1,223 research outputs found
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
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
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
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
Assessing the Role of Spin Noise in the Precision Timing of Millisecond Pulsars
We investigate rotational spin noise (referred to as timing noise) in
non-accreting pulsars: millisecond pulsars, canonical pulsars, and magnetars.
Particular attention is placed on quantifying the strength and non-stationarity
of timing noise in millisecond pulsars because the long-term stability of these
objects is required to detect nanohertz gravitational radiation. We show that a
single scaling law is sufficient to characterize timing noise in millisecond
and canonical pulsars while the same scaling law underestimates the levels of
timing noise in magnetars. The scaling law, along with a detailed study of the
millisecond pulsar B1937+21, leads us to conclude that timing noise is latent
in most millisecond pulsars and will be measurable in many objects when better
arrival time estimates are obtained over long data spans. The sensitivity of a
pulsar timing array to gravitational radiation is strongly affected by any
timing noise. We conclude that detection of proposed gravitational wave
backgrounds will require the analysis of more objects than previously suggested
over data spans that depend on the spectra of both the gravitational wave
background and of the timing noise. It is imperative to find additional
millisecond pulsars in current and future surveys in order to reduce the
effects of timing noise.Comment: 16 pages and 6 figures. ApJ, accepte
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
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
The Physics of Maxwell's demon and information
Maxwell's demon was born in 1867 and still thrives in modern physics. He
plays important roles in clarifying the connections between two theories:
thermodynamics and information. Here, we present the history of the demon and a
variety of interesting consequences of the second law of thermodynamics, mainly
in quantum mechanics, but also in the theory of gravity. We also highlight some
of the recent work that explores the role of information, illuminated by
Maxwell's demon, in the arena of quantum information theory.Comment: 24 pages, 13 figures. v2: some refs added, figs improve
Conceptual Inadequacy of the Shannon Information in Quantum Measurements
In a classical measurement the Shannon information is a natural measure of
our ignorance about properties of a system. There, observation removes that
ignorance in revealing properties of the system which can be considered to
preexist prior to and independent of observation. Because of the completely
different root of a quantum measurement as compared to a classical measurement
conceptual difficulties arise when we try to define the information gain in a
quantum measurement using the notion of Shannon information. The reason is
that, in contrast to classical measurement, quantum measurement, with very few
exceptions, cannot be claimed to reveal a property of the individual quantum
system existing before the measurement is performed.Comment: 11 pages, 5 figures, important Ref. [6] is now cited in all
appropriate place
Gravitational wave astronomy of single sources with a pulsar timing array
Abbreviated:
We investigate the potential of detecting the gravitational wave from
individual binary black hole systems using pulsar timing arrays (PTAs) and
calculate the accuracy for determining the GW properties. This is done in a
consistent analysis, which at the same time accounts for the measurement of the
pulsar distances via the timing parallax.
We find that, at low redshift, a PTA is able to detect the nano-Hertz GW from
super massive black hole binary systems with masses of \sim10^8 -
10^{10}\,M_{\sun} less than \,years before the final merger, and
those with less than years before merger may allow us to
detect the evolution of binaries.
We derive an analytical expression to describe the accuracy of a pulsar
distance measurement via timing parallax. We consider five years of bi-weekly
observations at a precision of 15\,ns for close-by (\,kpc)
pulsars. Timing twenty pulsars would allow us to detect a GW source with an
amplitude larger than . We calculate the corresponding GW and
binary orbital parameters and their measurement precision. The accuracy of
measuring the binary orbital inclination angle, the sky position, and the GW
frequency are calculated as functions of the GW amplitude. We note that the
"pulsar term", which is commonly regarded as noise, is essential for obtaining
an accurate measurement for the GW source location.
We also show that utilizing the information encoded in the GW signal passing
the Earth also increases the accuracy of pulsar distance measurements. If the
gravitational wave is strong enough, one can achieve sub-parsec distance
measurements for nearby pulsars with distance less than \,kpc.Comment: 16 pages, 5 figure,, accepted by MNRA
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