Entanglement-assisted quantum turbo codes

An unexpected breakdown in the existing theory of quantum serial turbo coding is that a quantum convolutional encoder cannot simultaneously be recursive and non-catastrophic. These properties are essential for quantum turbo code families to have a minimum distance growing with blocklength and for their iterative decoding algorithm to converge, respectively. Here, we show that the entanglement-assisted paradigm simplifies the theory of quantum turbo codes, in the sense that an entanglement-assisted quantum (EAQ) convolutional encoder can possess both of the aforementioned desirable properties. We give several examples of EAQ convolutional encoders that are both recursive and non-catastrophic and detail their relevant parameters. We then modify the quantum turbo decoding algorithm of Poulin et al., in order to have the constituent decoders pass along only "extrinsic information" to each other rather than a posteriori probabilities as in the decoder of Poulin et al., and this leads to a significant improvement in the performance of unassisted quantum turbo codes. Other simulation results indicate that entanglement-assisted turbo codes can operate reliably in a noise regime 4.73 dB beyond that of standard quantum turbo codes, when used on a memoryless depolarizing channel. Furthermore, several of our quantum turbo codes are within 1 dB or less of their hashing limits, so that the performance of quantum turbo codes is now on par with that of classical turbo codes. Finally, we prove that entanglement is the resource that enables a convolutional encoder to be both non-catastrophic and recursive because an encoder acting on only information qubits, classical bits, gauge qubits, and ancilla qubits cannot simultaneously satisfy them.Comment: 31 pages, software for simulating EA turbo codes is available at http://code.google.com/p/ea-turbo/ and a presentation is available at http://markwilde.com/publications/10-10-EA-Turbo.ppt ; v2, revisions based on feedback from journal; v3, modification of the quantum turbo decoding algorithm that leads to improved performance over results in v2 and the results of Poulin et al. in arXiv:0712.288

Quantum information in the Posner model of quantum cognition

Matthew Fisher recently postulated a mechanism by which quantum phenomena could influence cognition: Phosphorus nuclear spins may resist decoherence for long times, especially when in Posner molecules. The spins would serve as biological qubits. We imagine that Fisher postulates correctly. How adroitly could biological systems process quantum information (QI)? We establish a framework for answering. Additionally, we construct applications of biological qubits to quantum error correction, quantum communication, and quantum computation. First, we posit how the QI encoded by the spins transforms as Posner molecules form. The transformation points to a natural computational basis for qubits in Posner molecules. From the basis, we construct a quantum code that detects arbitrary single-qubit errors. Each molecule encodes one qutrit. Shifting from information storage to computation, we define the model of Posner quantum computation. To illustrate the model's quantum-communication ability, we show how it can teleport information incoherently: A state's weights are teleported. Dephasing results from the entangling operation's simulation of a coarse-grained Bell measurement. Whether Posner quantum computation is universal remains an open question. However, the model's operations can efficiently prepare a Posner state usable as a resource in universal measurement-based quantum computation. The state results from deforming the Affleck-Kennedy-Lieb-Tasaki (AKLT) state and is a projected entangled-pair state (PEPS). Finally, we show that entanglement can affect molecular-binding rates, boosting a binding probability from 33.6% to 100% in an example. This work opens the door for the QI-theoretic analysis of biological qubits and Posner molecules.Comment: Published versio

Three-dimensionality of space and the quantum bit: an information-theoretic approach

It is sometimes pointed out as a curiosity that the state space of quantum two-level systems, i.e. the qubit, and actual physical space are both three-dimensional and Euclidean. In this paper, we suggest an information-theoretic analysis of this relationship, by proving a particular mathematical result: suppose that physics takes place in d spatial dimensions, and that some events happen probabilistically (not assuming quantum theory in any way). Furthermore, suppose there are systems that carry "minimal amounts of direction information", interacting via some continuous reversible time evolution. We prove that this uniquely determines spatial dimension d=3 and quantum theory on two qubits (including entanglement and unitary time evolution), and that it allows observers to infer local spatial geometry from probability measurements.Comment: 13 + 22 pages, 9 figures. v4: some clarifications, in particular in Section V / Appendix C (added Example 39

An identity of Chernoff bounds with an interpretation in statistical physics and applications in information theory

An identity between two versions of the Chernoff bound on the probability a certain large deviations event, is established. This identity has an interpretation in statistical physics, namely, an isothermal equilibrium of a composite system that consists of multiple subsystems of particles. Several information--theoretic application examples, where the analysis of this large deviations probability naturally arises, are then described from the viewpoint of this statistical mechanical interpretation. This results in several relationships between information theory and statistical physics, which we hope, the reader will find insightful.Comment: 29 pages, 1 figure. Submitted to IEEE Trans. on Information Theor

Descodificação através de Machine Learning

In recent years, machine learning has become one of the most rapidly expanding technologies in a variety of technological fields. In general, it allows a computer to learn from data without being expressly designed for a particular purpose. This thesis investigates the application of decoding methods inspired by machine learning to linear block codes, such as Reed-Muller (RM) codes.Recentemente, o Machine Learning tornou-se uma das tecnologias em mais rápida expansão numa variedade de campos tecnológicos. Em geral, permite que um computador aprenda com os dados sem ser expressamente concebido para um fim específico. Esta dissertação investiga a aplicação de métodos de descodificação inspirados no Machine Learning a códigos de blocos lineares, tais como os códigos de Reed-Muller

Design and Validation of a Software Defined Radio Testbed for DVB-T Transmission

This paper describes the design and validation of a Software Defined Radio (SDR) testbed, which can be used for Digital Television transmission using the Digital Video Broadcasting - Terrestrial (DVB-T) standard. In order to generate a DVB-T-compliant signal with low computational complexity, we design an SDR architecture that uses the C/C++ language and exploits multithreading and vectorized instructions. Then, we transmit the generated DVB-T signal in real time, using a common PC equipped with multicore central processing units (CPUs) and a commercially available SDR modem board. The proposed SDR architecture has been validated using fixed TV sets, and portable receivers. Our results show that the proposed SDR architecture for DVB-T transmission is a low-cost low-complexity solution that, in the worst case, only requires less than 22% of CPU load and less than 170 MB of memory usage, on a 3.0 GHz Core i7 processor. In addition, using the same SDR modem board, we design an off-line software receiver that also performs time synchronization and carrier frequency offset estimation and compensation