Special Issue "Quantum Statistical Inference"
A special issue of Axioms (ISSN 2075-1680).
Deadline for manuscript submissions: closed (31 March 2015)
Dr. James D. Malley
Research Mathematical Statistician Building 12A, Room 2052 Mathematical and Statistical Computing Laboratory Division of Computational Bioscience Center for Information Technology National Institutes of Health Bethesda, MD 20892 USA
As quantum information theory advances, as new experimental quantum protocols are devised, and as the reality of practical quantum computing approaches, it is important to match these developments with appropriate statistical and data analysis methods. For this Special Issue the topic is understood to cover: advances in the probabilistic foundations of quantum mechanics; new developments for statistical methods and data analysis of quantum outcomes; quantum information perspectives on the analysis quantum outcomes and experiment; examination of classical statistical methods that have possible application to quantum outcomes and decisions, such as quantum based statistical learning machines, and Bayesian quantum state estimation. The emphasis in this Special Issue will be on experiment and applications of theory that advance our understanding of what quantum data can mean and how it might be used. More speculative revisions of the foundations of quantum mechanics are not obviously included in this discussion, unless grounded in current experiment or near term realizations of the proposed ideas and methods.
Dr. James D. Malley
Manuscript Submission Information
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The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.
Type of paper: Article
Title: The Universe as a Quantum Computer
Author: Stanley P. Gudder
Abstract: This article presents a sequential growth model for the universe that acts like a quantum computer. The basic constituents of the model are a special type of causal set (causet) called a \(c\)-causet. A \(c\)-causet is defined to be a causet that is independent of its labeling. We characterize \(c\)-causets as those causets that form a multipartite graph or equivalently those causets whose elements are comparable whenever their heights are different. We show that a \(c\)-causet has precisely two \(c\)-causet offspring. It follows that there are \(2^n\) \(c\)-causets of cardinality \(n+1\). This enables us to classify \(c\)-causets of cardinality \(n+1\) in terms of \(n\)-bits. We then quantize the model by introducing a quantum sequential growth process. This is accomplished by replacing the \(n\)-bits by \(n\)-qubits and defining transition amplitudes for the growth transitions. We mainly consider two types of processes called stationary and completely stationary. We show that for stationary processes, the probability operators are tensor products of positive rank-1 qubit operators. Moreover, the converse of this result holds. Simplifications occur for completely stationary processes. We close with examples of precluded events.