512 research outputs found
Entanglement Typicality
We provide a summary of both seminal and recent results on typical
entanglement. By typical values of entanglement, we refer here to values of
entanglement quantifiers that (given a reasonable measure on the manifold of
states) appear with arbitrarily high probability for quantum systems of
sufficiently high dimensionality. We work within the Haar measure framework for
discrete quantum variables, where we report on results concerning the average
von Neumann and linear entropies as well as arguments implying the typicality
of such values in the asymptotic limit. We then proceed to discuss the
generation of typical quantum states with random circuitry. Different phases of
entanglement, and the connection between typical entanglement and
thermodynamics are discussed. We also cover approaches to measures on the
non-compact set of Gaussian states of continuous variable quantum systems.Comment: Review paper with two quotes and minimalist figure
Qubit-portraits of qudit states and quantum correlations
The machinery of qubit-portraits of qudit states, recently presented, is
consider here in more details in order to characterize the presence of quantum
correlations in bipartite qudit states. In the tomographic representation of
quantum mechanics, Bell-like inequalities are interpreted as peculiar
properties of a family of classical joint probability distributions which
describe the quantum state of two qudits. By means of the qubit-portraits
machinery a semigroup of stochastic matrices can be associated to a given
quantum state. The violation of the CHSH inequalities is discussed in this
framework with some examples, we found that quantum correlations in qutrit
isotropic states can be detected by the suggested method while it cannot in the
case of qutrit Werner states.Comment: 12 pages, 4 figure
On the classical capacity of quantum Gaussian channels
The set of quantum Gaussian channels acting on one bosonic mode can be
classified according to the action of the group of Gaussian unitaries. We look
for bounds on the classical capacity for channels belonging to such a
classification. Lower bounds can be efficiently calculated by restricting to
Gaussian encodings, for which we provide analytical expressions.Comment: 10 pages, IOP style. v2: minor corrections, close to the published
versio
A note on the realignment criterion
For a quantum state in a bipartite system represented as a density matrix,
researchers used the realignment matrix and functions on its singular values to
study the separability of the quantum state. We obtain bounds for elementary
symmetric functions of singular values of realignment matrices. This answers
some open problems proposed by Lupo, Aniello, and Scardicchio. As a
consequence, we show that the proposed scheme by these authors for testing
separability would not work if the two subsystems of the bipartite system have
the same dimension.Comment: 11 pages, to appear in Journal of Physics A: Mathematical and
Theoretica
Bell's inequalities in the tomographic representation
The tomographic approach to quantum mechanics is revisited as a direct tool
to investigate violation of Bell-like inequalities. Since quantum tomograms are
well defined probability distributions, the tomographic approach is emphasized
to be the most natural one to compare the predictions of classical and quantum
theory. Examples of inequalities for two qubits an two qutrits are considered
in the tomographic probability representation of spin states.Comment: 11 pages, comments and references adde
Partial scaling transform of multiqubit states as a criterion of separability
The partial scaling transform of the density matrix for multiqubit states is
introduced to detect entanglement of quantum states. The transform contains
partial transposition as a special case. The scaling transform corresponds to
partial time scaling of subsystem (or partial Planck's constant scaling) which
was used to formulate recently separability criterion for continous variables.A
measure of entanglement which is a generalization of negativity measure is
introduced being based on tomographic probability description of spin states.Comment: 16 pages, 5 figures, submitted to J. Phys. A: Math. Ge
Quantumness tests and witnesses in the tomographic-probability representation
In view of the tomographic-probability representation of quantum states, we
reconsider the approach to quantumness tests of a single system developed in
[Alicki and Van Ryn 2008 J. Phys. A: Math. Theor. 41 062001]. For qubits we
introduce a general family of quantumness witnesses which are operators
depending on an extra parameter. Spin tomogram and dual spin tomographic
symbols are used to study qubit examples and the test inequalities which are
shown to satisfy simple relations within the framework of the standard
probability theory.Comment: 9 pages, 1 figure, LaTex file, submitted to Physica Script
Bipartite quantum systems: on the realignment criterion and beyond
Inspired by the `computable cross norm' or `realignment' criterion, we
propose a new point of view about the characterization of the states of
bipartite quantum systems. We consider a Schmidt decomposition of a bipartite
density operator. The corresponding Schmidt coefficients, or the associated
symmetric polynomials, are regarded as quantities that can be used to
characterize bipartite quantum states. In particular, starting from the
realignment criterion, a family of necessary conditions for the separability of
bipartite quantum states is derived. We conjecture that these conditions, which
are weaker than the parent criterion, can be strengthened in such a way to
obtain a new family of criteria that are independent of the original one. This
conjecture is supported by numerical examples for the low dimensional cases.
These ideas can be applied to the study of quantum channels, leading to a
relation between the rate of contraction of a map and its ability to preserve
entanglement.Comment: 19 pages, 4 figures, improved versio
Effect of nanostructuration on compressibility of cubic BN
Compressibility of high-purity nanostructured cBN has been studied under
quasi-hydrostatic conditions at 300 K up to 35 GPa using diamond anvil cell and
angle-dispersive synchrotron X-ray powder diffraction. A data fit to the Vinet
equation of state yields the values of the bulk modulus B0 of 375(4) GPa with
its first pressure derivative B0' of 2.3(3). The nanometer grain size (\sim20
nm) results in decrease of the bulk modulus by ~9%
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