Results 1  10
of
59
Quantum Equilibrium and the Origin of Absolute Uncertainty
, 1992
"... The quantum formalism is a "measurement" formalisma phenomenological formalism describing certain macroscopic regularities. We argue that it can be regarded, and best be understood, as arising from Bohmian mechanics, which is what emerges from Schr6dinger's equation for a system of particles when ..."
Abstract

Cited by 112 (47 self)
 Add to MetaCart
The quantum formalism is a "measurement" formalisma phenomenological formalism describing certain macroscopic regularities. We argue that it can be regarded, and best be understood, as arising from Bohmian mechanics, which is what emerges from Schr6dinger's equation for a system of particles when we merely insist that "particles " means particles. While distinctly nonNewtonian, Bohmian mechanics is a fully deterministic theory of particles in motion, a motion choreographed by the wave function. We find that a Bohmian universe, though deterministic, evolves in such a manner that an appearance of randomness emerges, precisely as described by the quantum formalism and given, for example, by "p = IV [ 2.,, A crucial ingredient in our analysis of the origin of this randomness is the notion of the effective wave function of a subsystem, a notion of interest in its own right and of relevance to any discussion of quantum theory. When the quantum formalism is regarded as arising in this way, the paradoxes and perplexities so often associated with (nonrelativistic) quantum theory simply evaporate.
Unknown quantum states: the quantum de Finetti representation
 J. Math. Phys
"... We present an elementary proof of the quantum de Finetti representation theorem, a quantum analogue of de Finetti’s classical theorem on exchangeable probability assignments. This contrasts with the original proof of Hudson and Moody [Z. Wahrschein. verw. Geb. 33, 343 (1976)], which relies on advanc ..."
Abstract

Cited by 44 (7 self)
 Add to MetaCart
We present an elementary proof of the quantum de Finetti representation theorem, a quantum analogue of de Finetti’s classical theorem on exchangeable probability assignments. This contrasts with the original proof of Hudson and Moody [Z. Wahrschein. verw. Geb. 33, 343 (1976)], which relies on advanced mathematics and does not share the same potential for generalization. The classical de Finetti theorem provides an operational definition of the concept of an unknown probability in Bayesian probability theory, where probabilities are taken to be degrees of belief instead of objective states of nature. The quantum de Finetti theorem, in a closely analogous fashion, deals with exchangeable densityoperator assignments and provides an operational definition of the concept of an “unknown quantum state ” in quantumstate tomography. This result is especially important for informationbased interpretations of quantum mechanics, where quantum states, like probabilities, are taken to be states of knowledge rather than states of nature. We further demonstrate that the theorem fails for real Hilbert spaces and discuss the significance of this point. I.
Characterizing quantum theory in terms of informationtheoretic constraints
 Foundations of Physics
, 2003
"... We show that three fundamental informationtheoretic 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 in an unknown physical state, and the impossibil ..."
Abstract

Cited by 28 (3 self)
 Add to MetaCart
We show that three fundamental informationtheoretic 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 in an unknown physical state, and the impossibility of unconditionally secure bit commitment—suffice to entail that the observables and state space of a physical theory are quantummechanical. We demonstrate the converse derivation in part, and consider the implications of alternative answers to a remaining open question about nonlocality and bit commitment. KEY WORDS: quantum theory; informationtheoretic constraints. Of John Wheeler’s ‘‘Really Big Questions,’ ’ the one on which most progress has been made is It from Bit?—does information play a significant role at the foundations of physics? It is perhaps less ambitious than some of the other Questions, such as How Come Existence?, because it does not necessarily require a metaphysical answer. And unlike, say, Why the Quantum?, it does not require the discovery of new laws of nature: there was room for hope that it might be answered through a better understanding of the laws as we currently know them, particularly those of quantum physics. And this is what has happened: the better understanding is the quantum theory of information and computation. 1
Quantum entanglement and projective ring geometry
 SIGMA 2, Paper 66
, 2006
"... The paper explores the basic geometrical properties of the observables characterizing twoqubit systems by employing a novel projective ring geometric approach. After introducing the basic facts about quantum complementarity and maximal quantum entanglement in such systems, we demonstrate that the 1 ..."
Abstract

Cited by 19 (14 self)
 Add to MetaCart
The paper explores the basic geometrical properties of the observables characterizing twoqubit systems by employing a novel projective ring geometric approach. After introducing the basic facts about quantum complementarity and maximal quantum entanglement in such systems, we demonstrate that the 15×15 multiplication table of the associated fourdimensional matrices exhibits a sofarunnoticed geometrical structure that can be regarded as three pencils of lines in the projective plane of order two. All lines in each pencil carry mutually commuting operators; in one of the pencils, which we call the kernel, the observables on two lines share a base of maximally entangled states. The three operators on any line in each pencil represent a row or column of some Mermin’s “magic ” square, thus revealing an inherent geometrical nature of the latter. In the complement of the kernel, the eight vertices/observables are joined by twelve lines which form the edges of a cube. A substantial part of the paper is devoted to showing that the nature of this geometry has much to do with the structure of the projective lines defined over the rings that are the direct product of n copies of the Galois field GF(2), with n = 2, 3 and 4.
Interpreting the Quantum
, 1997
"... This paper is a commentary on the foundational significance of the CliftonBubHalvorson theorem characterizing quantum theory in terms of three informationtheoretic constraints. I argue that: (1) a quantum theory is best understood as a theory about the possibilities and impossibilities of informa ..."
Abstract

Cited by 16 (1 self)
 Add to MetaCart
This paper is a commentary on the foundational significance of the CliftonBubHalvorson theorem characterizing quantum theory in terms of three informationtheoretic constraints. I argue that: (1) a quantum theory is best understood as a theory about the possibilities and impossibilities of information transfer, as opposed to a theory about the mechanics of nonclassical waves or particles, (2) given the informationtheoretic constraints, any mechanical theory of quantum phenomena that includes an account of the measuring instruments that reveal these phenomena must be empirically equivalent to a quantum theory, and (3) assuming the informationtheoretic constraints are in fact satisfied in our world, no mechanical theory of quantum phenomena that includes an account of measurement interactions can be acceptable, and the appropriate aim of physics at the fundamental level then becomes the representation and manipulation of information.
NonBoolean Descriptions for MindMatter Problems
"... A framework for the mindmatter problem in a holistic universe which has no parts is outlined. The conceptual structure of modern quantum theory suggests to use complementary Boolean descriptions as elements for a more comprehensive nonBoolean description of a world without an apriorigiven mindmat ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
A framework for the mindmatter problem in a holistic universe which has no parts is outlined. The conceptual structure of modern quantum theory suggests to use complementary Boolean descriptions as elements for a more comprehensive nonBoolean description of a world without an apriorigiven mindmatter distinction. Such a description in terms of a locally Boolean but globally nonBoolean structure makes allowance for the fact that Boolean descriptions play a privileged role in science. If we accept the insight that there are no ultimate building blocks, the existence of holistic correlations between contextually chosen parts is a natural consequence. The main problem of a genuinely nonBoolean description is to find an appropriate partition of the universe of discourse. If we adopt the idea that all fundamental laws of physics are invariant under time translations, then we can consider a partition of the world into a tenseless and a tensed domain. In the sense of a regulative principle, the material domain is defined as the tenseless domain with its homogeneous time. The tensed domain contains the mental domain with a tensed time characterized by a privileged position, the Now. Since this partition refers to two complementary descriptions which are not given apriori,wehavetoexpectcorrelations between these two domains. In physics it corresponds to Newton’s separation of universal laws of nature and contingent initial conditions. Both descriptions have a nonBoolean structure and can be encompassed into a single nonBoolean description. Tensed and tenseless time can be synchronized by holistic correlations. 1.
Quantum Mechanics as a Principle Theory
, 2000
"... I show how quantum mechanics, like the theory of relativity, can be understood as a 'principle theory' in Einstein's sense, and I use this notion to explore the approach to the problem of interpretation developed in my book ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
I show how quantum mechanics, like the theory of relativity, can be understood as a 'principle theory' in Einstein's sense, and I use this notion to explore the approach to the problem of interpretation developed in my book
Quantum mechanics is about quantum information. Forthcoming
 in Foundations of Physics. quantph/0408020
"... I argue that quantum mechanics is fundamentally a theory about the representation and manipulation of information, not a theory about the mechanics of nonclassical waves or particles. The notion of quantum information is to be understood as a new physical primitive—just as, following Einstein’s spec ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
I argue that quantum mechanics is fundamentally a theory about the representation and manipulation of information, not a theory about the mechanics of nonclassical waves or particles. The notion of quantum information is to be understood as a new physical primitive—just as, following Einstein’s special theory of relativity, a field is no longer regarded as the physical manifestation of vibrations in a mechanical medium, but recognized as a new physical primitive in its own right. 1
Quantum information and computation
 arXiv:quantph/0512125. Forthcoming in Butterfield and Earman (eds.) Handbook of Philosophy of Physics
, 2005
"... This Chapter 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, ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
This Chapter 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