616 research outputs found
Quantum Counterfactuals and Locality
Stapp's counterfactual argument for quantum nonlocality based upon a Hardy
entangled state is shown to be flawed. While he has correctly analyzed a
particular framework using the method of consistent histories, there are
alternative frameworks which do not support his argument. The framework
dependence of quantum counterfactual arguments, with analogs in classical
counterfactuals, vitiates the claim that nonlocal (superluminal) influences
exist in the quantum world. Instead it shows that counterfactual arguments are
of limited use for analyzing these questions.Comment: 8 pages, 1 PSTricks figur
The Nature and Location of Quantum Information
Quantum information is defined by applying the concepts of ordinary (Shannon)
information theory to a quantum sample space consisting of a single framework
or consistent family. A classical analogy for a spin-half particle and other
arguments show that the infinite amount of information needed to specify a
precise vector in its Hilbert space is not a measure of the information carried
by a quantum entity with a -dimensional Hilbert space; the latter is,
instead, bounded by log d bits (1 bit per qubit). The two bits of information
transmitted in dense coding are located not in one but in the correlation
between two qubits, consistent with this bound. A quantum channel can be
thought of as a "structure" or collection of frameworks, and the physical
location of the information in the individual frameworks can be used to
identify the location of the channel. Analysis of a quantum circuit used as a
model of teleportation shows that the location of the channel depends upon
which structure is employed; for ordinary teleportation it is not (contrary to
Deutsch and Hayden) present in the two bits resulting from the Bell-basis
measurement, but in correlations of these with a distant qubit. In neither
teleportation nor dense coding does information travel backwards in time, nor
is it transmitted by nonlocal (superluminal) influences. It is (tentatively)
proposed that all aspects of quantum information can in principle be understood
in terms of the (basically classical) behavior of information in a particular
framework, along with the framework dependence of this information.Comment: Latex 29 pages, uses PSTricks for figure
A Generalized Circle Theorem on Zeros of Partition Function at Asymmetric First Order Transitions
We present a generalized circle theorem which includes the Lee-Yang theorem
for symmetric transitions as a special case. It is found that zeros of the
partition function can be written in terms of discontinuities in the
derivatives of the free energy. For asymmetric transitions, the locus of the
zeros is tangent to the unit circle at the positive real axis in the
thermodynamic limit. For finite-size systems, they lie off the unit circle if
the partition functions of the two phases are added up with unequal prefactors.
This conclusion is substantiated by explicit calculation of zeros of the
partition function for the Blume-Capel model near and at the triple line at low
temperatures.Comment: 10 pages, RevTeX. To be published in PRL. 3 Figures will be sent upon
reques
Decoherence of Histories and Hydrodynamic Equations for a Linear Oscillator Chain
We investigate the decoherence of histories of local densities for linear
oscillators models. It is shown that histories of local number, momentum and
energy density are approximately decoherent, when coarse-grained over
sufficiently large volumes. Decoherence arises directly from the proximity of
these variables to exactly conserved quantities (which are exactly decoherent),
and not from environmentally-induced decoherence. We discuss the approach to
local equilibrium and the subsequent emergence of hydrodynamic equations for
the local densities.Comment: 37 pages, RevTe
Uniformly accelerating black holes in a de Sitter universe
A class of exact solutions of Einstein's equations is analysed which
describes uniformly accelerating charged black holes in an asymptotically de
Sitter universe. This is a generalisation of the C-metric which includes a
cosmological constant. The physical interpretation of the solutions is
facilitated by the introduction of a new coordinate system for de Sitter space
which is adapted to accelerating observers in this background. The solutions
considered reduce to this form of the de Sitter metric when the mass and charge
of the black holes vanish.Comment: 6 pages REVTeX, 3 figures, to appear in Phys. Rev. D. Figure 2
correcte
Quantum Locality
It is argued that while quantum mechanics contains nonlocal or entangled
states, the instantaneous or nonlocal influences sometimes thought to be
present due to violations of Bell inequalities in fact arise from mistaken
attempts to apply classical concepts and introduce probabilities in a manner
inconsistent with the Hilbert space structure of standard quantum mechanics.
Instead, Einstein locality is a valid quantum principle: objective properties
of individual quantum systems do not change when something is done to another
noninteracting system. There is no reason to suspect any conflict between
quantum theory and special relativity.Comment: Introduction has been revised, references added, minor corrections
elsewhere. To appear in Foundations of Physic
The Global Renormalization Group Trajectory in a Critical Supersymmetric Field Theory on the Lattice Z^3
We consider an Euclidean supersymmetric field theory in given by a
supersymmetric perturbation of an underlying massless Gaussian measure
on scalar bosonic and Grassmann fields with covariance the Green's function of
a (stable) L\'evy random walk in . The Green's function depends on the
L\'evy-Khintchine parameter with . For
the interaction is marginal. We prove for
sufficiently small and initial
parameters held in an appropriate domain the existence of a global
renormalization group trajectory uniformly bounded on all renormalization group
scales and therefore on lattices which become arbitrarily fine. At the same
time we establish the existence of the critical (stable) manifold. The
interactions are uniformly bounded away from zero on all scales and therefore
we are constructing a non-Gaussian supersymmetric field theory on all scales.
The interest of this theory comes from the easily established fact that the
Green's function of a (weakly) self-avoiding L\'evy walk in is a second
moment (two point correlation function) of the supersymmetric measure governing
this model. The control of the renormalization group trajectory is a
preparation for the study of the asymptotics of this Green's function. The
rigorous control of the critical renormalization group trajectory is a
preparation for the study of the critical exponents of the (weakly)
self-avoiding L\'evy walk in .Comment: 82 pages, Tex with macros supplied. Revision includes 1. redefinition
of norms involving fermions to ensure uniqueness. 2. change in the definition
of lattice blocks and lattice polymer activities. 3. Some proofs have been
reworked. 4. New lemmas 5.4A, 5.14A, and new Theorem 6.6. 5.Typos
corrected.This is the version to appear in Journal of Statistical Physic
Problems with the definition of renormalized Hamiltonians for momentum-space renormalization transformations
For classical lattice systems with finite (Ising) spins, we show that the
implementation of momentum-space renormalization at the level of Hamiltonians
runs into the same type of difficulties as found for real-space
transformations: Renormalized Hamiltonians are ill-defined in certain regions
of the phase diagram.Comment: 14 pages, late
Renormalization group maps for Ising models in lattice gas variables
Real space renormalization group maps, e.g., the majority rule
transformation, map Ising type models to Ising type models on a coarser
lattice. We show that each coefficient of the renormalized Hamiltonian in the
lattice gas variables depends on only a finite number of values of the
renormalized Hamiltonian. We introduce a method which computes the values of
the renormalized Hamiltonian with high accuracy and so computes the
coefficients in the lattice gas variables with high accuracy. For the critical
nearest neighbor Ising model on the square lattice with the majority rule
transformation, we compute over 1,000 different coefficients in the lattice gas
variable representation of the renormalized Hamiltonian and study the decay of
these coefficients. We find that they decay exponentially in some sense but
with a slow decay rate. We also show that the coefficients in the spin
variables are sensitive to the truncation method used to compute them.Comment: 22 pages, 9 color postscript figures; minor revisions in version
The Hidden Subgroup Problem and Eigenvalue Estimation on a Quantum Computer
A quantum computer can efficiently find the order of an element in a group,
factors of composite integers, discrete logarithms, stabilisers in Abelian
groups, and `hidden' or `unknown' subgroups of Abelian groups. It is already
known how to phrase the first four problems as the estimation of eigenvalues of
certain unitary operators. Here we show how the solution to the more general
Abelian `hidden subgroup problem' can also be described and analysed as such.
We then point out how certain instances of these problems can be solved with
only one control qubit, or `flying qubits', instead of entire registers of
control qubits.Comment: 16 pages, 3 figures, LaTeX2e, to appear in Proceedings of the 1st
NASA International Conference on Quantum Computing and Quantum Communication
(Springer-Verlag
- …