794 research outputs found
Generic Bell correlation between arbitrary local algebras in quantum field theory
We prove that for any two commuting von Neumann algebras of infinite type,
the open set of Bell correlated states for the two algebras is norm dense. We
then apply this result to algebraic quantum field theory -- where all local
algebras are of infinite type -- in order to show that for any two spacelike
separated regions, there is an open dense set of field states that dictate Bell
correlations between the regions. We also show that any vector state cyclic for
one of a pair of commuting nonabelian von Neumann algebras is entangled (i.e.,
nonseparable) across the algebras -- from which it follows that every field
state with bounded energy is entangled across any two spacelike separated
regions.Comment: Third version; correction in the proof of Proposition
Non-local Correlations are Generic in Infinite-Dimensional Bipartite Systems
It was recently shown that the nonseparable density operators for a bipartite
system are trace norm dense if either factor space has infinite dimension. We
show here that non-local states -- i.e., states whose correlations cannot be
reproduced by any local hidden variable model -- are also dense. Our
constructions distinguish between the cases where both factor spaces are
infinite-dimensional, where we show that states violating the CHSH inequality
are dense, and the case where only one factor space is infinite-dimensional,
where we identify open neighborhoods of nonseparable states that do not violate
the CHSH inequality but show that states with a subtler form of non-locality
(often called "hidden" non-locality) remain dense.Comment: 8 pages, RevTe
In defense of the epistemic view of quantum states: a toy theory
We present a toy theory that is based on a simple principle: the number of
questions about the physical state of a system that are answered must always be
equal to the number that are unanswered in a state of maximal knowledge. A wide
variety of quantum phenomena are found to have analogues within this toy
theory. Such phenomena include: the noncommutativity of measurements,
interference, the multiplicity of convex decompositions of a mixed state, the
impossibility of discriminating nonorthogonal states, the impossibility of a
universal state inverter, the distinction between bi-partite and tri-partite
entanglement, the monogamy of pure entanglement, no cloning, no broadcasting,
remote steering, teleportation, dense coding, mutually unbiased bases, and many
others. The diversity and quality of these analogies is taken as evidence for
the view that quantum states are states of incomplete knowledge rather than
states of reality. A consideration of the phenomena that the toy theory fails
to reproduce, notably, violations of Bell inequalities and the existence of a
Kochen-Specker theorem, provides clues for how to proceed with this research
program.Comment: 32 pages, REVTEX, based on a talk given at the Rob Clifton Memorial
Conference, College Park, May 2003; v2: minor modifications throughout,
updated reference
On the nature of continuous physical quantities in classical and quantum mechanics
Within the traditional Hilbert space formalism of quantum mechanics, it is
not possible to describe a particle as possessing, simultaneously, a sharp
position value and a sharp momentum value. Is it possible, though, to describe
a particle as possessing just a sharp position value (or just a sharp momentum
value)? Some, such as Teller (Journal of Philosophy, 1979), have thought that
the answer to this question is No -- that the status of individual continuous
quantities is very different in quantum mechanics than in classical mechanics.
On the contrary, I shall show that the same subtle issues arise with respect to
continuous quantities in classical and quantum mechanics; and that it is, after
all, possible to describe a particle as possessing a sharp position value
without altering the standard formalism of quantum mechanics.Comment: 26 pages, LaTe
Remarks on Causality in Relativistic Quantum Field Theory
It is shown that the correlations predicted by relativistic quantum field
theory in locally normal states between projections in local von Neumann
algebras \cA(V_1),\cA(V_2) associated with spacelike separated spacetime
regions have a (Reichenbachian) common cause located in the union of
the backward light cones of and . Further comments on causality and
independence in quantum field theory are made.Comment: 10 pages, Latex, Quantum Structures 2002 Conference Proceedings
submission. Minor revision of the order of definitions on p.
Connes' embedding problem and Tsirelson's problem
We show that Tsirelson's problem concerning the set of quantum correlations
and Connes' embedding problem on finite approximations in von Neumann algebras
(known to be equivalent to Kirchberg's QWEP conjecture) are essentially
equivalent. Specifically, Tsirelson's problem asks whether the set of bipartite
quantum correlations generated between tensor product separated systems is the
same as the set of correlations between commuting C*-algebras. Connes'
embedding problem asks whether any separable II factor is a subfactor of
the ultrapower of the hyperfinite II factor. We show that an affirmative
answer to Connes' question implies a positive answer to Tsirelson's.
Conversely, a positve answer to a matrix valued version of Tsirelson's problem
implies a positive one to Connes' problem
Microlocal analysis of quantum fields on curved spacetimes: Analytic wavefront sets and Reeh-Schlieder theorems
We show in this article that the Reeh-Schlieder property holds for states of
quantum fields on real analytic spacetimes if they satisfy an analytic
microlocal spectrum condition. This result holds in the setting of general
quantum field theory, i.e. without assuming the quantum field to obey a
specific equation of motion. Moreover, quasifree states of the Klein-Gordon
field are further investigated in this work and the (analytic) microlocal
spectrum condition is shown to be equivalent to simpler conditions. We also
prove that any quasifree ground- or KMS-state of the Klein-Gordon field on a
stationary real analytic spacetime fulfills the analytic microlocal spectrum
condition.Comment: 31 pages, latex2
Electron-lattice relaxation, and soliton structures and their interactions in polyenes
Density matrix renormalisation group calculations of a suitably parametrised
model of long polyenes (polyacetylene oligomers), which incorporates both long
range Coulomb interactions and adiabatic lattice relaxation, are presented. The
triplet and 2Ag states are found to have a 2-soliton and 4-soliton form,
respectively, both with large relaxation energies. The 1Bu state forms an
exciton-polaron and has a very small relaxation energy. The relaxed energy of
the 2Ag state lies below that of the 1Bu state. The soliton/anti-soliton pairs
are bound.Comment: RevTeX, 5 pages, 4 eps figures included using epsf. To appear in
Physical Review Letters. Fig. 1 fixed u
Categorical formulation of quantum algebras
We describe how dagger-Frobenius monoids give the correct categorical
description of certain kinds of finite-dimensional 'quantum algebras'. We
develop the concept of an involution monoid, and use it to construct a
correspondence between finite-dimensional C*-algebras and certain types of
dagger-Frobenius monoids in the category of Hilbert spaces. Using this
technology, we recast the spectral theorems for commutative C*-algebras and for
normal operators into an explicitly categorical language, and we examine the
case that the results of measurements do not form finite sets, but rather
objects in a finite Boolean topos. We describe the relevance of these results
for topological quantum field theory.Comment: 34 pages, to appear in Communications in Mathematical Physic
A model balancing cooperation and competition explains our right-handed world and the dominance of left-handed athletes
An overwhelming majority of humans are right-handed. Numerous explanations
for individual handedness have been proposed, but this population-level
handedness remains puzzling. Here we use a minimal mathematical model to
explain this population-level hand preference as an evolved balance between
cooperative and competitive pressures in human evolutionary history. We use
selection of elite athletes as a test-bed for our evolutionary model and
account for the surprising distribution of handedness in many professional
sports. Our model predicts strong lateralization in social species with limited
combative interaction, and elucidates the rarity of compelling evidence for
"pawedness" in the animal world.Comment: 5 pages of text and 3 figures in manuscript, 8 pages of text and two
figures in supplementary materia
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