49 research outputs found
Counterexample to an additivity conjecture for output purity of quantum channels
A conjecture arising naturally in the investigation of additivity of
classical information capacity of quantum channels states that the maximal
purity of outputs from a quantum channel, as measured by the p-norm, should be
multiplicative with respect to the tensor product of channels. We disprove this
conjecture for p>4.79. The same example (with p=infinity) also disproves a
conjecture for the multiplicativity of the injective norm of Hilbert space
tensor products.Comment: 3 pages, 3 figures, revte
On separability of quantum states and the violation of Bell-type inequalities
In contrast to the wide-spread opinion that any separable quantum state
satisfies every classical probabilistic constraint, we present a simple example
where a separable quantum state does not satisfy the original Bell inequality
although the latter inequality, in its perfect correlation form, is valid for
all joint classical measurements. In a very general setting, we discuss
inequalities for joint experiments upon a bipartite quantum system in a
separable state. We derive quantum analogues of the original Bell inequality
and specify the conditions sufficient for a separable state to satisfy the
original Bell inequality. We introduce the extended CHSH inequality and prove
that, for any separable quantum state, this inequality holds for a variety of
linear combinations.Comment: 13 pages, extended versio
Bound entangled Gaussian states
We discuss the entanglement properties of bipartite states with Gaussian
Wigner functions. Separability and the positivity of the partial transpose are
characterized in terms of the covariance matrix of the state, and it is shown
that for systems composed of a single oscillator for Alice and an arbitrary
number for Bob, positivity of the partial transpose implies separability.
However, this implications fails with two oscillators on each side, as we show
by a five parameter family of explicit counterexamples.Comment: 4 page
The optimal cloning of quantum coherent states is non-Gaussian
We consider the optimal cloning of quantum coherent states with single-clone
and joint fidelity as figures of merit. Both optimal fidelities are attained
for phase space translation covariant cloners. Remarkably, the joint fidelity
is maximized by a Gaussian cloner, whereas the single-clone fidelity can be
enhanced by non-Gaussian operations: a symmetric non-Gaussian 1-to-2 cloner can
achieve a single-clone fidelity of approximately 0.6826, perceivably higher
than the optimal fidelity of 2/3 in a Gaussian setting. This optimal cloner can
be realized by means of an optical parametric amplifier supplemented with a
particular source of non-Gaussian bimodal states. Finally, we show that the
single-clone fidelity of the optimal 1-to-infinity cloner, corresponding to a
measure-and-prepare scheme, cannot exceed 1/2. This value is achieved by a
Gaussian scheme and cannot be surpassed even with supplemental bound entangled
states.Comment: 4 pages, 2 figures, revtex; changed title, extended list of authors,
included optical implementation of optimal clone
Squeezing the limit: Quantum benchmarks for the teleportation and storage of squeezed states
We derive fidelity benchmarks for the quantum storage and teleportation of
squeezed states of continuous variable systems, for input ensembles where the
degree of squeezing is fixed, no information about its orientation in phase
space is given, and the distribution of phase space displacements is a
Gaussian. In the limit where the latter becomes flat, we prove analytically
that the maximal classical achievable fidelity (which is 1/2 without squeezing,
for ) is given by , vanishing when the degree of squeezing
diverges. For mixed states, as well as for general distributions of
displacements, we reduce the determination of the benchmarks to the solution of
a finite-dimensional semidefinite program, which yields accurate, certifiable
bounds thanks to a rigorous analysis of the truncation error. This approach may
be easily adapted to more general ensembles of input states.Comment: 19 pages, 4figure
Quantization and noiseless measurements
In accordance with the fact that quantum measurements are described in terms
of positive operator measures (POMs), we consider certain aspects of a
quantization scheme in which a classical variable is associated
with a unique positive operator measure (POM) , which is not necessarily
projection valued. The motivation for such a scheme comes from the well-known
fact that due to the noise in a quantum measurement, the resulting outcome
distribution is given by a POM and cannot, in general, be described in terms of
a traditional observable, a selfadjoint operator. Accordingly, we notice that
the noiseless measurements are the ones which are determined by a selfadjoint
operator. The POM in our quantization is defined through its moment
operators, which are required to be of the form , , with
a fixed map from classical variables to Hilbert space operators. In
particular, we consider the quantization of classical \emph{questions}, that
is, functions taking only values 0 and 1. We compare two concrete
realizations of the map in view of their ability to produce noiseless
measurements: one being the Weyl map, and the other defined by using phase
space probability distributions.Comment: 15 pages, submitted to Journal of Physics
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