Review of The Theory of Quantum Information John Watrous

2021 ◽  
Vol 52 (1) ◽  
pp. 16-24
Author(s):  
Stephen A. Fenner
Keyword(s):  
Quantum Mechanics ◽  
Quantum Information ◽  
Graduate Course ◽  
The Core ◽  
Pure Mathematics ◽  
Self Study ◽  
Information Studies ◽  
Processing Information ◽  
Proof Techniques ◽  
Classical Information Theory

This is an extremely clear, carefully written book that covers the most important results in the sprawling field of quantum information. It is perfect for a reference, self-study, or a graduate course in quantum information. It makes no attempt to be broad or encyclopedic, but instead goes deep into the core topics. The definitions and theorems are all precisely worded, and (starting in Chapter 2) all results have complete proofs, making the book largely self-contained. The book focuses heavily on the mathematical results and nuts-and-bolts techniques underpinning current research, and as such gives the reader a thorough and flexible toolkit for proving new results. If you are just looking for a broad but cursory survey of the field, then this is probably not the book for you. If, however, you want a working knowledge of the core results and proof techniques of quantum information with an eye toward doing cutting-edge research in the field, then this book will be an indispensable addition to your library. The mathematical theory of quantum information studies the ultimate abilities and limits of transmitting and processing information using the laws of quantum mechanics. It owes much of its motivation to classical information theory, which was largely developed by Claude Shannon in the mid 20th century, and to quantum mechanics itself (of course). It addresses basic questions like: how much information can be transmitted through quantum channels, noisy or otherwise, and how entanglement helps. The theory informs, and is informed by, its sister disciplines of quantum computation and quantum communication (which overlap with physics and computer science), although in some sense it is more fundamental. Though he occasionally mentions applications to these other areas, Watrous seats his book squarely in the realm of pure mathematics.

scholarly journals Quantum Information: A Brief Overview and Some Mathematical Aspects

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 273
Author(s):  
Maurice Kibler
Keyword(s):  
Quantum Mechanics ◽  
Quantum Computing ◽  
Quantum Information ◽  
Quantum Information Processing ◽  
Short Review ◽  
Mutually Unbiased Bases ◽  
Quantum Bits ◽  
Mathematical Problems ◽  
Classical Information Theory ◽  
Main Ideas

The aim of the present paper is twofold. First, to give the main ideas behind quantum computing and quantum information, a field based on quantum-mechanical phenomena. Therefore, a short review is devoted to (i) quantum bits or qubits (and more generally qudits), the analogues of the usual bits 0 and 1 of the classical information theory, and to (ii) two characteristics of quantum mechanics, namely, linearity, which manifests itself through the superposition of qubits and the action of unitary operators on qubits, and entanglement of certain multi-qubit states, a resource that is specific to quantum mechanics. A, second, focus is on some mathematical problems related to the so-called mutually unbiased bases used in quantum computing and quantum information processing. In this direction, the construction of mutually unbiased bases is presented via two distinct approaches: one based on the group SU(2) and the other on Galois fields and Galois rings.

scholarly journals On the nature of Time and Entanglement

2021 ◽  
Author(s):  
Alessandro Capurso
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Quantum Information ◽  
Free Will ◽  
Imaginary Time ◽  
The Core ◽  
Time Order ◽  
Non Local ◽  
Nature Of Time ◽  
Free Will Theorem

The nature of Time is often at the root of the physical debate and possibly sits at the core of General Relativity and Quantum Mechanics frameworks incompatibility. In the context of the Free Will theorem and of a spacetime described through information, we identify in a thick present the only quantum information potential needed to describe evolution. The analysis of undefined causal orders (through a quantum Controlled-NOT gate and the evolution of the information along an imaginary time) allowed us to describe entanglement (both in space position and time order) as the potential related to an open choice and expressed in a CTC, which develops in a non-local imaginary space within the thick present considered.

scholarly journals Beyond Causal Explanation: Einstein’s Principle Not Reichenbach’s

Entropy ◽  
2021 ◽  
Vol 23 (1) ◽  
pp. 114
Author(s):  
Michael Silberstein ◽  
William Mark Stuckey ◽  
Timothy McDevitt
Keyword(s):  
Quantum Mechanics ◽  
Quantum Information ◽  
Causal Explanation ◽  
Causal Structure ◽  
Minkowski Spacetime ◽  
Physical Principle ◽  
Causal Principle ◽  
Complete Rejection ◽  
Epr Correlations ◽  
Tsirelson Bound

Our account provides a local, realist and fully non-causal principle explanation for EPR correlations, contextuality, no-signalling, and the Tsirelson bound. Indeed, the account herein is fully consistent with the causal structure of Minkowski spacetime. We argue that retrocausal accounts of quantum mechanics are problematic precisely because they do not fully transcend the assumption that causal or constructive explanation must always be fundamental. Unlike retrocausal accounts, our principle explanation is a complete rejection of Reichenbach’s Principle. Furthermore, we will argue that the basis for our principle account of quantum mechanics is the physical principle sought by quantum information theorists for their reconstructions of quantum mechanics. Finally, we explain why our account is both fully realist and psi-epistemic.

scholarly journals Free Will in Human Behavior and Physics

2020 ◽  
Author(s):  
Vasil Dinev Penchev
Keyword(s):  
Quantum Mechanics ◽  
Quantum Information ◽  
Free Will ◽  
Human Behavior ◽  
Physical World ◽  
Classical Physics ◽  
Quantum Bit ◽  
The Past ◽  
The Mean ◽  
The One

If the concept of “free will” is reduced to that of “choice” all physical world share the latter quality. Anyway the “free will” can be distinguished from the “choice”: The “free will” involves implicitly a certain goal, and the choice is only the mean, by which the aim can be achieved or not by the one who determines the target. Thus, for example, an electron has always a choice but not free will unlike a human possessing both. Consequently, and paradoxically, the determinism of classical physics is more subjective and more anthropomorphic than the indeterminism of quantum mechanics for the former presupposes certain deterministic goal implicitly following the model of human freewill behavior. Quantum mechanics introduces the choice in the fundament of physical world involving a generalized case of choice, which can be called “subjectless”: There is certain choice, which originates from the transition of the future into the past. Thus that kind of choice is shared of all existing and does not need any subject: It can be considered as a low of nature. There are a few theorems in quantum mechanics directly relevant to the topic: two of them are called “free will theorems” by their authors (Conway and Kochen 2006; 2009). Any quantum system either a human or an electron or whatever else has always a choice: Its behavior is not predetermined by its past. This is a physical law. It implies that a form of information, the quantum information underlies all existing for the unit of the quantity of information is an elementary choice: either a bit or a quantum bit (qubit).

Philosophy of Physics: A Very Short Introduction

2021 ◽  
Author(s):  
David Wallace
Keyword(s):  
Quantum Mechanics ◽  
Scientific Method ◽  
Philosophy Of Physics ◽  
Short Introduction ◽  
Fundamental Physics ◽  
The Core ◽  
The World ◽  
Modern Physics ◽  
Parallel Universes ◽  
Large Systems

Philosophy of Physics: A Very Short Introduction explores the core topics of philosophy of physics through three key themes: the nature of space and time; the origin of irreversibility and probability in the physics of large systems; how we can make sense of quantum mechanics. Central issues discussed include: the scientific method as it applies in modern physics; the distinction between absolute and relative motion; the way that distinction changes between Newton’s physics and special relativity; what spacetime is and how it relates to the laws of physics; how fundamental physics can make no distinction between past and future and yet a clear distinction exists in the world we see around us; why it is so difficult to understand quantum mechanics, and why doing so might push us to change our fundamental physics, to rethink the nature of science, or even to accept the existence of parallel universes.

A resource-based view of quantum information

2004 ◽  
Vol 4 (6&7) ◽  
pp. 460-466
Author(s):  
C.H. Bennett
Keyword(s):  
Quantum Information ◽  
Source Coding ◽  
Adequate Description ◽  
Tripartite Entanglement ◽  
Classical Communication ◽  
Resource Based View ◽  
Open Questions ◽  
Classical Information Theory

We survey progress in understanding quantum information in terms of equivalences, reducibilities, and asymptotically achievable rates for transformations among nonlocal resources such as classical communication, entanglement, and particular quantum states or channels. In some areas, eg source coding, there are straightforward parallels to classical information theory; in others eg entanglement-assisted communication, new effects and tradeoffs appear that are beginning to be fairly well understood, or the remaining uncertainty has become focussed on a few simple open questions, such as conjectured additivity of the Holevo capacity. In still other areas, e.g. the role of the back communication and the classification of tripartite entanglement, much remains unknown, and it appears unlikely that an adequate description exists in terms of a finite number of resources.

scholarly journals Cosmic Inflation, Quantum Information and the Pioneering Role of John S Bell in Cosmology

Universe ◽  
2019 ◽  
Vol 5 (4) ◽  
pp. 92 ◽  
Author(s):  
Jérôme Martin
Keyword(s):  
Quantum Mechanics ◽  
Quantum Information ◽  
Large Scale ◽  
Gravitational Instability ◽  
Cosmic Inflation ◽  
Large Scale Structures ◽  
Scale Structures ◽  
Accuracy Data ◽  
Made In

According to the theory of cosmic inflation, the large scale structures observed in our Universe (galaxies, clusters of galaxies, Cosmic Background Microwave—CMB—anisotropy...) are of quantum mechanical origin. They are nothing but vacuum fluctuations, stretched to cosmological scales by the cosmic expansion and amplified by gravitational instability. At the end of inflation, these perturbations are placed in a two-mode squeezed state with the strongest squeezing ever produced in Nature (much larger than anything that can be made in the laboratory on Earth). This article studies whether astrophysical observations could unambiguously reveal this quantum origin by borrowing ideas from quantum information theory. It is argued that some of the tools needed to carry out this task have been discussed long ago by J. Bell in a, so far, largely unrecognized contribution. A detailled study of his paper and of the criticisms that have been put forward against his work is presented. Although J. Bell could not have realized it when he wrote his letter since the quantum state of cosmological perturbations was not yet fully characterized at that time, it is also shown that Cosmology and cosmic inflation represent the most interesting frameworks to apply the concepts he investigated. This confirms that cosmic inflation is not only a successful paradigm to understand the early Universe. It is also the only situation in Physics where one crucially needs General Relativity and Quantum Mechanics to derive the predictions of a theory and, where, at the same time, we have high-accuracy data to test these predictions, making inflation a playground of utmost importance to discuss foundational issues in Quantum Mechanics.

scholarly journals Reality, Indeterminacy, Probability, and Information in Quantum Theory

Entropy ◽  
2020 ◽  
Vol 22 (7) ◽  
pp. 747
Author(s):  
Arkady Plotnitsky
Keyword(s):  
Information Theory ◽  
Quantum Mechanics ◽  
Quantum Theory ◽  
Quantum Information ◽  
Quantum Correlations ◽  
Quantum Information Theory ◽  
Quantum Phenomena

Following the view of several leading quantum-information theorists, this paper argues that quantum phenomena, including those exhibiting quantum correlations (one of their most enigmatic features), and quantum mechanics may be best understood in quantum-informational terms. It also argues that this understanding is implicit already in the work of some among the founding figures of quantum mechanics, in particular W. Heisenberg and N. Bohr, half a century before quantum information theory emerged and confirmed, and gave a deeper meaning to, to their insights. These insights, I further argue, still help this understanding, which is the main reason for considering them here. My argument is grounded in a particular interpretation of quantum phenomena and quantum mechanics, in part arising from these insights as well. This interpretation is based on the concept of reality without realism, RWR (which places the reality considered beyond representation or even conception), introduced by this author previously, in turn, following Heisenberg and Bohr, and in response to quantum information theory.

Quantum mechanics as quantum information, mostly

2003 ◽  
Vol 50 (6-7) ◽  
pp. 987-1023 ◽  
Author(s):  
Christopher A. Fuchs
Keyword(s):  
Quantum Mechanics ◽  
Quantum Information
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