Unconditional Security of Single-Photon Differential Phase Shift Quantum Key Distribution

In this Letter, we prove the unconditional security of single-photon differential phase shift quantum key distribution (DPS-QKD) protocol, based on the conversion to an equivalent entanglement-based protocol. We estimate the upper bound of the phase error rate from the bit error rate, and show that DPS-QKD can generate unconditionally secure key when the bit error rate is not greater than 4.12%. This proof is the first step to the unconditional security proof of coherent state DPS-QKD.Comment: 5 pages, 2 figures; shorten the length, improve clarity, and correct typos; accepted for publication in Physical Review Letter

Noisy Preprocessing and the Distillation of Private States

We provide a simple security proof for prepare & measure quantum key distribution protocols employing noisy processing and one-way postprocessing of the key. This is achieved by showing that the security of such a protocol is equivalent to that of an associated key distribution protocol in which, instead of the usual maximally-entangled states, a more general {\em private state} is distilled. Besides a more general target state, the usual entanglement distillation tools are employed (in particular, Calderbank-Shor-Steane (CSS)-like codes), with the crucial difference that noisy processing allows some phase errors to be left uncorrected without compromising the privacy of the key.Comment: 4 pages, to appear in Physical Review Letters. Extensively rewritten, with a more detailed discussion of coherent --> iid reductio

Matroids and Quantum Secret Sharing Schemes

A secret sharing scheme is a cryptographic protocol to distribute a secret state in an encoded form among a group of players such that only authorized subsets of the players can reconstruct the secret. Classically, efficient secret sharing schemes have been shown to be induced by matroids. Furthermore, access structures of such schemes can be characterized by an excluded minor relation. No such relations are known for quantum secret sharing schemes. In this paper we take the first steps toward a matroidal characterization of quantum secret sharing schemes. In addition to providing a new perspective on quantum secret sharing schemes, this characterization has important benefits. While previous work has shown how to construct quantum secret sharing schemes for general access structures, these schemes are not claimed to be efficient. In this context the present results prove to be useful; they enable us to construct efficient quantum secret sharing schemes for many general access structures. More precisely, we show that an identically self-dual matroid that is representable over a finite field induces a pure state quantum secret sharing scheme with information rate one

A simple proof of the unconditional security of quantum key distribution

Quantum key distribution is the most well-known application of quantum cryptography. Previous proposed proofs of security of quantum key distribution contain various technical subtleties. Here, a conceptually simpler proof of security of quantum key distribution is presented. The new insight is the invariance of the error rate of a teleportation channel: We show that the error rate of a teleportation channel is independent of the signals being transmitted. This is because the non-trivial error patterns are permuted under teleportation. This new insight is combined with the recently proposed quantum to classical reduction theorem. Our result shows that assuming that Alice and Bob have fault-tolerant quantum computers, quantum key distribution can be made unconditionally secure over arbitrarily long distances even against the most general type of eavesdropping attacks and in the presence of all types of noises.Comment: 13 pages, extended abstract. Comments will be appreciate

Unconditionally Secure Bit Commitment

We describe a new classical bit commitment protocol based on cryptographic constraints imposed by special relativity. The protocol is unconditionally secure against classical or quantum attacks. It evades the no-go results of Mayers, Lo and Chau by requiring from Alice a sequence of communications, including a post-revelation verification, each of which is guaranteed to be independent of its predecessor.Comment: Typos corrected. Reference details added. To appear in Phys. Rev. Let

One-way quantum key distribution: Simple upper bound on the secret key rate

We present a simple method to obtain an upper bound on the achievable secret key rate in quantum key distribution (QKD) protocols that use only unidirectional classical communication during the public-discussion phase. This method is based on a necessary precondition for one-way secret key distillation; the legitimate users need to prove that there exists no quantum state having a symmetric extension that is compatible with the available measurements results. The main advantage of the obtained upper bound is that it can be formulated as a semidefinite program, which can be efficiently solved. We illustrate our results by analysing two well-known qubit-based QKD protocols: the four-state protocol and the six-state protocol. Recent results by Renner et al., Phys. Rev. A 72, 012332 (2005), also show that the given precondition is only necessary but not sufficient for unidirectional secret key distillation.Comment: 11 pages, 1 figur

A Normal Electrocardiogram Does Not Exclude Infra-Hisian Conduction Disease in Patients With Myotonic Dystrophy Type 1

Objectives: This study aimed to identify electrocardiographic (ECG) predictors of a prolonged His-ventricular (HV) interval in patients with type 1 myotonic dystrophy (DM1).\ud Background: Patients with DM1 have an increased risk of sudden cardiac death. The presence of His-Purkinje system disease/prolonged HV interval (≥70 ms) is associated with a higher risk of potentially life-threatening bradyarrhythmic events. Methods: Electrophysiology studies (EPSs) were performed in all DM1 patients referred to 2 tertiary centers for routine cardiac assessment. In a subgroup of patients, the EPS was repeated at varying intervals. Results: A total of 154 patients (mean age: 43.7 ± 13.3; 58.1% male) underwent 202 diagnostic EPSs. HV ≥70 ms was found on 58 EPSs (28.7%); 9 of 59 patients (15.2%) with PR <200 ms and QRS interval <110 ms on baseline ECG had an HV ≥70 ms on EPS. Among those with PR ≥200 ms and/or QRS interval ≥100 ms, only 33.9% had an HV ≥70 ms on EPS. There were 38 patients who underwent repeated EPS, in which 28.8% demonstrated a prolongation of the HV interval overall compared with baseline. QRS duration demonstrated the most powerful discriminative capacity for HV ≥70 ms (area under the receiver operating characteristic curve: 0.76; 95% confidence interval [CI]: 0.68 to 0.84; p < 0.001). On multivariate analysis, QRS interval ≥112 ms had the highest predictive value for HV ≥70 ms (odds ratio: 7.94; 95% CI: 3.85 to 16.37. Conclusions: ECG parameters have a poor predictive value for infra-Hisian conduction block in DM1 patients. QRS and PR intervals are normal in up to 15.2% of DM1 patients with prolonged HV, and 66.1% of those with PR ≥200 ms and/or QRS ≥100 ms do not have advanced His-Purkinje conduction system disease on EPS. Electrophysiology testing should be a mandatory part of screening for all patients to guide prophylactic pacemaker implantation

Quantum repeaters and quantum key distribution: analysis of secret key rates

We analyze various prominent quantum repeater protocols in the context of long-distance quantum key distribution. These protocols are the original quantum repeater proposal by Briegel, D\"ur, Cirac and Zoller, the so-called hybrid quantum repeater using optical coherent states dispersively interacting with atomic spin qubits, and the Duan-Lukin-Cirac-Zoller-type repeater using atomic ensembles together with linear optics and, in its most recent extension, heralded qubit amplifiers. For our analysis, we investigate the most important experimental parameters of every repeater component and find their minimally required values for obtaining a nonzero secret key. Additionally, we examine in detail the impact of device imperfections on the final secret key rate and on the optimal number of rounds of distillation when the entangled states are purified right after their initial distribution.Comment: Published versio