261 research outputs found
Information and communication in polygon theories
Generalized probabilistic theories (GPT) provide a framework in which one can
formulate physical theories that includes classical and quantum theories, but
also many other alternative theories. In order to compare different GPTs, we
advocate an approach in which one views a state in a GPT as a resource, and
quantifies the cost of interconverting between different such resources. We
illustrate this approach on polygon theories (Janotta et al. New J. Phys 13,
063024, 2011) that interpolate (as the number n of edges of the polygon
increases) between a classical trit (when n=3) and a real quantum bit (when
n=infinity). Our main results are that simulating the transmission of a single
n-gon state requires more than one qubit, or more than log(log(n)) bits, and
that n-gon states with n odd cannot be simulated by n'-gon states with n' even
(for all n,n'). These results are obtained by showing that the classical
capacity of a single n-gon state with n even is 1 bit, whereas it is larger
than 1 bit when n is odd; by showing that transmitting a single n-gon state
with n even violates information causality; and by showing studying the
communication complexity cost of the nondeterministic not equal function using
n-gon states.Comment: 18 page
Uncertainty Relation for the Discrete Fourier Transform
We derive an uncertainty relation for two unitary operators which obey a
commutation relation of the form UV=exp[i phi] VU. Its most important
application is to constrain how much a quantum state can be localised
simultaneously in two mutually unbiased bases related by a Discrete Fourier
Transform. It provides an uncertainty relation which smoothly interpolates
between the well known cases of the Pauli operators in 2 dimensions and the
continuous variables position and momentum. This work also provides an
uncertainty relation for modular variables, and could find applications in
signal processing. In the finite dimensional case the minimum uncertainty
states, discrete analogues of coherent and squeezed states, are minimum energy
solutions of Harper's equation, a discrete version of the Harmonic oscillator
equation.Comment: Extended Version; 13 pages; In press in Phys. Rev. Let
Hyperdense coding and superadditivity of classical capacities in hypersphere theories
In quantum superdense coding, two parties previously sharing entanglement can
communicate a two bit message by sending a single qubit. We study this feature
in the broader framework of general probabilistic theories. We consider a
particular class of theories in which the local state space of the
communicating parties corresponds to Euclidean hyperballs of dimension n (the
case n = 3 corresponds to the Bloch ball of quantum theory). We show that a
single n-ball can encode at most one bit of information, independently of n. We
introduce a bipartite extension of such theories for which there exist dense
coding protocols such that log_2 (n+1) bits are communicated if entanglement is
previously shared by the communicating parties. For n > 3, these protocols are
more powerful than the quantum one, because more than two bits are communicated
by transmission of a system that locally encodes at most one bit. We call this
phenomenon hyperdense coding. Our hyperdense coding protocols imply
superadditive classical capacities: two entangled systems can encode log_2
(n+1) > 2 bits, even though each system individually encodes at most one bit.
In our examples, hyperdense coding and superadditivity of classical capacities
come at the expense of violating tomographic locality or dynamical continuous
reversibility.Comment: Expanded discussion in response to referee comments. Accepted for
publication in New Journal of Physic
The Extent of Multi-particle Quantum Non-locality
It is well known that entangled quantum states can be nonlocal: the
correlations between local measurements carried out on these states cannot
always be reproduced by local hidden variable models. Svetlichny, followed by
others, showed that multipartite quantum states are even more nonlocal than
bipartite ones in the sense that nonlocal classical models with (super-luminal)
communication between some of the parties cannot reproduce the quantum
correlations. Here we study in detail the kinds of nonlocality present in
quantum states. More precisely we enquire what kinds of classical communication
patterns cannot reproduce quantum correlations. By studying the extremal points
of the space of all multiparty probability distributions, in which all parties
can make one of a pair of measurements each with two possible outcomes, we find
a necessary condition for classical nonlocal models to reproduce the statistics
of all quantum states. This condition extends and generalises work of
Svetlichny and others in which it was shown that a particular class of
classical nonlocal models, the ``separable'' models, cannot reproduce the
statistics of all multiparticle quantum states. Our condition shows that the
nonlocality present in some entangled multiparticle quantum states is much
stronger than previously thought. We also study the sufficiency of our
condition.Comment: 10 pages, 2 figures, journal versio
Device-Independent Bit Commitment based on the CHSH Inequality
Bit commitment and coin flipping occupy a unique place in the
device-independent landscape, as the only device-independent protocols thus far
suggested for these tasks are reliant on tripartite GHZ correlations. Indeed,
we know of no other bipartite tasks, which admit a device-independent
formulation, but which are not known to be implementable using only bipartite
nonlocality. Another interesting feature of these protocols is that the
pseudo-telepathic nature of GHZ correlations -- in contrast to the generally
statistical character of nonlocal correlations, such as those arising in the
violation of the CHSH inequality -- is essential to their formulation and
analysis. In this work, we present a device-independent bit commitment protocol
based on CHSH testing, which achieves the same security as the optimal
GHZ-based protocol. The protocol is analyzed in the most general settings,
where the devices are used repeatedly and may have long-term quantum memory. We
also recast the protocol in a post-quantum setting where both honest and
dishonest parties are restricted only by the impossibility of signaling, and
find that overall the supra-quantum structure allows for greater security.Comment: 15 pages, 3 figure
A Primer for Black Hole Quantum Physics
The mechanisms which give rise to Hawking radiation are revealed by analyzing
in detail pair production in the presence of horizons. In preparation for the
black hole problem, three preparatory problems are dwelt with at length: pair
production in an external electric field, thermalization of a uniformly
accelerated detector and accelerated mirrors. In the light of these examples,
the black hole evaporation problem is then presented.
The leitmotif is the singular behavior of modes on the horizon which gives
rise to a steady rate of production. Special emphasis is put on how each
produced particle contributes to the mean albeit arising from a particular
vacuum fluctuation. It is the mean which drives the semiclassical back
reaction. This aspect is analyzed in more detail than heretofore and in
particular its drawbacks are emphasized. It is the semiclassical theory which
gives rise to Hawking's famous equation for the loss of mass of the black hole
due to evaporation . Black hole thermodynamics is derived
from the evaporation process whereupon the reservoir character of the black
hole is manifest. The relation to the thermodynamics of the eternal black hole
through the Hartle--Hawking vacuum and the Killing identity are displayed.
It is through the analysis of the fluctuations of the field configurations
which give rise to a particular Hawking photon that the dubious character of
the semiclassical theory is manifest. The present frontier of research revolves
around this problem and is principally concerned with the fact that one calls
upon energy scales that are greater than Planckian and the possibility of a non
unitary evolution as well. These last subjects are presented in qualitative
fashion only, so that this review stops at the threshold of quantum gravity.Comment: An old review article on black hole evaporation and black hole
thermodynamics, put on the archive following popular demand, 178 pages, 21
figures (This text differs in slightly from the published version
Optimality of the genetic code with respect to protein stability and amino acid frequencies
How robust is the natural genetic code with respect to mistranslation errors?
It has long been known that the genetic code is very efficient in limiting the
effect of point mutation. A misread codon will commonly code either for the
same amino acid or for a similar one in terms of its biochemical properties, so
the structure and function of the coded protein remain relatively unaltered.
Previous studies have attempted to address this question more quantitatively,
namely by statistically estimating the fraction of randomly generated codes
that do better than the genetic code regarding its overall robustness. In this
paper, we extend these results by investigating the role of amino acid
frequencies in the optimality of the genetic code. When measuring the relative
fitness of the natural code with respect to a random code, it is indeed natural
to assume that a translation error affecting a frequent amino acid is less
favorable than that of a rare one, at equal mutation cost. We find that taking
the amino acid frequency into account accordingly decreases the fraction of
random codes that beat the natural code, making the latter comparatively even
more robust. This effect is particularly pronounced when more refined measures
of the amino acid substitution cost are used than hydrophobicity. To show this,
we devise a new cost function by evaluating with computer experiments the
change in folding free energy caused by all possible single-site mutations in a
set of known protein structures. With this cost function, we estimate that of
the order of one random code out of 100 millions is more fit than the natural
code when taking amino acid frequencies into account. The genetic code seems
therefore structured so as to minimize the consequences of translation errors
on the 3D structure and stability of proteins.Comment: 31 pages, 2 figures, postscript fil
Resource efficient single photon source based on active frequency multiplexing
We propose a new single photon source based on the principle of active
multiplexing of heralded single photons which, unlike previously reported
architecture, requires a limited amount of physical resources. We discuss both
its feasibility and the purity and indistinguishability of single photons as
function of the key parameters of a possible implementation
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