6,904 research outputs found

### Continuous-variable entropic uncertainty relations

Uncertainty relations are central to quantum physics. While they were
originally formulated in terms of variances, they have later been successfully
expressed with entropies following the advent of Shannon information theory.
Here, we review recent results on entropic uncertainty relations involving
continuous variables, such as position $x$ and momentum $p$. This includes the
generalization to arbitrary (not necessarily canonically-conjugate) variables
as well as entropic uncertainty relations that take $x$-$p$ correlations into
account and admit all Gaussian pure states as minimum uncertainty states. We
emphasize that these continuous-variable uncertainty relations can be
conveniently reformulated in terms of entropy power, a central quantity in the
information-theoretic description of random signals, which makes a bridge with
variance-based uncertainty relations. In this review, we take the quantum
optics viewpoint and consider uncertainties on the amplitude and phase
quadratures of the electromagnetic field, which are isomorphic to $x$ and $p$,
but the formalism applies to all such variables (and linear combinations
thereof) regardless of their physical meaning. Then, in the second part of this
paper, we move on to new results and introduce a tighter entropic uncertainty
relation for two arbitrary vectors of intercommuting continuous variables that
take correlations into account. It is proven conditionally on reasonable
assumptions. Finally, we present some conjectures for new entropic uncertainty
relations involving more than two continuous variables.Comment: Review paper, 42 pages, 1 figure. We corrected some minor errors in
V

### Multidimensional entropic uncertainty relation based on a commutator matrix in position and momentum spaces

The uncertainty relation for continuous variables due to Byalinicki-Birula
and Mycielski expresses the complementarity between two $n$-uples of
canonically conjugate variables $(x_1,x_2,\cdots x_n)$ and $(p_1,p_2,\cdots
p_n)$ in terms of Shannon differential entropy. Here, we consider the
generalization to variables that are not canonically conjugate and derive an
entropic uncertainty relation expressing the balance between any two
$n$-variable Gaussian projective measurements. The bound on entropies is
expressed in terms of the determinant of a matrix of commutators between the
measured variables. This uncertainty relation also captures the complementarity
between any two incompatible linear canonical transforms, the bound being
written in terms of the corresponding symplectic matrices in phase space.
Finally, we extend this uncertainty relation to R\'enyi entropies and also
prove a covariance-based uncertainty relation which generalizes Robertson
relation.Comment: 8 pages, 1 figur

### Representing molecule-surface interactions with symmetry-adapted neural networks

The accurate description of molecule-surface interactions requires a detailed
knowledge of the underlying potential-energy surface (PES). Recently, neural
networks (NNs) have been shown to be an efficient technique to accurately
interpolate the PES information provided for a set of molecular configurations,
e.g. by first-principles calculations. Here, we further develop this approach
by building the NN on a new type of symmetry functions, which allows to take
the symmetry of the surface exactly into account. The accuracy and efficiency
of such symmetry-adapted NNs is illustrated by the application to a
six-dimensional PES describing the interaction of oxygen molecules with the
Al(111) surface.Comment: 13 pages including 8 figures; related publications can be found at
http://www.fhi-berlin.mpg.de/th/th.htm

### Entropy-power uncertainty relations : towards a tight inequality for all Gaussian pure states

We show that a proper expression of the uncertainty relation for a pair of
canonically-conjugate continuous variables relies on entropy power, a standard
notion in Shannon information theory for real-valued signals. The resulting
entropy-power uncertainty relation is equivalent to the entropic formulation of
the uncertainty relation due to Bialynicki-Birula and Mycielski, but can be
further extended to rotated variables. Hence, based on a reasonable assumption,
we give a partial proof of a tighter form of the entropy-power uncertainty
relation taking correlations into account and provide extensive numerical
evidence of its validity. Interestingly, it implies the generalized
(rotation-invariant) Schr\"odinger-Robertson uncertainty relation exactly as
the original entropy-power uncertainty relation implies Heisenberg relation. It
is saturated for all Gaussian pure states, in contrast with hitherto known
entropic formulations of the uncertainty principle.Comment: 15 pages, 5 figures, the new version includes the n-mode cas

### Vernal Pool Conservation: Enhancing Existing Regulation Through the Creation of the Maine Vernal Pool Special Area Management Plan

Conservation of natural resources is challenging given the competing economic and ecological goals humans have for landscapes. Vernal pools in the northeastern US are seasonal, small wetlands that provide critical breeding habitat for amphibians and invertebrates adapted to temporary waters, and are exceptionally hard to conserve as their function is dependent on connections to other wetlands and upland forests. A team of researchers in Maine joined forces with a diverse array of governmental and private stakeholders to develop an alternative to existing top-down vernal pool regulation. Through creative adoption and revision of various resource management tools, they produced a vernal pool conservation mechanism, the Maine Vernal Pool Special Management Area Plan that meets the needs of diverse stakeholders from developers to ecologists. This voluntary mitigation tool uses fees from impacts to vernal pools in locally identified growth areas to fund conservation of â€śpoolscapesâ€ť (pools plus appropriate adjacent habitat) in areas locally designated for rural use. In this case study, we identify six key features of this mechanism that illustrate the use of existing tools to balance growth and pool conservation. This case study will provide readers with key concepts that can be applied to any conservation problem: namely, how to work with diverse interests toward a common goal, how to evaluate and use existing policy tools in new ways, and how to approach solutions to sticky problems through a willingness to accept uncertainty and risk

### Dynamic mean-field and cavity methods for diluted Ising systems

We compare dynamic mean-field and dynamic cavity as methods to describe the
stationary states of dilute kinetic Ising models. We compute dynamic mean-field
theory by expanding in interaction strength to third order, and compare to the
exact dynamic mean-field theory for fully asymmetric networks. We show that in
diluted networks the dynamic cavity method generally predicts magnetizations of
individual spins better than both first order ("naive") and second order
("TAP") dynamic mean field theory

### Detection of non-Gaussian entangled states with an improved continuous-variable separability criterion

Currently available separability criteria for continuous-variable states are
generally based on the covariance matrix of quadrature operators. The
well-known separability criterion of Duan et al. [Phys. Rev. Lett. 84, 2722
(2000)] and Simon [Phys. Rev. Lett. 84, 2726 (2000)] , for example, gives a
necessary and sufficient condition for a two-mode Gaussian state to be
separable, but leaves many entangled non-Gaussian states undetected. Here, we
introduce an improvement of this criterion that enables a stronger entanglement
detection. The improved condition is based on the knowledge of an additional
parameter, namely the degree of Gaussianity, and exploits a connection with
Gaussianity-bounded uncertainty relations [Phys. Rev. A 86, 030102 (2012)]. We
exhibit families of non-Gaussian entangled states whose entanglement remains
undetected by the Duan-Simon criterion.Comment: Revised presentation, results unchanged. 10 pages, 6 figure

### p>2 spin glasses with first order ferromagnetic transitions

We consider an infinite-range spherical p-spin glass model with an additional
r-spin ferromagnetic interaction, both statically using a replica analysis and
dynamically via a generating functional method. For r>2 we find that there are
first order transitions to ferromagnetic phases. For r<p there are two
ferromagnetic phases, one non-glassy replica symmetric and one exhibiting
glassy one-step replica symmetry breaking and aging, whereas for r>=p only the
replica symmetric phase exists.Comment: AMSLaTeX, 13 pages, 23 EPS figures ; one figure correcte

- â€¦