1,120 research outputs found
Improving zero-error classical communication with entanglement
Given one or more uses of a classical channel, only a certain number of
messages can be transmitted with zero probability of error. The study of this
number and its asymptotic behaviour constitutes the field of classical
zero-error information theory, the quantum generalisation of which has started
to develop recently. We show that, given a single use of certain classical
channels, entangled states of a system shared by the sender and receiver can be
used to increase the number of (classical) messages which can be sent with no
chance of error. In particular, we show how to construct such a channel based
on any proof of the Bell-Kochen-Specker theorem. This is a new example of the
use of quantum effects to improve the performance of a classical task. We
investigate the connection between this phenomenon and that of
``pseudo-telepathy'' games. The use of generalised non-signalling correlations
to assist in this task is also considered. In this case, a particularly elegant
theory results and, remarkably, it is sometimes possible to transmit
information with zero-error using a channel with no unassisted zero-error
capacity.Comment: 6 pages, 2 figures. Version 2 is the same as the journal version plus
figure 1 and the non-signalling box exampl
Information-theoretic temporal Bell inequality and quantum computation
An information-theoretic temporal Bell inequality is formulated to contrast
classical and quantum computations. Any classical algorithm satisfies the
inequality, while quantum ones can violate it. Therefore, the violation of the
inequality is an immediate consequence of the quantumness in the computation.
Furthermore, this approach suggests a notion of temporal nonlocality in quantum
computation.Comment: v2: 5 pages, refereces added, discussion slightly revised, main
result unchanged. v3: typos correcte
The thermodynamics of prediction
A system responding to a stochastic driving signal can be interpreted as
computing, by means of its dynamics, an implicit model of the environmental
variables. The system's state retains information about past environmental
fluctuations, and a fraction of this information is predictive of future ones.
The remaining nonpredictive information reflects model complexity that does not
improve predictive power, and thus represents the ineffectiveness of the model.
We expose the fundamental equivalence between this model inefficiency and
thermodynamic inefficiency, measured by dissipation. Our results hold
arbitrarily far from thermodynamic equilibrium and are applicable to a wide
range of systems, including biomolecular machines. They highlight a profound
connection between the effective use of information and efficient thermodynamic
operation: any system constructed to keep memory about its environment and to
operate with maximal energetic efficiency has to be predictive.Comment: 5 pages, 1 figur
Non-local correlations as an information theoretic resource
It is well known that measurements performed on spatially separated entangled
quantum systems can give rise to correlations that are non-local, in the sense
that a Bell inequality is violated. They cannot, however, be used for
super-luminal signalling. It is also known that it is possible to write down
sets of ``super-quantum'' correlations that are more non-local than is allowed
by quantum mechanics, yet are still non-signalling. Viewed as an information
theoretic resource, super-quantum correlations are very powerful at reducing
the amount of communication needed for distributed computational tasks. An
intriguing question is why quantum mechanics does not allow these more powerful
correlations. We aim to shed light on the range of quantum possibilities by
placing them within a wider context. With this in mind, we investigate the set
of correlations that are constrained only by the no-signalling principle. These
correlations form a polytope, which contains the quantum correlations as a
(proper) subset. We determine the vertices of the no-signalling polytope in the
case that two observers each choose from two possible measurements with d
outcomes. We then consider how interconversions between different sorts of
correlations may be achieved. Finally, we consider some multipartite examples.Comment: Revtex. 12 pages, 6 figure
Quantum conditional operator and a criterion for separability
We analyze the properties of the conditional amplitude operator, the quantum
analog of the conditional probability which has been introduced in
[quant-ph/9512022]. The spectrum of the conditional operator characterizing a
quantum bipartite system is invariant under local unitary transformations and
reflects its inseparability. More specifically, it is shown that the
conditional amplitude operator of a separable state cannot have an eigenvalue
exceeding 1, which results in a necessary condition for separability. This
leads us to consider a related separability criterion based on the positive map
, where is an Hermitian operator. Any
separable state is mapped by the tensor product of this map and the identity
into a non-negative operator, which provides a simple necessary condition for
separability. In the special case where one subsystem is a quantum bit,
reduces to time-reversal, so that this separability condition is
equivalent to partial transposition. It is therefore also sufficient for
and systems. Finally, a simple connection between this
map and complex conjugation in the "magic" basis is displayed.Comment: 19 pages, RevTe
Madelung Fluid Model for The Most Likely Wave Function of a Single Free Particle in Two Dimensional Space with a Given Average Energy
We consider spatially two dimensional Madelung fluid whose irrotational
motion reduces into the Schr\"odinger equation for a single free particle. In
this respect, we regard the former as a direct generalization of the latter,
allowing a rotational quantum flow. We then ask for the most likely wave
function possessing a given average energy by maximizing the Shannon
information entropy over the quantum probability density. We show that there
exists a class of solutions in which the wave function is self-trapped,
rotationally symmetric, spatially localized with finite support, and spinning
around its center, yet stationary. The stationarity comes from the balance
between the attractive quantum force field of a trapping quantum potential
generated by quantum probability density and the repulsive centrifugal force of
a rotating velocity vector field. We further show that there is a limiting case
where the wave function is non-spinning and yet still stationary. This special
state turns out to be the lowest stationary state of the ordinary Schr\"odinger
equation for a particle in a cylindrical tube classical potential.Comment: 19 page
The Bell Theorem as a Special Case of a Theorem of Bass
The theorem of Bell states that certain results of quantum mechanics violate
inequalities that are valid for objective local random variables. We show that
the inequalities of Bell are special cases of theorems found ten years earlier
by Bass and stated in full generality by Vorob'ev. This fact implies precise
necessary and sufficient mathematical conditions for the validity of the Bell
inequalities. We show that these precise conditions differ significantly from
the definition of objective local variable spaces and as an application that
the Bell inequalities may be violated even for objective local random
variables.Comment: 15 pages, 2 figure
Entropy Encoding, Hilbert Space and Karhunen-Loeve Transforms
By introducing Hilbert space and operators, we show how probabilities,
approximations and entropy encoding from signal and image processing allow
precise formulas and quantitative estimates. Our main results yield orthogonal
bases which optimize distinct measures of data encoding.Comment: 25 pages, 1 figur
Chemical Toxicants in Water: A \u3ci\u3eGeoHealth\u3c/i\u3e Perspective in the Context of Climate Change
The editorial focuses on four major themes contextualized in a virtual GeoHealth workshop that occurred from June 14 to 16, 2021. Topics in that workshop included drinking water and chronic chemical exposure, environmental injustice, public health and drinking water policy, and the fate, transport, and human impact of aqueous contaminants in the context of climate change. The intent of the workshop was to further define the field of GeoHealth. This workshop emphasized on chemical toxicants that drive human health. The major calls for action emerged from the workshop include enhancing community engagement, advocating for equity and justice, and training the next generation
Low-Level Groundwater Atrazine in High Atrazine Usage Nebraska Counties: Likely Effects of Excessive Groundwater Abstraction
Recent studies observed a correlation between estrogen-related cancers and groundwater atrazine in eastern Nebraska counties. However, the mechanisms of human exposure to atrazine are unclear because low groundwater atrazine concentration was observed in counties with high cancer incidence despite having the highest atrazine usage. We studied groundwater atrazine fate in high atrazine usage Nebraska counties. Data were collected from Quality Assessed Agrichemical Contaminant Nebraska Groundwater, Parameter–Elevation Regressions on Independent Slopes Model (PRISM), and water use databases. Descriptive statistics and cluster analysis were performed. Domestic wells (59%) were the predominant well type. Groundwater atrazine was affected by well depth. Clusters consisting of wells with low atrazine were characterized by excessive groundwater abstraction, reduced precipitation, high population, discharge areas, and metropolitan counties. Hence, low groundwater atrazine may be due to excessive groundwater abstraction accompanied by atrazine. Human exposure to atrazine in abstracted groundwater may be higher than the estimated amount in groundwater
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