28,082 research outputs found
Manifold dimension of a causal set: Tests in conformally flat spacetimes
This paper describes an approach that uses flat-spacetime dimension
estimators to estimate the manifold dimension of causal sets that can be
faithfully embedded into curved spacetimes. The approach is invariant under
coarse graining and can be implemented independently of any specific curved
spacetime. Results are given based on causal sets generated by random
sprinklings into conformally flat spacetimes in 2, 3, and 4 dimensions, as well
as one generated by a percolation dynamics.Comment: 8 pages, 8 figure
Criteria for generalized macroscopic and mesoscopic quantum coherence
We consider macroscopic, mesoscopic and "S-scopic" quantum superpositions of
eigenstates of an observable, and develop some signatures for their existence.
We define the extent, or size of a superposition, with respect to an
observable \hat{x}, as being the range of outcomes of \hat{x} predicted by that
superposition. Such superpositions are referred to as generalized -scopic
superpositions to distinguish them from the extreme superpositions that
superpose only the two states that have a difference in their prediction
for the observable. We also consider generalized -scopic superpositions of
coherent states. We explore the constraints that are placed on the statistics
if we suppose a system to be described by mixtures of superpositions that are
restricted in size. In this way we arrive at experimental criteria that are
sufficient to deduce the existence of a generalized -scopic superposition.
The signatures developed are useful where one is able to demonstrate a degree
of squeezing. We also discuss how the signatures enable a new type of
Einstein-Podolsky-Rosen gedanken experiment.Comment: 15 pages, accepted for publication in Phys. Rev.
Bell inequalities for continuous-variable correlations
We derive a new class of correlation Bell-type inequalities. The inequalities
are valid for any number of outcomes of two observables per each of n parties,
including continuous and unbounded observables. We show that there are no
first-moment correlation Bell inequalities for that scenario, but such
inequalities can be found if one considers at least second moments. The
derivation stems from a simple variance inequality by setting local commutators
to zero. We show that above a constant detector efficiency threshold, the
continuous variable Bell violation can survive even in the macroscopic limit of
large n. This method can be used to derive other well-known Bell inequalities,
shedding new light on the importance of non-commutativity for violations of
local realism.Comment: 4 pages, 1 figure. v2: New results on detector efficiencies and
macroscopic limit, new co-author, changed title and abstract, changed figure,
added journal reference and DO
Spin entanglement, decoherence and Bohm's EPR paradox
We obtain criteria for entanglement and the EPR paradox
for spin-entangled particles and analyse the effects of decoherence caused
by absorption and state purity errors. For a two qubit photonic state,
entanglement can occur for all transmission efficiencies. In this case,
the state preparation purity must be above a threshold value. However,
Bohm’s spin EPR paradox can be achieved only above a critical level of
loss. We calculate a required efficiency of 58%, which appears achievable
with current quantum optical technologies. For a macroscopic number of
particles prepared in a correlated state, spin entanglement and the EPR
paradox can be demonstrated using our criteria for efficiencies η > 1/3
and η > 2/3 respectively. This indicates a surprising insensitivity to loss
decoherence, in a macroscopic system of ultra-cold atoms or photons
Lie discrete symmetries of lattice equations
We extend two of the methods previously introduced to find discrete
symmetries of differential equations to the case of difference and
differential-difference equations. As an example of the application of the
methods, we construct the discrete symmetries of the discrete Painlev\'e I
equation and of the Toda lattice equation
Effects of reset stators and a rotating, grooved stator hub on performance of a 1.92-pressure-ratio compressor stage
The overall performance and blade-element performance of a transonic fan stage are presented for two modified test configurations and are compared with the unmodified stage. Tests were conducted with reset stators 2 deg open and reset stators with a rotating grooved stator hub. Detailed radial and circumferential (behind stator) surveys of the flow conditions were made over the stable operating range at rotative speeds of 70, 90, and 100 percent of design speed. Reset stator blade tests indicated a small increase in stage efficiency, pressure ratio, and maximum weight flow at each speed. Performance with reset stators and a rotating, grooved stator hub resulted in an additional increase in stage efficiency and pressure ratio at all speeds. The rotating grooved stator hub reduced hub losses considerably
Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox
We formally link the concept of steering (a concept created by Schrodinger
but only recently formalised by Wiseman, Jones and Doherty [Phys. Rev. Lett.
98, 140402 (2007)] and the criteria for demonstrations of
Einstein-Podolsky-Rosen (EPR) paradox introduced by Reid [Phys. Rev. A, 40, 913
(1989)]. We develop a general theory of experimental EPR-steering criteria,
derive a number of criteria applicable to discrete as well as
continuous-variables observables, and study their efficacy in detecting that
form of nonlocality in some classes of quantum states. We show that previous
versions of EPR-type criteria can be rederived within this formalism, thus
unifying these efforts from a modern quantum-information perspective and
clarifying their conceptual and formal origin. The theory follows in close
analogy with criteria for other forms of quantum nonlocality (Bell-nonlocality,
entanglement), and because it is a hybrid of those two, it may lead to insights
into the relationship between the different forms of nonlocality and the
criteria that are able to detect them.Comment: Changed title, updated references, minor corrections, added
journal-ref and DO
Violations of Bell Inequalities for Measurements with Macroscopic Uncertainties: What does it Mean to Violate Macroscopic Local Realism?
We suggest to test the premise of ``macroscopic local realism'' which is
sufficient to derive Bell inequalities when measurements of photon number are
only accurate to an uncertainty of order photons, where is macroscopic.
Macroscopic local realism is only sufficient to imply, in the context of the
original Einstein-Podolsky-Rosen argument, fuzzy ``elements of reality'' which
have a macroscopic indeterminacy. We show therefore how the violation of local
realism in the presence of macroscopic uncertainties implies the failure of
``macroscopic local realism''. Quantum states violating this macroscopic local
realism are presented.Comment: 28 pages, 5 figures- new version is unchanged but tightened-20 pages,
5 figure
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