quantum information theory research papers
Equivalence of additivity questions in quantum information theory
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We reduce the number of open additivity problems in quantum information theory by showing that four of them are equivalent. Namely, we show that the conjectures of additivity of the minimum output entropy of a quantum channel, additivity of the Holevo expression
Quantum Information Theory
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P Bastani Entropy: amount of uncertainty in the state of a physical system Shannon entropy of a random variable X: average amount of uncertainty about X before we learn its value average amount of information gain after we learn the value of X Less probable events convey
Quantum Information Theory
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Quantum Information Theory
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The very process of doing physics is to acquire information about the world around us. At the same time, the storage and processing of information is necessarily a physical process. It is thus not surprising that physics and the theory of information are inherently connected. 1
Classical and quantum information theory
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417 20.7 Public-key cryptography 424 20.8 Exercises 429 21 Quantum information theory 431 21.1 Von Neumann entropy 431 21.2 Relative, joint, and conditional entropy, and mutual information 437 21.3 Quantum communication channel and Holevo bound 450
Quantum information theory-an invitation
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Quantum information and quantum computers have received a lot of public attention recently. Quantum computers have been advertised as a kind of warp drive for computing, and indeed the promise of the algorithms of Shor and Grover is to perform computations
Simplification of additivity conjecture in quantum information theory
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We simplify some conjectures in quantum information theory; the additivity of minimal output entropy, the multiplicativity of maximal output p-norm and the superadditivity of convex closure of output entropy. In this paper, by using some unital extension of quantum
Quantum information theory: results and open problems
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The discipline of information theory was founded by Claude Shannon in a truly remarkable paper [Sh] which laid down the foundations of the subject. We begin with a quote from this paper which is an excellent summary of the main concern of information theory: The
Characterizing quantum theory in terms of information-theoretic constraints
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Abstract We show that three fundamental information-theoretic constraints-the impossibility of superluminal information transfer between two physical systems by performing measurements on one of them, the impossibility of broadcasting the information contained
Noiseless subsystems for collective rotation channels in quantum information theory
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Collective rotation channels are a fundamental class of channels in quantum computing and quantum information theory. The commutant of the noise operators for such a channel is a C*-algebra which is equal to the set of fixed points for the channel. Finding the precise
Quantum algorithmic information theory
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ABSTRACT The agenda of quantum algorithmic information theory, orderedtop-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
Entanglement in frequency standards and quantum information theory
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ABSTRACT. Entanglement is a key property of quantum information theory. Here we describe ways to quantify the amount of entanglement. We point out the statistical interpretation of these entanglement measures and some connections between entanglement
Instruments and channels in quantum information theory
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Abstract While a positive operator valued measure gives the probabilities in a quantum measurement, an instrument gives both the probabilities and the a posteriori states. By interpreting the instrument as a quantum channel and by using the typical inequalities for
Frames, designs, and spherical codes in quantum information theory
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Abstract Frame theory offers a lens through which to view a large portion of quantum information theory, providing an organizational principle to those topics in its purview. In this thesis, I cut a trail from foundational questions to practical applications, from the origin of
Theory of quantum information
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This section introduces the simple notion of a complex Euclidean space, which is used throughout this course. In particular, with every discrete and finite physical system we will associate some complex Euclidean space; and fundamental notions such as states and
What information theory can tell us about quantum reality
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An investigation of Einstein s physical reality and the concept of quantum reality in terms of information theory suggests a solution to quantum paradoxes such as the Einstein-Podolsky- Rosen (EPR) and the Schrdinger-cat paradoxes. Quantum reality, the picture based on
Alternative new notation for quantum information theory
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ABSTRACT The notation [Li, Song, and Luo (2002) Physics Letters A 297, 121] has been generalized to quantum information theory. By this notation, we present three useful criteria for bipartite entanglement, a formula for general quantum swapping, and a formula for
The quantum reverse Shannon theorem based on one-shot information theory
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Abstract The Quantum Reverse Shannon Theorem states that any quantum channel can be simulated by an unlimited amount of shared entanglement and an amount of classical communication equal to the channel s entanglement assisted classical capacity. In this
Nanochaos and quantum information for a physical theory of evolvable semantic automata
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The concept of automaton in its historical development, from the earlier attempts to mimic motions of men and animals to the recent ambitious goals of designing and building biomimetic, ie, evolvable and self-reproducing machines, is very briefly outlined to stress
Quantum Probability and Quantum Information Theory
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From its very birth in the 1920s, quantum theory has been characterized by a certain strangeness: It seems to run counter to the intuitions that we humans have about the world we live in. According to these realistic intuitions all things have their definite place and
Lectures on Quantum Computation, Quantum Error Correcting Codes and Information Theory
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These notes were prepared by Amitava Bhattacharya on a course of lectures I gave at the Tata Institute of Fundamental Research (Mumbai) in the months of April 2001 and February 2002. I am grateful to my colleagues at the TIFR, in general, and Professor Parimala
Quantum mechanics emerges from information theory applied to causal horizons
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ABSTRACT It is suggested that quantum mechanics is not fundamental but emerges from classical information theory applied to causal horizons. The path integral quantization and quantum randomness can be derived by considering information loss of fields or particles
Multiaccess channels in quantum information theory
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ABSTRACT A quantum channel is investigated that transmits quantum messages from two independent sources to a unique receiver. Several general assertions about the system throughput are proved, and physically important coherent-and squeezed-state
Quantum theory of ur-objects as a theory of information
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The quantum theory of ur-objects proposed by CF von Weizsäcker has to be interpreted as a quantum theory of information. Ur-objects, or urs, are thought to be the simplest objects in quantum theory. Thus an ur is represented by a two-dimensional Hilbert space with the
CS 798: Theory of quantum information
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The purpose of this first set of lecture notes is to summarize background material on linear algebra and analysis that is used throughout the course. Proofs of most of the stated facts may be found in the references listed at the end of the notes. It is my intention that this first
Pure quantum states are fundamental, mixtures (composite states) are mathematical constructions: An argument using algorithmic information theory
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ABSTRACT From the philosophical viewpoint, two interpretations of the quantum measurement process are possible: According to the first interpretation, when we measure an observable, the measured system moves into one of the eigenstates of this observable (the wave
Structured information retrieval and quantum theory
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Information Retrieval (IR) systems try to identify documents relevant to user queries, which are representations of user information needs. Interaction, context, and document structure are three important and active themes in IR research. We present how we propose to
Information density functional theory: A quantum approach to intent
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ABSTRACT Trust from the perspective of traditional social theory is a function of the cooperation promoted across a system of multiple human or artificial agents, assuring that conflict ends with a consensus of the facts drawn from reality, R. Overlooked is the downside of
Quantum theory beyond the physical: information in context
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ABSTRACT Measures and theories of information abound, but there are few formalised methods for treating the contextuality that can manifest in different information systems. Quantum theory provides one possible formalism for treating information in context. This
Notes on Quantum Information Theory
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? This is a rough outline to accompany lectures. It is not intended to be self-contained. There is a hierarchy of bullets:If they don t make sense to you, ignore them. ? References: CQT = RB Griffiths, Consistent Quantum Theory (Cambridge 2002) QCQI =
Thermodynamical analogues in quantum information theory
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ABSTRACT The first step in quantum information theory is the identification of entanglement as a valuable resource. The next step is learning how to efficiently exploit this resource. We learn how to efficiently exploit entanglement by applying analogues of thermodynamical
On unentangled Gleason theorems for quantum information theory
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It is shown here that a strengthening of Wallach s Unentangled Gleason Theorem can be obtained by applying results of the present authors on generalised Gleason theorems for quantum multi-measures arising from investigations of quantum decoherence functionals.
Vacuum fluctuations, geometric modular action and relativistic quantum information theory
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A summary of some lines of ideas leading to model-independent frameworks of relativistic quantum field theory is given. It is followed by a discussion of the Reeh-Schlieder theorem and geometric modular action of Tomita-Takesaki modular objects associated with the
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