13,660 research outputs found
Energy-time entanglement, Elements of Reality, and Local Realism
The Franson interferometer, proposed in 1989 [J. D. Franson, Phys. Rev. Lett.
62:2205-2208 (1989)], beautifully shows the counter-intuitive nature of light.
The quantum description predicts sinusoidal interference for specific outcomes
of the experiment, and these predictions can be verified in experiment. In the
spirit of Einstein, Podolsky, and Rosen it is possible to ask if the
quantum-mechanical description (of this setup) can be considered complete. This
question will be answered in detail in this paper, by delineating the quite
complicated relation between energy-time entanglement experiments and
Einstein-Podolsky-Rosen (EPR) elements of reality. The mentioned sinusoidal
interference pattern is the same as that giving a violation in the usual Bell
experiment. Even so, depending on the precise requirements made on the local
realist model, this can imply a) no violation, b) smaller violation than usual,
or c) full violation of the appropriate statistical bound. Alternatives include
a) using only the measurement outcomes as EPR elements of reality, b) using the
emission time as EPR element of reality, c) using path realism, or d) using a
modified setup. This paper discusses the nature of these alternatives and how
to choose between them. The subtleties of this discussion needs to be taken
into account when designing and setting up experiments intended to test local
realism. Furthermore, these considerations are also important for quantum
communication, for example in Bell-inequality-based quantum cryptography,
especially when aiming for device independence.Comment: 18 pages, 7 figures, v2 rewritten and extende
Representations of hom-Lie algebras
In this paper, we study representations of hom-Lie algebras. In particular,
the adjoint representation and the trivial representation of hom-Lie algebras
are studied in detail. Derivations, deformations, central extensions and
derivation extensions of hom-Lie algebras are also studied as an application.Comment: 16 pages, multiplicative and regular hom-Lie algebras are used,
Algebra and Representation Theory, 15 (6) (2012), 1081-109
Inequalities for dealing with detector inefficiencies in Greenberger-Horne-Zeilinger-type experiments
In this article we show that the three-particle GHZ theorem can be
reformulated in terms of inequalities, allowing imperfect correlations due to
detector inefficiencies. We show quantitatively that taking into accout those
inefficiencies, the published results of the Innsbruck experiment support the
nonexistence of local hidden variables that explain the experimental result.Comment: LaTeX2e, 9 pages, 3 figures, to appear in Phys. Rev. Let
ASIC Implementation of Time-Domain Digital Backpropagation with Deep-Learned Chromatic Dispersion Filters
We consider time-domain digital backpropagation with chromatic dispersion
filters jointly optimized and quantized using machine-learning techniques.
Compared to the baseline implementations, we show improved BER performance and
>40% power dissipation reductions in 28-nm CMOS.Comment: 3 pages, 3 figures, updated reference list, added one sentence in the
result section for clarit
Reducing the Bias of Causality Measures
Measures of the direction and strength of the interdependence between two
time series are evaluated and modified in order to reduce the bias in the
estimation of the measures, so that they give zero values when there is no
causal effect. For this, point shuffling is employed as used in the frame of
surrogate data. This correction is not specific to a particular measure and it
is implemented here on measures based on state space reconstruction and
information measures. The performance of the causality measures and their
modifications is evaluated on simulated uncoupled and coupled dynamical systems
and for different settings of embedding dimension, time series length and noise
level. The corrected measures, and particularly the suggested corrected
transfer entropy, turn out to stabilize at the zero level in the absence of
causal effect and detect correctly the direction of information flow when it is
present. The measures are also evaluated on electroencephalograms (EEG) for the
detection of the information flow in the brain of an epileptic patient. The
performance of the measures on EEG is interpreted, in view of the results from
the simulation study.Comment: 30 pages, 12 figures, accepted to Physical Review
The monomial representations of the Clifford group
We show that the Clifford group - the normaliser of the Weyl-Heisenberg group
- can be represented by monomial phase-permutation matrices if and only if the
dimension is a square number. This simplifies expressions for SIC vectors, and
has other applications to SICs and to Mutually Unbiased Bases. Exact solutions
for SICs in dimension 16 are presented for the first time.Comment: Additional author and exact solutions to the SIC problem in dimension
16 adde
Approximating functions on stratified sets
We investigate smooth approximations of functions, with prescribed gradient
behavior on a distinguished stratified subset of the domain. As an application,
we outline how our results yield important consequences for a recently
introduced class of stochastic processes, called the matrix-valued Bessel
processes.Comment: This is the version appearing in Trans. Amer. Math. Soc. 367 (2015),
725-74
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