544 research outputs found
Types of quantum information
Quantum, in contrast to classical, information theory, allows for different
incompatible types (or species) of information which cannot be combined with
each other. Distinguishing these incompatible types is useful in understanding
the role of the two classical bits in teleportation (or one bit in one-bit
teleportation), for discussing decoherence in information-theoretic terms, and
for giving a proper definition, in quantum terms, of ``classical information.''
Various examples (some updating earlier work) are given of theorems which
relate different incompatible kinds of information, and thus have no
counterparts in classical information theory.Comment: Minor changes so as to agree with published versio
EPR, Bell, and Quantum Locality
Maudlin has claimed that no local theory can reproduce the predictions of
standard quantum mechanics that violate Bell's inequality for Bohm's version
(two spin-half particles in a singlet state) of the Einstein-Podolsky-Rosen
problem. It is argued that, on the contrary, standard quantum mechanics itself
is a counterexample to Maudlin's claim, because it is local in the appropriate
sense (measurements at one place do not influence what occurs elsewhere there)
when formulated using consistent principles in place of the inconsistent
appeals to "measurement" found in current textbooks. This argument sheds light
on the claim of Blaylock that counterfactual definiteness is an essential
ingredient in derivations of Bell's inequality.Comment: Minor revisions to previous versio
There exist non orthogonal quantum measurements that are perfectly repeatable
We show that, contrarily to the widespread belief, in quantum mechanics
repeatable measurements are not necessarily described by orthogonal
projectors--the customary paradigm of "observable". Nonorthogonal
repeatability, however, occurs only for infinite dimensions. We also show that
when a non orthogonal repeatable measurement is performed, the measured system
retains some "memory" of the number of times that the measurement has been
performed.Comment: 4 pages, 1 figure, revtex4, minor change
Unsharp Quantum Reality
The positive operator (valued) measures (POMs) allow one to generalize the notion of observable beyond the traditional one based on projection valued measures (PVMs). Here, we argue that this generalized conception of observable enables a consistent notion of unsharp reality and with it an adequate concept of joint properties. A sharp or unsharp property manifests itself as an element of sharp or unsharp reality by its tendency to become actual or to actualize a specific measurement outcome. This actualization tendency-or potentiality-of a property is quantified by the associated quantum probability. The resulting single-case interpretation of probability as a degree of reality will be explained in detail and its role in addressing the tensions between quantum and classical accounts of the physical world will be elucidated. It will be shown that potentiality can be viewed as a causal agency that evolves in a well-defined way
Type-Decomposition of a Pseudo-Effect Algebra
The theory of direct decomposition of a centrally orthocomplete effect
algebra into direct summands of various types utilizes the notion of a
type-determining (TD) set. A pseudo-effect algebra (PEA) is a (possibly)
noncommutative version of an effect algebra. In this article we develop the
basic theory of centrally orthocomplete PEAs, generalize the notion of a TD set
to PEAs, and show that TD sets induce decompositions of centrally orthocomplete
PEAs into direct summands.Comment: 18 page
Firm size diversity, functional richness, and resilience
This paper applies recent advances in ecology to our understanding of firm development, sustainability, and economic development. The ecological literature indicates that the greater the functional richness of species in a system, the greater its resilience â that is, its ability to persist in the face of substantial changes in the environment. This paper focuses on the effects of functional richness across firm size on the ability of industries to survive in the face of economic change. Our results indicate that industries with a richness of industrial functions are more resilient to employment volatility
Channel kets, entangled states, and the location of quantum information
The well-known duality relating entangled states and noisy quantum channels
is expressed in terms of a channel ket, a pure state on a suitable tripartite
system, which functions as a pre-probability allowing the calculation of
statistical correlations between, for example, the entrance and exit of a
channel, once a framework has been chosen so as to allow a consistent set of
probabilities. In each framework the standard notions of ordinary (classical)
information theory apply, and it makes sense to ask whether information of a
particular sort about one system is or is not present in another system.
Quantum effects arise when a single pre-probability is used to compute
statistical correlations in different incompatible frameworks, and various
constraints on the presence and absence of different kinds of information are
expressed in a set of all-or-nothing theorems which generalize or give a
precise meaning to the concept of ``no-cloning.'' These theorems are used to
discuss: the location of information in quantum channels modeled using a
mixed-state environment; the (classical-quantum) channels introduced by
Holevo; and the location of information in the physical carriers of a quantum
code. It is proposed that both channel and entanglement problems be classified
in terms of pure states (functioning as pre-probabilities) on systems of parts, with mixed bipartite entanglement and simple noisy channels belonging
to the category , a five-qubit code to the category , etc.; then by
the dimensions of the Hilbert spaces of the component parts, along with other
criteria yet to be determined.Comment: Latex 32 pages, 4 figures in text using PSTricks. Version 3: Minor
typographical errors correcte
A quantum logical and geometrical approach to the study of improper mixtures
We study improper mixtures from a quantum logical and geometrical point of
view. Taking into account the fact that improper mixtures do not admit an
ignorance interpretation and must be considered as states in their own right,
we do not follow the standard approach which considers improper mixtures as
measures over the algebra of projections. Instead of it, we use the convex set
of states in order to construct a new lattice whose atoms are all physical
states: pure states and improper mixtures. This is done in order to overcome
one of the problems which appear in the standard quantum logical formalism,
namely, that for a subsystem of a larger system in an entangled state, the
conjunction of all actual properties of the subsystem does not yield its actual
state. In fact, its state is an improper mixture and cannot be represented in
the von Neumann lattice as a minimal property which determines all other
properties as is the case for pure states or classical systems. The new lattice
also contains all propositions of the von Neumann lattice. We argue that this
extension expresses in an algebraic form the fact that -alike the classical
case- quantum interactions produce non trivial correlations between the
systems. Finally, we study the maps which can be defined between the extended
lattice of a compound system and the lattices of its subsystems.Comment: submitted to the Journal of Mathematical Physic
The Definition of Mach's Principle
Two definitions of Mach's principle are proposed. Both are related to gauge
theory, are universal in scope and amount to formulations of causality that
take into account the relational nature of position, time, and size. One of
them leads directly to general relativity and may have relevance to the problem
of creating a quantum theory of gravity.Comment: To be published in Foundations of Physics as invited contribution to
Peter Mittelstaedt's 80th Birthday Festschrift. 30 page
The development of path integration: combining estimations of distance and heading
Efficient daily navigation is underpinned by path integration, the mechanism by which we use self-movement information to update our position in space. This process is well-understood in adulthood, but there has been relatively little study of path integration in childhood, leading to an underrepresentation in accounts of navigational development. Previous research has shown that calculation of distance and heading both tend to be less accurate in children as they are in adults, although there have been no studies of the combined calculation of distance and heading that typifies naturalistic path integration. In the present study 5-year-olds and 7-year-olds took part in a triangle-completion task, where they were required to return to the startpoint of a multi-element path using only idiothetic information. Performance was compared to a sample of adult participants, who were found to be more accurate than children on measures of landing error, heading error, and distance error. 7-year-olds were significantly more accurate than 5-year-olds on measures of landing error and heading error, although the difference between groups was much smaller for distance error. All measures were reliably correlated with age, demonstrating a clear development of path integration abilities within the age range tested. Taken together, these data make a strong case for the inclusion of path integration within developmental models of spatial navigational processing
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