18 research outputs found
A dynamical model for quantum memory channels
A dynamical model for quantum channel is introduced which allows one to pass
continuously from the memoryless case to the case in which memory effects are
present. The quantum and classical communication rates of the model are defined
and explicit expression are provided in some limiting case. In this context we
introduce noise attenuation strategies where part of the signals are sacrificed
to modify the channel environment. The case of qubit channel with phase damping
noise is analyzed in details.Comment: 11 pages, 4 figures; minor correction adde
Tema Con Variazioni: Quantum Channel Capacity
Channel capacity describes the size of the nearly ideal channels, which can
be obtained from many uses of a given channel, using an optimal error
correcting code. In this paper we collect and compare minor and major
variations in the mathematically precise statements of this idea which have
been put forward in the literature. We show that all the variations considered
lead to equivalent capacity definitions. In particular, it makes no difference
whether one requires mean or maximal errors to go to zero, and it makes no
difference whether errors are required to vanish for any sequence of block
sizes compatible with the rate, or only for one infinite sequence.Comment: 32 pages, uses iopart.cl
Nonadditivity effects in classical capacities of quantum multiple-access channels
We study classical capacities of quantum multi-access channels in geometric
terms revealing breaking of additivity of Holevo-like capacity. This effect is
purely quantum since, as one points out, any classical multi-access channels
have their regions additive. The observed non-additivity in quantum version
presented here seems to be the first effect of this type with no additional
resources like side classical or quantum information (or entanglement)
involved. The simplicity of quantum channels involved resembles butterfly
effect in case of classical channel with two senders and two receivers.Comment: 5 pages, 5 figure
Simple test for quantum channel capacity
Basing on states and channels isomorphism we point out that semidefinite
programming can be used as a quick test for nonzero one-way quantum channel
capacity. This can be achieved by search of symmetric extensions of states
isomorphic to a given quantum channel. With this method we provide examples of
quantum channels that can lead to high entanglement transmission but still have
zero one-way capacity, in particular, regions of symmetric extendibility for
isotropic states in arbitrary dimensions are presented. Further we derive {\it
a new entanglement parameter} based on (normalised) relative entropy distance
to the set of states that have symmetric extensions and show explicitly the
symmetric extension of isotropic states being the nearest to singlets in the
set of symmetrically extendible states. The suitable regularisation of the
parameter provides a new upper bound on one-way distillable entanglement.Comment: 6 pages, no figures, RevTeX4. Signifficantly corrected version. Claim
on continuity of channel capacities removed due to flaw in the corresponding
proof. Changes and corrections performed in the part proposing a new upper
bound on one-way distillable etanglement which happens to be not one-way
entanglement monoton
On asymptotic continuity of functions of quantum states
A useful kind of continuity of quantum states functions in asymptotic regime
is so-called asymptotic continuity. In this paper we provide general tools for
checking if a function possesses this property. First we prove equivalence of
asymptotic continuity with so-called it robustness under admixture. This allows
us to show that relative entropy distance from a convex set including maximally
mixed state is asymptotically continuous. Subsequently, we consider it arrowing
- a way of building a new function out of a given one. The procedure originates
from constructions of intrinsic information and entanglement of formation. We
show that arrowing preserves asymptotic continuity for a class of functions
(so-called subextensive ones). The result is illustrated by means of several
examples.Comment: Minor corrections, version submitted for publicatio
Faithful Squashed Entanglement
Squashed entanglement is a measure for the entanglement of bipartite quantum
states. In this paper we present a lower bound for squashed entanglement in
terms of a distance to the set of separable states. This implies that squashed
entanglement is faithful, that is, strictly positive if and only if the state
is entangled. We derive the bound on squashed entanglement from a bound on
quantum conditional mutual information, which is used to define squashed
entanglement and corresponds to the amount by which strong subadditivity of von
Neumann entropy fails to be saturated. Our result therefore sheds light on the
structure of states that almost satisfy strong subadditivity with equality. The
proof is based on two recent results from quantum information theory: the
operational interpretation of the quantum mutual information as the optimal
rate for state redistribution and the interpretation of the regularised
relative entropy of entanglement as an error exponent in hypothesis testing.
The distance to the set of separable states is measured by the one-way LOCC
norm, an operationally-motivated norm giving the optimal probability of
distinguishing two bipartite quantum states, each shared by two parties, using
any protocol formed by local quantum operations and one-directional classical
communication between the parties. A similar result for the Frobenius or
Euclidean norm follows immediately. The result has two applications in
complexity theory. The first is a quasipolynomial-time algorithm solving the
weak membership problem for the set of separable states in one-way LOCC or
Euclidean norm. The second concerns quantum Merlin-Arthur games. Here we show
that multiple provers are not more powerful than a single prover when the
verifier is restricted to one-way LOCC operations thereby providing a new
characterisation of the complexity class QMA.Comment: 24 pages, 1 figure, 1 table. Due to an error in the published
version, claims have been weakened from the LOCC norm to the one-way LOCC
nor
Unbounded violation of tripartite Bell inequalities
We prove that there are tripartite quantum states (constructed from random
unitaries) that can lead to arbitrarily large violations of Bell inequalities
for dichotomic observables. As a consequence these states can withstand an
arbitrary amount of white noise before they admit a description within a local
hidden variable model. This is in sharp contrast with the bipartite case, where
all violations are bounded by Grothendieck's constant. We will discuss the
possibility of determining the Hilbert space dimension from the obtained
violation and comment on implications for communication complexity theory.
Moreover, we show that the violation obtained from generalized GHZ states is
always bounded so that, in contrast to many other contexts, GHZ states do in
this case not lead to extremal quantum correlations. The results are based on
tools from the theories of operator spaces and tensor norms which we exploit to
prove the existence of bounded but not completely bounded trilinear forms from
commutative C*-algebras.Comment: Substantial changes in the presentation to make the paper more
accessible for a non-specialized reade