50,267 research outputs found
A quantum-inspired algorithm for estimating the permanent of positive semidefinite matrices
We construct a quantum-inspired classical algorithm for computing the
permanent of Hermitian positive semidefinite matrices, by exploiting a
connection between these mathematical structures and the boson sampling model.
Specifically, the permanent of a Hermitian positive semidefinite matrix can be
expressed in terms of the expected value of a random variable, which stands for
a specific photon-counting probability when measuring a linear-optically
evolved random multimode coherent state. Our algorithm then approximates the
matrix permanent from the corresponding sample mean and is shown to run in
polynomial time for various sets of Hermitian positive semidefinite matrices,
achieving a precision that improves over known techniques. This work
illustrates how quantum optics may benefit algorithms development.Comment: 9 pages, 1 figure. Updated version for publicatio
Proposal for a loophole-free Bell test using homodyne detection
We propose a feasible optical setup allowing for a loophole-free Bell test
with efficient homodyne detection. A non-gaussian entangled state is generated
from a two-mode squeezed vacuum by subtracting a single photon from each mode,
using beamsplitters and standard low-efficiency single-photon detectors. A Bell
violation exceeding 1% is achievable with 6-dB squeezed light and an homodyne
efficiency around 95%. A detailed feasibility analysis, based upon the recent
generation of single-mode non-gaussian states, confirms that this method opens
a promising avenue towards a complete experimental Bell test.Comment: 4 pages RevTex, 2 figure
Evolving wormhole geometries within nonlinear electrodynamics
In this work, we explore the possibility of evolving (2+1) and
(3+1)-dimensional wormhole spacetimes, conformally related to the respective
static geometries, within the context of nonlinear electrodynamics. For the
(3+1)-dimensional spacetime, it is found that the Einstein field equation
imposes a contracting wormhole solution and the obedience of the weak energy
condition. Nevertheless, in the presence of an electric field, the latter
presents a singularity at the throat, however, for a pure magnetic field the
solution is regular. For the (2+1)-dimensional case, it is also found that the
physical fields are singular at the throat. Thus, taking into account the
principle of finiteness, which states that a satisfactory theory should avoid
physical quantities becoming infinite, one may rule out evolving
(3+1)-dimensional wormhole solutions, in the presence of an electric field, and
the (2+1)-dimensional case coupled to nonlinear electrodynamics.Comment: 17 pages, 1 figure; to appear in Classical and Quantum Gravity. V2:
minor corrections, including a referenc
A new method for constructing small-bias spaces from Hermitian codes
We propose a new method for constructing small-bias spaces through a
combination of Hermitian codes. For a class of parameters our multisets are
much faster to construct than what can be achieved by use of the traditional
algebraic geometric code construction. So, if speed is important, our
construction is competitive with all other known constructions in that region.
And if speed is not a matter of interest the small-bias spaces of the present
paper still perform better than the ones related to norm-trace codes reported
in [12]
Norm estimates of complex symmetric operators applied to quantum systems
This paper communicates recent results in theory of complex symmetric
operators and shows, through two non-trivial examples, their potential
usefulness in the study of Schr\"odinger operators. In particular, we propose a
formula for computing the norm of a compact complex symmetric operator. This
observation is applied to two concrete problems related to quantum mechanical
systems. First, we give sharp estimates on the exponential decay of the
resolvent and the single-particle density matrix for Schr\"odinger operators
with spectral gaps. Second, we provide new ways of evaluating the resolvent
norm for Schr\"odinger operators appearing in the complex scaling theory of
resonances
Gauge invariant Boltzmann equation and the fluid limit
This article investigates the collisionless Boltzmann equation up to second
order in the cosmological perturbations. It describes the gauge dependence of
the distribution function and the construction of a gauge invariant
distribution function and brightness, and then derives the gauge invariant
fluid limit.Comment: 36 page
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