9,709 research outputs found
Simulations of closed timelike curves
Proposed models of closed timelike curves (CTCs) have been shown to enable
powerful information-processing protocols. We examine the simulation of models
of CTCs both by other models of CTCs and by physical systems without access to
CTCs. We prove that the recently proposed transition probability CTCs (T-CTCs)
are physically equivalent to postselection CTCs (P-CTCs), in the sense that one
model can simulate the other with reasonable overhead. As a consequence, their
information-processing capabilities are equivalent. We also describe a method
for quantum computers to simulate Deutschian CTCs (but with a reasonable
overhead only in some cases). In cases for which the overhead is reasonable, it
might be possible to perform the simulation in a table-top experiment. This
approach has the benefit of resolving some ambiguities associated with the
equivalent circuit model of Ralph et al. Furthermore, we provide an explicit
form for the state of the CTC system such that it is a maximum-entropy state,
as prescribed by Deutsch.Comment: 15 pages, 1 figure, accepted for publication in Foundations of
Physic
p-topological and p-regular: dual notions in convergence theory
The natural duality between "topological" and "regular," both considered as
convergence space properties, extends naturally to p-regular convergence
spaces, resulting in the new concept of a p-topological convergence space.
Taking advantage of this duality, the behavior of p-topological and p-regular
convergence spaces is explored, with particular emphasis on the former, since
they have not been previously studied. Their study leads to the new notion of a
neighborhood operator for filters, which in turn leads to an especially simple
characterization of a topology in terms of convergence criteria. Applications
include the topological and regularity series of a convergence space.Comment: 12 pages in Acrobat 3.0 PDF forma
Risk homeostasis theory - A study of intrinsic compensation
Risk homeostasis theory (RHT) suggests that changes made to the intrinsic risk of environments are negated in one of three ways: behavioural adjustments within the environment, mode migration, and avoidance of the physical risk. To date, this three-way model of RHT has little empirical support, whilst research findings on RHT have at times been diametrically opposed. A reconciliation of apparently opposing findings might be possible by suggesting that extrinsic compensation fails to restore previously existing levels of actual risk in cases where behavioural adjustments within the environment are incapable of negating intrinsic risk changes. This paper reports a study in which behavioural adjustments within the physical risk-taking environment are capable of reconciling target with actual risk. The results provide positive support for RHT in the form of overcompensation for the intrinsic risk change on specific driver behaviours
Extra Shared Entanglement Reduces Memory Demand in Quantum Convolutional Coding
We show how extra entanglement shared between sender and receiver reduces the
memory requirements for a general entanglement-assisted quantum convolutional
code. We construct quantum convolutional codes with good error-correcting
properties by exploiting the error-correcting properties of an arbitrary basic
set of Pauli generators. The main benefit of this particular construction is
that there is no need to increase the frame size of the code when extra shared
entanglement is available. Then there is no need to increase the memory
requirements or circuit complexity of the code because the frame size of the
code is directly related to these two code properties. Another benefit, similar
to results of previous work in entanglement-assisted convolutional coding, is
that we can import an arbitrary classical quaternary code for use as an
entanglement-assisted quantum convolutional code. The rate and error-correcting
properties of the imported classical code translate to the quantum code. We
provide an example that illustrates how to import a classical quaternary code
for use as an entanglement-assisted quantum convolutional code. We finally show
how to "piggyback" classical information to make use of the extra shared
entanglement in the code.Comment: 7 pages, 1 figure, accepted for publication in Physical Review
Quantum state cloning using Deutschian closed timelike curves
We show that it is possible to clone quantum states to arbitrary accuracy in
the presence of a Deutschian closed timelike curve (D-CTC), with a fidelity
converging to one in the limit as the dimension of the CTC system becomes
large---thus resolving an open conjecture from [Brun et al., Physical Review
Letters 102, 210402 (2009)]. This result follows from a D-CTC-assisted scheme
for producing perfect clones of a quantum state prepared in a known eigenbasis,
and the fact that one can reconstruct an approximation of a quantum state from
empirical estimates of the probabilities of an informationally-complete
measurement. Our results imply more generally that every continuous, but
otherwise arbitrarily non-linear map from states to states can be implemented
to arbitrary accuracy with D-CTCs. Furthermore, our results show that Deutsch's
model for CTCs is in fact a classical model, in the sense that two arbitrary,
distinct density operators are perfectly distinguishable (in the limit of a
large CTC system); hence, in this model quantum mechanics becomes a classical
theory in which each density operator is a distinct point in a classical phase
space.Comment: 6 pages, 1 figure; v2: modifications to the interpretation of our
results based on the insightful comments of the referees; v3: minor change,
accepted for publication in Physical Review Letter
Coherent Communication with Continuous Quantum Variables
The coherent bit (cobit) channel is a resource intermediate between classical
and quantum communication. It produces coherent versions of teleportation and
superdense coding. We extend the cobit channel to continuous variables by
providing a definition of the coherent nat (conat) channel. We construct
several coherent protocols that use both a position-quadrature and a
momentum-quadrature conat channel with finite squeezing. Finally, we show that
the quality of squeezing diminishes through successive compositions of coherent
teleportation and superdense coding.Comment: 4 pages, 3 figure
Stochastic resonance in Gaussian quantum channels
We determine conditions for the presence of stochastic resonance in a lossy
bosonic channel with a nonlinear, threshold decoding. The stochastic resonance
effect occurs if and only if the detection threshold is outside of a "forbidden
interval". We show that it takes place in different settings: when transmitting
classical messages through a lossy bosonic channel, when transmitting over an
entanglement-assisted lossy bosonic channel, and when discriminating channels
with different loss parameters. Moreover, we consider a setting in which
stochastic resonance occurs in the transmission of a qubit over a lossy bosonic
channel with a particular encoding and decoding. In all cases, we assume the
addition of Gaussian noise to the signal and show that it does not matter who,
between sender and receiver, introduces such a noise. Remarkably, different
results are obtained when considering a setting for private communication. In
this case the symmetry between sender and receiver is broken and the "forbidden
interval" may vanish, leading to the occurrence of stochastic resonance effects
for any value of the detection threshold.Comment: 17 pages, 6 figures. Manuscript improved in many ways. New results on
private communication adde
Duality in Entanglement-Assisted Quantum Error Correction
The dual of an entanglement-assisted quantum error-correcting (EAQEC) code is
defined from the orthogonal group of a simplified stabilizer group. From the
Poisson summation formula, this duality leads to the MacWilliams identities and
linear programming bounds for EAQEC codes. We establish a table of upper and
lower bounds on the minimum distance of any maximal-entanglement EAQEC code
with length up to 15 channel qubits.Comment: This paper is a compact version of arXiv:1010.550
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