A Unified and Generalized Approach to Quantum Error Correction

We present a unified approach to quantum error correction, called operator quantum error correction. This scheme relies on a generalized notion of noiseless subsystems that is not restricted to the commutant of the interaction algebra. We arrive at the unified approach, which incorporates the known techniques -- i.e. the standard error correction model, the method of decoherence-free subspaces, and the noiseless subsystem method -- as special cases, by combining active error correction with this generalized noiseless subsystem method. Moreover, we demonstrate that the quantum error correction condition from the standard model is a necessary condition for all known methods of quantum error correction.Comment: 5 page

Unconditional Security of Three State Quantum Key Distribution Protocols

Quantum key distribution (QKD) protocols are cryptographic techniques with security based only on the laws of quantum mechanics. Two prominent QKD schemes are the BB84 and B92 protocols that use four and two quantum states, respectively. In 2000, Phoenix et al. proposed a new family of three state protocols that offers advantages over the previous schemes. Until now, an error rate threshold for security of the symmetric trine spherical code QKD protocol has only been shown for the trivial intercept/resend eavesdropping strategy. In this paper, we prove the unconditional security of the trine spherical code QKD protocol, demonstrating its security up to a bit error rate of 9.81%. We also discuss on how this proof applies to a version of the trine spherical code QKD protocol where the error rate is evaluated from the number of inconclusive events.Comment: 4 pages, published versio

Three path interference using nuclear magnetic resonance: a test of the consistency of Born's rule

The Born rule is at the foundation of quantum mechanics and transforms our classical way of understanding probabilities by predicting that interference occurs between pairs of independent paths of a single object. One consequence of the Born rule is that three way (or three paths) quantum interference does not exist. In order to test the consistency of the Born rule, we examine detection probabilities in three path intereference using an ensemble of spin-1/2 quantum registers in liquid state nuclear magnetic resonance (LSNMR). As a measure of the consistency, we evaluate the ratio of three way interference to two way interference. Our experiment bounded the ratio to the order of $10^{-3} \pm 10^{-3}$, and hence it is consistent with Born's rule.Comment: 11 pages, 4 figures; Improved presentation of figures 1 and 4, changes made in section 2 to better describe the experiment, minor changes throughout, and added several reference

Simultaneous Ipsilateral Quadriceps and Triceps Tendon Rupture in a Patient with End-Stage Renal Failure.

Quadriceps tendon ruptures (QTR) frequently occur in patients with end-stage renal failure, while triceps brachii tendon ruptures (TTR) are less common. This is the first properly documented report of a simultaneous ipsilateral traumatic rupture of both of these tendons. A 50-year-old patient, on hemodialysis for end-stage renal failure, fell on his right side. He presented with sudden right knee and elbow pain, with functional impairment of both joints. X-rays showed avulsion-like osseous lesions on the olecranon and patella with a low-riding patella. Ultrasound confirmed complete quadriceps and triceps avulsion ruptures. Both lesions were treated surgically. Fixation was performed with anchors using the Krackow suture technique for both tendons. Postoperative clinical and radiological results were satisfactory, and follow-up was uneventful. The patient regained his preinjury functional level with a complete range of motion of both his knee and elbow. Isolated QTR and TTR are frequent lesions in chronic renal failure patients treated with hemodialysis. Simultaneous ipsilateral rupture of both tendons however is extremely rare and should therefore not be overlooked. Surgical treatment is recommended for complete ruptures

Étude de la modulation de l'activité du système nerveux sympathique dans les maladies cardio-vasculaires : rôle du système rénine angiotensine et du monoxyde d'azote

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal

Higher Security Thresholds for Quantum Key Distribution by Improved Analysis of Dark Counts

We discuss the potential of quantum key distribution (QKD) for long distance communication by proposing a new analysis of the errors caused by dark counts. We give sufficient conditions for a considerable improvement of the key generation rates and the security thresholds of well-known QKD protocols such as Bennett-Brassard 1984, Phoenix-Barnett-Chefles 2000, and the six-state protocol. This analysis is applicable to other QKD protocols like Bennett 1992. We examine two scenarios: a sender using a perfect single-photon source and a sender using a Poissonian source.Comment: 6 pages, 2 figures, v2: We obtained better results by using reverse reconciliation as suggested by Nicolas Gisi

Protecting Quantum Information Encoded in Decoherence Free States Against Exchange Errors

The exchange interaction between identical qubits in a quantum information processor gives rise to unitary two-qubit errors. It is shown here that decoherence free subspaces (DFSs) for collective decoherence undergo Pauli errors under exchange, which however do not take the decoherence free states outside of the DFS. In order to protect DFSs against these errors it is sufficient to employ a recently proposed concatenated DFS-quantum error correcting code scheme [D.A. Lidar, D. Bacon and K.B. Whaley, Phys. Rev. Lett. {\bf 82}, 4556 (1999)].Comment: 7 pages, no figures. Discussion in section V.A. significantly expanded. Several small changes. Two authors adde

Fidelity enhancement by logical qubit encoding

We demonstrate coherent control of two logical qubits encoded in a decoherence free subspace (DFS) of four dipolar-coupled protons in an NMR quantum information processor. A pseudo-pure fiducial state is created in the DFS, and a unitary logical qubit entangling operator evolves the system to a logical Bell state. The four-spin molecule is partially aligned by a liquid crystal solvent, which introduces strong dipolar couplings among the spins. Although the system Hamiltonian is never fully specified, we demonstrate high fidelity control over the logical degrees of freedom. In fact, the DFS encoding leads to higher fidelity control than is available in the full four-spin Hilbert space.Comment: 10 pages, 2 figure