Recursive quantum convolutional encoders are catastrophic: A simple proof

Poulin, Tillich, and Ollivier discovered an important separation between the classical and quantum theories of convolutional coding, by proving that a quantum convolutional encoder cannot be both non-catastrophic and recursive. Non-catastrophicity is desirable so that an iterative decoding algorithm converges when decoding a quantum turbo code whose constituents are quantum convolutional codes, and recursiveness is as well so that a quantum turbo code has a minimum distance growing nearly linearly with the length of the code, respectively. Their proof of the aforementioned theorem was admittedly "rather involved," and as such, it has been desirable since their result to find a simpler proof. In this paper, we furnish a proof that is arguably simpler. Our approach is group-theoretic---we show that the subgroup of memory states that are part of a zero physical-weight cycle of a quantum convolutional encoder is equivalent to the centralizer of its "finite-memory" subgroup (the subgroup of memory states which eventually reach the identity memory state by identity operator inputs for the information qubits and identity or Pauli-Z operator inputs for the ancilla qubits). After proving that this symmetry holds for any quantum convolutional encoder, it easily follows that an encoder is non-recursive if it is non-catastrophic. Our proof also illuminates why this no-go theorem does not apply to entanglement-assisted quantum convolutional encoders---the introduction of shared entanglement as a resource allows the above symmetry to be broken.Comment: 15 pages, 1 figure. v2: accepted into IEEE Transactions on Information Theory with minor modifications. arXiv admin note: text overlap with arXiv:1105.064

Multi-Agent Coverage Control with Energy Depletion and Repletion

We develop a hybrid system model to describe the behavior of multiple agents cooperatively solving an optimal coverage problem under energy depletion and repletion constraints. The model captures the controlled switching of agents between coverage (when energy is depleted) and battery charging (when energy is replenished) modes. It guarantees the feasibility of the coverage problem by defining a guard function on each agent's battery level to prevent it from dying on its way to a charging station. The charging station plays the role of a centralized scheduler to solve the contention problem of agents competing for the only charging resource in the mission space. The optimal coverage problem is transformed into a parametric optimization problem to determine an optimal recharging policy. This problem is solved through the use of Infinitesimal Perturbation Analysis (IPA), with simulation results showing that a full recharging policy is optimal

The role of BK potassium channels in analgesia produced by alpha-2 adrenergic receptors

BACKGROUND AND OBJECTIVE: Millions of people suffer from pain worldwide, and annually, great economic costs are imposed on societies for pain relief. Analgesics such as alpha-2 adrenergic receptor agonists, which have low risk of complications, can be effective in assuaging pain and reducing costs. According to former studies, potassium channels play an important role in the analgesic mechanism of these receptors. This study aimed to determine the role of BK potassium channels in analgesia induced by alpha-2 adrenergic receptors. METHODS: This study was performed on 56 male Wistar rats weighing 250-300 g that were divided into seven groups of eight rats. We administered 0. 7 mg/kg intraperitoneal (IP) injection of clonidine, 1 mg/kg IP injection of yohimbine, and 5 mg/kg intracerebroventricular (ICV) injection of yohimbine. Iberiotoxin at a dose of 100 nm was also injected ICV. Normal saline and DMSO were applied as solvents. Pain severity was evaluated using formalin test at a concentration of 2%. FINDINGS: The chronic pain induced by formalin injection was relieved by IP injection of 0. 7 mg/kg clonidine. Moreover, 5 μg/kg and 1 μg/kg ICV administration of yohimbine with mean chronic pain scores of 2. 29±0. 13 and 2. 09±0. 07, respectively, could significantly inhibit analgesic effect of clonidine with mean chronic pain score of 1. 55±0. 14 (p<0. 001). ICV injection of iberiotoxin with mean chronic pain score of 2. 33±0. 16 at a dose of 100 nm significantly diminished analgesic effects of clonidine. CONCLUSION: Alpha-2 adrenergic receptor agonists could induce analgesia in the animals, and the antagonist of this receptor inhibited the analgesic effect of agonists of these receptors. BK channel inhibition prevented analgesic effect of adrenergic receptor agonists, as well. © 2016, Babol University of Medical Sciences. All rights reserved

Examples of minimal-memory, non-catastrophic quantum convolutional encoders

One of the most important open questions in the theory of quantum convolutional coding is to determine a minimal-memory, non-catastrophic, polynomial-depth convolutional encoder for an arbitrary quantum convolutional code. Here, we present a technique that finds quantum convolutional encoders with such desirable properties for several example quantum convolutional codes (an exposition of our technique in full generality will appear elsewhere). We first show how to encode the well-studied Forney-Grassl-Guha (FGG) code with an encoder that exploits just one memory qubit (the former Grassl-Roetteler encoder requires 15 memory qubits). We then show how our technique can find an online decoder corresponding to this encoder, and we also detail the operation of our technique on a different example of a quantum convolutional code. Finally, the reduction in memory for the FGG encoder makes it feasible to simulate the performance of a quantum turbo code employing it, and we present the results of such simulations.Comment: 5 pages, 2 figures, Accepted for the International Symposium on Information Theory 2011 (ISIT 2011), St. Petersburg, Russia; v2 has minor change