10 pages, Latex, no figures. To appear in 'Proceedings of the Second Winter Institute on Foundations of Quantum Theory and Quantum Optics: Quantum Information Processing', ed. R. Ghosh (Indian Academy of Science, Bangalore, 2002). Second version: shortened at editor's request; extra material on outpacing quantum computation (solving NP-complete problems in polynomial time)
It is argued that immense physical resources - for nonlocal communication, espionage, and exponentially-fast computation - are hidden from us by quantum noise, and that this noise is not fundamental but merely a property of an equilibrium state in which the universe happens to be at the present time. It is suggested that 'non-quantum' or nonequilibrium matter might exist today in the form of relic particles from the early universe. We describe how such matter could be detected and put to practical use. Nonequilibrium matter could be used to send instantaneous signals, to violate the uncertainty principle, to distinguish non-orthogonal quantum states without disturbing them, to eavesdrop on quantum key distribution, and to outpace quantum computation (solving NP-complete problems in polynomial time).
It is proven that any deterministic hidden-variables theory, that reproduces quantum theory for a 'quantum equilibrium' distribution of hidden variables, must predict the existence of instantaneous signals at the statistical level for hypothetical 'nonequilibrium ensembles'. This 'signal-locality theorem' generalises yet another feature of the pilot-wave theory of de Broglie and Bohm, for which it is already known that signal-locality is true only in equilibrium. Assuming certain symmetries, lower bounds are derived on the 'degree of nonlocality' of the singlet state, defined as the (equilibri…
Recently, the one particle quantum mechanics has been obtained in the framework of an entirely classical subquantum kinetics. In the present paper we argue that, within the same scheme and without any additional assumption, it is possible to obtain also the $n$-particle non relativistic quantum mechanics. The main goal of the present effort is to show that the classical BBGKY hierarchical equation, for the $n$-particle reduced distribution function, is the ancestor of the $n$-particle Schrödinger equation. On the other hand we show that within the scenario of the subquantum structure of quantu…
This article deals with theoretical developments in the subject of quantum information and quantum computation, and includes an overview of classical information and some relevant quantum mechanics. The discussion covers topics in quantum communication, quantum cryptography, and quantum computation, and concludes by considering whether a perspective in terms of quantum information sheds new light on the conceptual problems of quantum mechanics.
An information-theoretic temporal Bell inequality is formulated to contrast classical and quantum computations. Any classical algorithm satisfies the inequality, while quantum ones can violate it. Therefore, the violation of the inequality is an immediate consequence of the quantumness in the computation. Furthermore, this approach suggests a notion of temporal nonlocality in quantum computation.
We derive a new variational principle for the quantum Fisher information leading to a simple iterative alternating algorithm, the convergence of which is proved. The case of a fixed measurement, i.e. the classical Fisher information, is also discussed.
A research programme is set out for developing the use of high-level methods for quantum computation and information, based on the categorical formulation of quantum mechanics introduced by the author and Bob Coecke.
In this work, we introduce a new concatenation scheme which aims at protecting information against the occurrence of both computational errors and quantum erasures. According to our scheme, the internal code must be a quantum loss-correcting code that does not perform measurements, while the external code must be a quantum error-correcting code. We illustrate the concatenation proposed with an example in which one qubit of information is protected against the occurrence of two erasures and one computational error.
The method of using concepts and insight from quantum information theory in order to solve problems in reversible classical computing (introduced in Ref. [1]) have been generalized to irreversible classical computing. The method have been successfully tested on two computational tasks. Several basic logic gates have been analyzed and the nonlocal content of the associate quantum transformations have been calculated. The results provide us with new interesting insight into the notion of complexity of logic operations.
On the basis of introspective analysis, we establish a crucial requirement for the physical computation basis of consciousness: it should allow processing a significant amount of information together at the same time. Classical computation does not satisfy the requirement. At the fundamental physical level, it is a network of two body interactions, each the input-output transformation of a universal Boolean gate. Thus, it cannot process together at the same time more than the three bit input of this gate - many such gates in parallel do not count since the information is not processed together…
We address the problem related to the extraction of the information in the simulation of complex dynamics quantum computation. Here we present an example where important information can be extracted efficiently by means of quantum simulations. We show how to extract efficiently the localization length, the mean square deviation and the system characteristic frequency. We show how this methods work on a dynamical model, the Sawtooth Map, that is characterized by very different dynamical regimes: from near integrable to fully developed chaos; it also exhibits quantum dynamical localization.
We review both the Einstein, Podolsky, Rosen (EPR) paper about the completeness of quantum theory, and Schrodinger's responses to the EPR paper. We find that both the EPR paper and Schrodinger's responses, including the cat paradox, are not consistent with the current understanding of quantum theory and thermodynamics. Because both the EPR paper and Schrodinger's responses play a leading role in discussions of the fascinating and promising fields of quantum computation and quantum information, we hope our review will be helpful to researchers in these fields.
We propose a new composable and information-theoretically secure protocol to verify that a server has the power to sample from a sub-universal quantum machine implementing only commuting gates. By allowing the client to manipulate single qubits, we exploit properties of Measurement based Blind Quantum Computing to prove security against a malicious Server and therefore certify quantum supremacy without the need for a universal quantum computer.
Numerical investigations are an important research tool in quantum information theory. There already exists a wide range of computational tools for quantum information theory implemented in various programming languages. However, there is little effort in implementing this kind of tools in the Julia language. Julia is a modern programming language designed for numerical computation with excellent support for vector and matrix algebra, extended type system that allows for implementation of elegant application interfaces and support for parallel and distributed computing. QuantumInformation.jl i…
We discuss the usefulness of quantum cloning and present examples of quantum computation tasks for which cloning offers an advantage which cannot be matched by any approach that does not resort to it. In these quantum computations, we need to distribute quantum information contained in states about which we have some partial information. To perform quantum computations, we use state-dependent probabilistic quantum cloning procedure to distribute quantum information in the middle of a quantum computation.
Recoverable Quantum Computation: An Information-Centric Paradigm for Quantum Computing with Errors
Elmore Family School of Electrical and Computer Engineering, Purdue University（普渡大学埃尔莫尔电气与计算机工程学院）；Department of Physics and Astronomy, Purdue University（普渡大学物理与天文学系）；Purdue Quantum Science and Engineering Institute, Purdue University（普渡大学量子科学与工程研究所）
The advantages of quantum information processing are in many cases obtained as consequences of quantum interactions, especially for computational tasks where two-qubit interactions are essential. In this work, we establish the framework of analyzing and quantifying loss or gain of information on a quantum system when the system interacts with its environment. We show that the information flow, the theoretical method of characterizing (non-)Markovianity of quantum dynamics, corresponds to the rate of the minimum uncertainty about the system given quantum side information. Thereafter, we analyze…
We analyze how measured quantum dynamical systems store and process information, introducing sofic quantum dynamical systems. Using recently introduced information-theoretic measures for quantum processes, we quantify their information storage and processing in terms of entropy rate and excess entropy, giving closed-form expressions where possible. To illustrate the impact of measurement on information storage in quantum processes, we analyze two spin-1 sofic quantum systems that differ only in how they are measured.
The agenda of quantum algorithmic information theory, ordered `top-down,' is the quantum halting amplitude, followed by the quantum algorithmic information content, which in turn requires the theory of quantum computation. The fundamental atoms processed by quantum computation are the quantum bits which are dealt with in quantum information theory. The theory of quantum computation will be based upon a model of universal quantum computer whose elementary unit is a two-port interferometer capable of arbitrary $U(2)$ transformations. Basic to all these considerations is quantum theory, in partic…
Merely by existing, all physical systems register information. And by evolving dynamically in time, they transform and process that information. The laws of physics determine the amount of information that a physical system can register (number of bits) and the number of elementary logic operations that a system can perform (number of ops). The universe is a physical system. This paper quantifies the amount of information that the universe can register and the number of elementary operations that it can have performed over its history. The universe can have performed no more than $10^{120}$ op…
We introduce ways to measure information storage in quantum systems, using a recently introduced computation-theoretic model that accounts for measurement effects. The first, the quantum excess entropy, quantifies the shared information between a quantum process's past and its future. The second, the quantum transient information, determines the difficulty with which an observer comes to know the internal state of a quantum process through measurements. We contrast these with von Neumann entropy and quantum entropy rate and provide a closed-form expression for the latter for the class of deter…
It is generally accepted, following Landauer and Bennett, that the process of measurement involves no minimum entropy cost, but the erasure of information in resetting the memory register of a computer to zero requires dissipating heat into the environment. This thesis has been challenged recently in a two-part article by Earman and Norton. I review some relevant observations in the thermodynamics of computation and argue that Earman and Norton are mistaken: there is in principle no entropy cost to the acquisition of information, but the destruction of information does involve an irreducible e…
This thesis explores the use of entangled states in quantum computation and quantum information science. Entanglement, a quantum phenomenon with no classical counterpart, has been identified as an important and quantifiable resource in many areas of theoretical quantum information science, including quantum error correction, quantum cryptography, and quantum algorithms. We first investigate the equivalence classes of a particular class of entangled states (known as graph states due to their association with mathematical graphs) under local operations. We prove that for graph states correspondi…
Starting from Landauer's slogan "information is physical," we revise and modify Landauer's principle stating that the erasure of information has a minimal price in the form of a certain quantity of free energy. We establish a direct link between the erasure cost and the work value of a piece of information, and show that the former is essentially the length of the string's best compression by a reversible computation. We generalize the principle by deriving bounds on the free energy to be invested for --- or gained from, for that matter --- a general computation. We then revisit the second law…
Quantum computation and quantum information are of great current interest in computer science, mathematics, physical sciences and engineering. They will likely lead to a new wave of technological innovations in communication, computation and cryptography. As the theory of quantum physics is fundamentally stochastic, randomness and uncertainty are deeply rooted in quantum computation, quantum simulation and quantum information. Consequently quantum algorithms are random in nature, and quantum simulation utilizes Monte Carlo techniques extensively. Thus statistics can play an important role in q…
We reformulate the information causality in a more general framework by adopting the results of signal propagation and computation in a noisy circuit. In our framework, the information causality leads to a broad class of Tsirelson inequalities. This fact allows us to subject information causality to experimental scrutiny. A no-go theorem for reliable nonlocal computation is also derived. Information causality prevents any physical circuit from performing reliable computations.
In classical two-party computation, a trusted initializer who prepares certain initial correlations, known as one-time tables, can help make the inputs of both parties information-theoretically secure. We propose some bipartite quantum protocols with possible aborts for approximately generating such bipartite classical correlations with varying degrees of privacy, without introducing a third party. Under some weak requirements for the parties, the security level is nontrivial for use in bipartite computation. We show that the security is sometimes dependent on the noise level, but we propose a…
The possibility to save and process information in fundamentally indistinguishable states is the quantum mechanical resource that is not encountered in classical computing. I demonstrate that, if energy constraints are imposed, this resource can be used to accelerate information-processing without relying on entanglement or any other type of quantum correlations. In fact, there are computational problems that can be solved much faster, in comparison to currently used classical schemes, by saving intermediate information in nonorthogonal states of just a single qubit. There are also error corre…
The NSF Workshop in Quantum Information and Computation for Chemistry assembled experts from directly quantum-oriented fields such as algorithms, chemistry, machine learning, optics, simulation, and metrology, as well as experts in related fields such as condensed matter physics, biochemistry, physical chemistry, inorganic and organic chemistry, and spectroscopy. The goal of the workshop was to summarize recent progress in research at the interface of quantum information science and chemistry as well as to discuss the promising research challenges and opportunities in the field. Furthermore, t…
The present paper scrutinizes the principle of quantum determinism, which maintains that the complete information about the initial quantum state of a physical system should determine the system's quantum state at any other time. As it shown in the paper, assuming the strong exponential time hypothesis, SETH, which conjectures that known algorithms for solving computational NP-complete problems (often brute-force algorithms) are optimal, the quantum deterministic principle cannot be used generally, i.e., for randomly selected physical systems, particularly macroscopic systems. In other words, …
This volume constitutes the proceedings of the 7th International Workshop on Physics and Computation (PC 2016). The workshop was held on the 14th of July 2016 in Manchester, UK, as a satellite workshop to UCNC 2016, the 15th International Conference on Unconventional Computation and Natural Computation. The goal of the workshop series is to bring together researches working on the interaction between physics and the theory of computation. This intrinsically interdisciplinary domain of research strives to go beyond the traditional use of mathematics as a tool to model and understand the behavio…
Quantum theory has found a new field of applications in the realm of information and computation during the recent years. This paper reviews how quantum physics allows information coding in classically unexpected and subtle nonlocal ways, as well as information processing with an efficiency largely surpassing that of the present and foreseeable classical computers. Some outstanding aspects of classical and quantum information theory will be addressed here. Quantum teleportation, dense coding, and quantum cryptography are discussed as a few samples of the impact of quanta in the transmission of…
ZKCM is a C++ library developed for the purpose of multiprecision matrix computation, on the basis of the GNU MP and MPFR libraries. It provides an easy-to-use syntax and convenient functions for matrix manipulations including those often used in numerical simulations in quantum physics. Its extension library, ZKCM_QC, is developed for simulating quantum computing using the time-dependent matrix-product-state simulation method. This paper gives an introduction about the libraries with practical sample programs.
Quantum computational complexity estimates the difficulty of constructing quantum states from elementary operations, a problem of prime importance for quantum computation. Surprisingly, this quantity can also serve to study a completely different physical problem - that of information processing inside black holes. Quantum computational complexity was suggested as a new entry in the holographic dictionary, which extends the connection between geometry and information and resolves the puzzle of why black hole interiors keep growing for a very long time. In this pedagogical review, we present th…
Recent developments in quantum computation have made it clear that there is a lot more to computation than the conventional Boolean algebra. Is quantum computation the most general framework for processing information? Having gathered the courage to go beyond the traditional definitions, we are now in a position to answer: Certainly not. The meaning of a message being ``a collection of building blocks'' can be explored in a variety of situations. A generalised framework is proposed based on group theory, and it is illustrated with well-known physical examples. A systematic information theoreti…
In this paper, we explore algebraic structures and low dimensional topology underlying quantum information and computation. We revisit quantum teleportation from the perspective of the braid group, the symmetric group and the virtual braid group, and propose the braid teleportation, the teleportation swapping and the virtual braid teleportation, respectively. Besides, we present a physical interpretation for the braid teleportation and explain it as a sort of crossed measurement. On the other hand, we propose the extended Temperley--Lieb diagrammatical approach to various topics including quan…
Freie Universität Berlin（柏林自由大学）；Helmholtz-Zentrum Berlin für Materialien und Energie（亥姆霍兹柏林材料与能源中心）；Fraunhofer Heinrich Hertz Institute（弗劳恩霍夫海因里希赫兹研究所）
We consider quantum computation efficiency from a new perspective. The efficiency is reduced to its classical counterpart by imposing the semi-classical limit. We show that this reduction is caused by the fact that any elementary quantum logic operation (gate) suffers information loss during transition to its classical analogue. Amount of the information lost is estimated for any gate from the complete set. The largest loss is obtained for non-commuting gates that allows to consider them as quantum computational speed-up resource. Our method allows to quantify advantages of quantum computation…
