Results 11  20
of
416
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 35 (2 self)
 Add to MetaCart
(Show Context)
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
A theory of hyperfinite processes: the complete removal of individual uncertainty via exact LLN
, 1998
"... The aim of this paper is to provide a viable measuretheoretic framework for the study of random phenomena involving a large number of economic entities. The work is based on the fact that processes which are measurable with respect to hyperfinite Loeb product spaces capture the limiting behaviors ..."
Abstract

Cited by 32 (13 self)
 Add to MetaCart
The aim of this paper is to provide a viable measuretheoretic framework for the study of random phenomena involving a large number of economic entities. The work is based on the fact that processes which are measurable with respect to hyperfinite Loeb product spaces capture the limiting behaviors of triangular arrays of random variables and thus constitute the `right' class for general stochastic modeling. The primary concern of the paper is to characterize those hyperfinite processes satisfying the exact law of large numbers by using the basic notions of conditional expectation, orthogonality, uncorrelatedness and independence together with some unifying multiplicative properties of random variables. The general structure of the processes is also analyzed via a biorthogonal expansion of the KarhunenLoeve type and via the representation in terms of the simpler hyperfinite Loeb counting spaces. A universality property for atomless Loeb product spaces is formulated to show the abun...
Nuclear and Trace Ideals in Tensored *Categories
, 1998
"... We generalize the notion of nuclear maps from functional analysis by defining nuclear ideals in tensored categories. The motivation for this study came from attempts to generalize the structure of the category of relations to handle what might be called "probabilistic relations". The comp ..."
Abstract

Cited by 30 (9 self)
 Add to MetaCart
We generalize the notion of nuclear maps from functional analysis by defining nuclear ideals in tensored categories. The motivation for this study came from attempts to generalize the structure of the category of relations to handle what might be called "probabilistic relations". The compact closed structure associated with the category of relations does not generalize directly, instead one obtains nuclear ideals. Most tensored categories have a large class of morphisms which behave as if they were part of a compact closed category, i.e. they allow one to transfer variables between the domain and the codomain. We introduce the notion of nuclear ideals to analyze these classes of morphisms. In compact closed tensored categories, all morphisms are nuclear, and in the tensored category of Hilbert spaces, the nuclear morphisms are the HilbertSchmidt maps. We also introduce two new examples of tensored categories, in which integration plays the role of composition. In the first, mor...
An introduction to quantum filtering
, 2006
"... This paper provides an introduction to quantum filtering theory. An introduction to quantum probability theory is given, focusing on the spectral theorem and the conditional expectation as a ..."
Abstract

Cited by 30 (14 self)
 Add to MetaCart
(Show Context)
This paper provides an introduction to quantum filtering theory. An introduction to quantum probability theory is given, focusing on the spectral theorem and the conditional expectation as a
On Reichenbach's common cause principle and Reichenbach's notion of common cause
"... It is shown that, given any finite set of pairs of random events in a Boolean algebra which are correlated with respect to a fixed probability measure on the algebra, the algebra can be extended in such a way that the extension contains events that can be regarded as common causes of the correlation ..."
Abstract

Cited by 27 (6 self)
 Add to MetaCart
It is shown that, given any finite set of pairs of random events in a Boolean algebra which are correlated with respect to a fixed probability measure on the algebra, the algebra can be extended in such a way that the extension contains events that can be regarded as common causes of the correlations in the sense of Reichenbach's definition of common cause. It is shown, further, that, given any quantum probability space and any set of commuting events in it which are correlated with respect to a fixed quantum state, the quantum probability space can be extended in such a way that the extension contains common causes of all the selected correlations, where common cause is again taken in the sense of Reichenbach's definition. It is argued that these results very strongly restrict the possible ways of disproving Reichenbach's Common Cause Principle.
Amenability for dual Banach algebras
 Run 2] [Sel] [Spr] [Woo 1] [Woo 2] V. Runde, Lectures on Amenability. Lecture Notes in Mathematics 1774
, 2002
"... We define a Banach algebra A to be dual if A = (A∗) ∗ for a closed submodule A ∗ of A ∗. The class of dual Banach algebras includes all W ∗algebras, but also all algebras M(G) for locally compact groups G, all algebras L(E) for reflexive Banach spaces E, as well as all biduals of Arens regular Ban ..."
Abstract

Cited by 26 (6 self)
 Add to MetaCart
We define a Banach algebra A to be dual if A = (A∗) ∗ for a closed submodule A ∗ of A ∗. The class of dual Banach algebras includes all W ∗algebras, but also all algebras M(G) for locally compact groups G, all algebras L(E) for reflexive Banach spaces E, as well as all biduals of Arens regular Banach algebras. The general impression is that amenable, dual Banach algebras are rather the exception than the rule. We confirm this impression. We first show that under certain conditions an amenable dual Banach algebra is already superamenable and thus finitedimensional. We then develop two notions of amenability — Connesamenability and strong Connesamenability — which take the w ∗topology on dual Banach algebras into account. We relate the amenability of an Arens regular Banach algebra A to the (strong) Connesamenability of A ∗ ∗ ; as an application, we show that there are reflexive Banach spaces with the approximation property such that L(E) is not Connesamenable. We characterize the amenability of inner amenable locally compact groups in terms of their algebras of pseudomeasures. Finally, we give a proof of the known fact that the amenable von Neumann algebras are the subhomogeneous ones which avoids the equivalence of amenability and nuclearity for C ∗algebras.
Strong singularity for subalgebras of finite factors
 Internat. J. Math
"... In this paper we develop the theory of strongly singular subalgebras of von Neumann algebras, begun in earlier work. We mainly examine the situation of type II1 factors arising from countable discrete groups. We give simple criteria for strong singularity, and use them to construct strongly singular ..."
Abstract

Cited by 23 (6 self)
 Add to MetaCart
(Show Context)
In this paper we develop the theory of strongly singular subalgebras of von Neumann algebras, begun in earlier work. We mainly examine the situation of type II1 factors arising from countable discrete groups. We give simple criteria for strong singularity, and use them to construct strongly singular subalgebras. We particularly focus on groups which act on geometric objects, where the underlying geometry leads to strong singularity.
Tensor Product Space ANOVA Models
 Constraints of Human Hand Motion,” 5th Annual Federated Laboratory Symposium (ARL2001
"... this paper, we study the optimal rate of TPSANOVA model and the rate of convergence of the penalized likelihood estimator in fitting TPSANOVA model under general condition. We concentrate on regression and white noise settings. The rate of convergence of the penalized likelihood estimator in fittin ..."
Abstract

Cited by 23 (6 self)
 Add to MetaCart
this paper, we study the optimal rate of TPSANOVA model and the rate of convergence of the penalized likelihood estimator in fitting TPSANOVA model under general condition. We concentrate on regression and white noise settings. The rate of convergence of the penalized likelihood estimator in fitting TPSANOVA in other settings (such as generalized regression, density estimation, and hazard regression,) will be established in a separate paper. We show that the minimax mean integrated squared error for the TPSANOVA model goes to 0 at a rate that is within a log factor of the one dimensional optimal rate. This quick optimal rate for TPSANOVA makes the TPSANOVA model very preferable in high dimensional function estimation. We also show that the penalized likelihood estimator in TPSANOVA achieves this rate. This means that the penalized likelihood method has very good statistical properties. Since the optimal rate is a property of the model itself and does not depend on the method used to fit the model, and the formulation of the TPS6 ANOVA models actually does not depend on the smoothing spline method, we may also fit the model with nonparametric schemes other than smoothing splines, and it is reasonable to hypothesize that some other nonparametric methods can also achieve this favorable rate of convergence. Now let us explain intuitively how it can be that the TPSANOVA model includes higher order interactions and still has an optimal rate that is close to the one dimensional optimal rate. For this, let us introduce some concept first. For a nonnegative integer m, the Sobolev Hilbert space of univariate functions with order m and domain [0; 1], denoted by H
Entanglement and open systems in algebraic quantum field theory
 Studies in History and Philosophy of Modern Physics 32: 1–31
, 2001
"... Entanglement has long been the subject of discussion by philosophers of quantum theory, and has recently come to play an essential role for physicists in their development of quantum information theory. In this paper we show how the formalism of algebraic quantum "eld theory (AQFT) provides a r ..."
Abstract

Cited by 22 (4 self)
 Add to MetaCart
Entanglement has long been the subject of discussion by philosophers of quantum theory, and has recently come to play an essential role for physicists in their development of quantum information theory. In this paper we show how the formalism of algebraic quantum "eld theory (AQFT) provides a rigorous framework within which to analyse entanglement in the context of a fully relativistic formulation of quantum theory. What emerges from the analysis are new practical and theoretical limitations on an experimenter's ability to perform operations on a "eld in one spacetime region that can disentangle its state from the state of the "eld in other spacelikeseparated regions. These limitations show just how deeply entrenched entanglement is in relativistic quantum "eld theory, and yield a fresh perspective on the ways in which the theory di!ers conceptually from both standard nonrelativistic quantum theory and classical relativistic "eld theory. � 2001 Elsevier