available measurements results. This class of EWs can be used to provide a necessary and sufficient condition for the existence of quantum correlations even when a quantum state cannot be completely reconstructed. The set of optimal EWs for two well-known entanglement-based (EB) schemes, the six-state and the four-state EB protocols, has been obtained recently [M. Curty et al., Phys. Rev. Lett. 92, 217903 (2004).] Here we complete these results, now showing specifically the analysis for the case of prepare and measure (PM) schemes. For this, we investigate the signal states and detection methods of the four-state and the two-state PM schemes. For each of these protocols we obtain a reduced set of EWs. More importantly, each set of EWs can be used to derive a necessary and sufficient condition to prove that quantum correlations are present in these protocols.

Intercept-resend attacks in the Bennett-Brassard 1984 quantum-key-distribution protocol with weak coherent pulses

Unconditional security proofs of the Bennett-Brassard 1984 protocol of quantum key distribution have been obtained recently. These proofs cover also practical implementations that utilize weak coherent pulses in the four signal polarizations. Proven secure rates leave open the possibility that new proofs or new public discussion protocols will obtain larger rates over increased distance. In this paper we investigate limits to the error rate and signal losses that can be tolerated by future protocols and proofs.

Effect of finite detector efficiencies on the security evaluation of quantum key distribution

Quantum Key Distribution with the BB84 protocol has been shown to be unconditionally secure even using weak coherent pulses instead of single-photon signals. The distances that can be covered by these methods are limited due to the loss in the quantum channel (e.g. loss in the optical fiber) and in the single-photon counters of the receivers. One can argue that the loss in the detectors cannot be changed by an eavesdropper in order to increase the covered distance. Here we show that the security analysis of this scenario is not as easy as is commonly assumed, since already two-photon processes allow eavesdropping strategies that outperform the known photon-number splitting attack. For this reason there is, so far, no satisfactory security analysis available in the framework of individual attacks.

Quantum cryptography with malicious devices

The current paradigm for the security of quantum key distribution (QKD) relies on the legitimate users of the system trusting their devices, which include both the quantum communication components and the classical post-processing units. However, in view of the memory attacks recently proposed against device-independent QKD, as well as the many hardware and software Trojan Horse attacks that threaten the security of conventional cryptography today, such trust is a very strong and unjustified assumption. Here we review a recent proposal to solve this problem based on the use of verifiable secret sharing and redundancies. We show that this approach can deliver secret key rates which are comparable to those obtained in an ideal scenario with honest devices.

Detecting quantum correlations for quantum key distribution

Practical quantum key distribution can be understood as a two-step procedure: in a first step two parties exchange quantum mechanical signals and perform measurements on them, in a second step auxiliary classical communication protocols are performed over an authenticated public channel to transform the data of the first step into an information-theoretic secure key. In this article we address the question of necessary conditions on the correlated (classical) data of the first step such that there can be a successful second step at all. As it turns out, a necessary condition is that these data, together with the knowledge about the physical set-up of sender and receiver, allow to establish a proof of effective entanglement between the two parties. We then demonstrate methods to systematically search for such a proof in basic settings, involving the 2-, 4-, and 6-state protocols.

Quantum Correlations for Quantum Key Distribution Protocols

A necessary precondition for secure quantum key distribution (QKD) is that sender and receiver can prove the presence of entanglement in a quantum state that is effectively distributed between them. In order to deliver this entanglement proof one can use the class of entanglement witness operators that can be constructed from the available measurements results. This criterion provides a necessary and sufficient condition for the existence of quantum correlations even when a quantum state cannot be completely reconstructed. We apply such analysis to three well‐known qubit‐based QKD protocols, namely the 6‐state, the 4‐state and the 2‐state protocols.