48,304 research outputs found
Quadrature domains and kernel function zipping
It is proved that quadrature domains are ubiquitous in a very strong sense in
the realm of smoothly bounded multiply connected domains in the plane. In fact,
they are so dense that one might as well assume that any given smooth domain
one is dealing with is a quadrature domain, and this allows access to a host of
strong conditions on the classical kernel functions associated to the domain.
Following this string of ideas leads to the discovery that the Bergman kernel
can be zipped down to a strikingly small data set. It is also proved that the
kernel functions associated to a quadrature domain must be algebraic.Comment: 13 pages, to appear in Arkiv for matemati
Construction of optimal witness for unknown two-qubit entanglement
Whether entanglement in a state can be detected, distilled, and quantified
without full state reconstruction is a fundamental open problem. We demonstrate
a new scheme encompassing these three tasks for arbitrary two-qubit
entanglement, by constructing the optimal entanglement witness for
polarization-entangled mixed-state photon pairs without full state
reconstruction. With better efficiency than quantum state tomography, the
entanglement is maximally distilled by newly developed tunable polarization
filters, and quantified by the expectation value of the witness, which equals
the concurrence. This scheme is extendible to multiqubit
Greenberger-Horne-Zeilinger entanglement.Comment: Phys. Rev. Lett. 105, 230404 (2010); supplementary information
(OWitness_sup.pdf) is included in source zip fil
Super-activation of quantum non-locality
In this paper we show that quantum non-locality can be super-activated. That
is, one can obtain violations of Bell inequalities by tensorizing a local state
with itself. Moreover, previous results suggest that such Bell violations can
be very large.Comment: v2: Refs added. Same results, v3: Minor corrections. Close to the
published versio
Faithful test of non-local realism with entangled coherent states
We investigate the violation of Leggett's inequality for non-local realism
using entangled coherent states and various types of local measurements. We
prove mathematically the relation between the violation of the
Clauser-Horne-Shimony-Holt form of Bell's inequality and Leggett's one when
tested by the same resources. For Leggett inequalities, we generalize the
non-local realistic bound to systems in Hilbert spaces larger than
bidimensional ones and introduce an optimization technique that allows to
achieve larger degrees of violation by adjusting the local measurement
settings. Our work describes the steps that should be performed to produce a
self-consistent generalization of Leggett's original arguments to
continuous-variable states.Comment: 8 pages, 6 figures, to be published in Phys. Rev.
Causal Quantum Theory and the Collapse Locality Loophole
Causal quantum theory is an umbrella term for ordinary quantum theory
modified by two hypotheses: state vector reduction is a well-defined process,
and strict local causality applies. The first of these holds in some versions
of Copenhagen quantum theory and need not necessarily imply practically
testable deviations from ordinary quantum theory. The second implies that
measurement events which are spacelike separated have no non-local
correlations. To test this prediction, which sharply differs from standard
quantum theory, requires a precise theory of state vector reduction.
Formally speaking, any precise version of causal quantum theory defines a
local hidden variable theory. However, causal quantum theory is most naturally
seen as a variant of standard quantum theory. For that reason it seems a more
serious rival to standard quantum theory than local hidden variable models
relying on the locality or detector efficiency loopholes.
Some plausible versions of causal quantum theory are not refuted by any Bell
experiments to date, nor is it obvious that they are inconsistent with other
experiments. They evade refutation via a neglected loophole in Bell experiments
-- the {\it collapse locality loophole} -- which exists because of the possible
time lag between a particle entering a measuring device and a collapse taking
place. Fairly definitive tests of causal versus standard quantum theory could
be made by observing entangled particles separated by light
seconds.Comment: Discussion expanded; typos corrected; references adde
Bell's Jump Process in Discrete Time
The jump process introduced by J. S. Bell in 1986, for defining a quantum
field theory without observers, presupposes that space is discrete whereas time
is continuous. In this letter, our interest is to find an analogous process in
discrete time. We argue that a genuine analog does not exist, but provide
examples of processes in discrete time that could be used as a replacement.Comment: 7 pages LaTeX, no figure
No Signalling and Quantum Key Distribution
Standard quantum key distribution protocols are provably secure against
eavesdropping attacks, if quantum theory is correct. It is theoretically
interesting to know if we need to assume the validity of quantum theory to
prove the security of quantum key distribution, or whether its security can be
based on other physical principles. The question would also be of practical
interest if quantum mechanics were ever to fail in some regime, because a
scientifically and technologically advanced eavesdropper could perhaps use
post-quantum physics to extract information from quantum communications without
necessarily causing the quantum state disturbances on which existing security
proofs rely. Here we describe a key distribution scheme provably secure against
general attacks by a post-quantum eavesdropper who is limited only by the
impossibility of superluminal signalling. The security of the scheme stems from
violation of a Bell inequality.Comment: Clarifications and minor revisions in response to comments. Final
version; to appear in Phys. Rev. Let
Causality and Cirel'son bounds
An EPR-Bell type experiment carried out on an entangled quantum system can
produce correlations stronger than allowed by local realistic theories. However
there are correlations that are no-signaling and are more non local than the
quantum correlations. Here we show that any correlations more non local than
those achievable in an EPR-Bell type experiment necessarily allow -in the
context of the quantum formalism- both for signaling and for generation of
entanglement. We use our approach to rederive Cirel'son bound for the CHSH
expression, and we derive a new Cirel'son type bound for qutrits. We discuss in
detail the interpretation of our approach.Comment: 5 page
Testing non-local realism with entangled coherent states
We investigate the violation of non-local realism using entangled coherent
states (ECS) under nonlinear operations and homodyne measurements. We address
recently proposed Leggett-type inequalities, including a class of optimized
incompatibility ones and thoroughly assess the effects of detection
inefficiency.Comment: 7 pages, 6 figures, RevTeX4, accepted for publication in Phys. Rev.
Two-Photon Beatings Using Biphotons Generated from a Two-Level System
We propose a two-photon beating experiment based upon biphotons generated
from a resonant pumping two-level system operating in a backward geometry. On
the one hand, the linear optical-response leads biphotons produced from two
sidebands in the Mollow triplet to propagate with tunable refractive indices,
while the central-component propagates with unity refractive index. The
relative phase difference due to different refractive indices is analogous to
the pathway-length difference between long-long and short-short in the original
Franson interferometer. By subtracting the linear Rayleigh scattering of the
pump, the visibility in the center part of the two-photon beating interference
can be ideally manipulated among [0, 100%] by varying the pump power, the
material length, and the atomic density, which indicates a Bell-type inequality
violation. On the other hand, the proposed experiment may be an interesting way
of probing the quantum nature of the detection process. The interference will
disappear when the separation of the Mollow peaks approaches the fundamental
timescales for photon absorption in the detector.Comment: to appear in Phys. Rev. A (2008
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