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

Combinatorial channels from partially ordered sets

A central task of coding theory is the design of schemes to reliably transmit data though space, via communication systems, or through time, via storage systems. Our goal is to identify and exploit structural properties common to a wide variety of coding problems, classical and modern, using the framework of partially ordered sets. We represent adversarial error models as combinatorial channels, form combinatorial channels from posets, identify a structural property of posets that leads to families of channels with the same codes, and bound the size of codes by optimizing over a family of equivalent channels. A large number of previously studied coding problems that fit into this framework. This leads to a new upper bound on the size of s-deletion correcting codes. We use a linear programming framework to obtain sphere-packing upper bounds when there is little underlying symmetry in the coding problem. Finally, we introduce and investigate a strong notion of poset homomorphism: locally bijective cover preserving maps. We look for maps of this type to and from the subsequence partial order on q-ary strings

The Equivocation of Codes

EQUIVOCATION was introduced by Shannon in the late 1940’s in seminal papers that kick-started the whole field of information theory. Much ground has been covered on equivocation’s counterpart, channel capacity and in particular, its bounds. However, less work has been carried out on the evaluation of the equivocation of a code transmitted across a channel. The aim of the work covered in this thesis was to use a probabilistic approach to investigate and compare the equivocation of various codes across a range of channels. The probability and entropy of each output, given each input, can be used to calculate the equivocation. This gives a measure of the ambiguity and secrecy of a code when transmitted across a channel. The calculations increase exponentially in magnitude as both the message length and code length increase. In addition, the impact of factors such as erasures and deletions also serve to significantly complicate the process. In order to improve the calculation times offered by a conventional, linearly-programmed approach, an alternative strategy involving parallel processing with a CUDA-enabled (Compute Unified Device Architecture) graphical processor was employed. This enabled results to be obtained for codes of greater length than was possible with linear programming. However, the practical implementation of a CUDA driven, parallel processed solution gave rise to significant issues with both the software implementation and subsequent platform stability. By normalising equivocation results, it was possible to compare different codes under different conditions, making it possible to identify and select codes that gave a marked difference in the equivocation encountered by a legitimate receiver and an eavesdropper. The introduction of code expansion provided a novel method for enhancing equivocation differences still further. The work on parallel processing to calculate equivocation and the use of code expansion was published in the following conference: Schofield, M., Ahmed, M. & Tomlinson, M. (2015), Using parallel processing to calculate and improve equivocation, in ’IEEE Conference Publications - IEEE 16th International Conference on Communication Technology’. In addition to the novel use of a CUDA-enabled graphics process to calculated equivocation, equivocation calculations were also performed for expanded versions of the codes. Code expansion was shown to yield a dramatic increase in the achievable equivocation levels. Once methods had been developed with the Binary Symmetric Channel (BSC), they were extended to include work with intentional erasures on the BSC, intentional deletions on the BSC and work on the Binary Erasure Channel (BEC). The work on equivocation on the BSC with intentional erasures was published in: Schofield, M. et al, (2016), Intentional erasures and equivocation on the binary symmetric channel, in ’IEEE Conference Publications - International Computer Symposium’, IEEE, pp 233-235. The work on the BEC produced a novel outcome due to the erasure correction process employed. As the probability of an erasure occurring increases, the set of likely decoded outcomes diminishes. This directly impacts the output entropy of the system by decreasing it, thereby also affecting the equivocation value of the system. This aspect was something that had not been encountered previously. The work also extended to the consideration of intentional deletions on the BSC and the Binary Deletion Channel (BDC) itself. Although the methods used struggled to cope with the additional complexity brought by deletions, the use of Varshamov-Tenengolts codes on the BSC with intentional deletions showed that family of codes to be well suited to the channel arrangement as well as having the capability to be extended to enable the correction of multiple deletions.Plymouth Universit

Recognizing Speech in a Novel Accent: The Motor Theory of Speech Perception Reframed

The motor theory of speech perception holds that we perceive the speech of another in terms of a motor representation of that speech. However, when we have learned to recognize a foreign accent, it seems plausible that recognition of a word rarely involves reconstruction of the speech gestures of the speaker rather than the listener. To better assess the motor theory and this observation, we proceed in three stages. Part 1 places the motor theory of speech perception in a larger framework based on our earlier models of the adaptive formation of mirror neurons for grasping, and for viewing extensions of that mirror system as part of a larger system for neuro-linguistic processing, augmented by the present consideration of recognizing speech in a novel accent. Part 2 then offers a novel computational model of how a listener comes to understand the speech of someone speaking the listener's native language with a foreign accent. The core tenet of the model is that the listener uses hypotheses about the word the speaker is currently uttering to update probabilities linking the sound produced by the speaker to phonemes in the native language repertoire of the listener. This, on average, improves the recognition of later words. This model is neutral regarding the nature of the representations it uses (motor vs. auditory). It serve as a reference point for the discussion in Part 3, which proposes a dual-stream neuro-linguistic architecture to revisits claims for and against the motor theory of speech perception and the relevance of mirror neurons, and extracts some implications for the reframing of the motor theory

Optical Communication

Optical communication is very much useful in telecommunication systems, data processing and networking. It consists of a transmitter that encodes a message into an optical signal, a channel that carries the signal to its desired destination, and a receiver that reproduces the message from the received optical signal. It presents up to date results on communication systems, along with the explanations of their relevance, from leading researchers in this field. The chapters cover general concepts of optical communication, components, systems, networks, signal processing and MIMO systems. In recent years, optical components and other enhanced signal processing functions are also considered in depth for optical communications systems. The researcher has also concentrated on optical devices, networking, signal processing, and MIMO systems and other enhanced functions for optical communication. This book is targeted at research, development and design engineers from the teams in manufacturing industry, academia and telecommunication industries

Decoding algorithms for surface codes

Quantum technologies have the potential to solve computationally hard problems that are intractable via classical means. Unfortunately, the unstable nature of quantum information makes it prone to errors. For this reason, quantum error correction is an invaluable tool to make quantum information reliable and enable the ultimate goal of fault-tolerant quantum computing. Surface codes currently stand as the most promising candidates to build error corrected qubits given their two-dimensional architecture, a requirement of only local operations, and high tolerance to quantum noise. Decoding algorithms are an integral component of any error correction scheme, as they are tasked with producing accurate estimates of the errors that affect quantum information, so that it can subsequently be corrected. A critical aspect of decoding algorithms is their speed, since the quantum state will suffer additional errors with the passage of time. This poses a connundrum-like tradeoff, where decoding performance is improved at the expense of complexity and viceversa. In this review, a thorough discussion of state-of-the-art surface code decoding algorithms is provided. The core operation of these methods is described along with existing variants that show promise for improved results. In addition, both the decoding performance, in terms of error correction capability, and decoding complexity, are compared. A review of the existing software tools regarding surface code decoding is also provided.Comment: 54 pages, 31 figure