20,688 research outputs found
Characterizing finite-dimensional quantum behavior
We study and extend the semidefinite programming (SDP) hierarchies introduced
in [Phys. Rev. Lett. 115, 020501] for the characterization of the statistical
correlations arising from finite dimensional quantum systems. First, we
introduce the dimension-constrained noncommutative polynomial optimization
(NPO) paradigm, where a number of polynomial inequalities are defined and
optimization is conducted over all feasible operator representations of bounded
dimensionality. Important problems in device independent and semi-device
independent quantum information science can be formulated (or almost
formulated) in this framework. We present effective SDP hierarchies to attack
the general dimension-constrained NPO problem (and related ones) and prove
their asymptotic convergence. To illustrate the power of these relaxations, we
use them to derive new dimension witnesses for temporal and Bell-type
correlation scenarios, and also to bound the probability of success of quantum
random access codes.Comment: 17 page
Generation of unpredictable time series by a Neural Network
A perceptron that learns the opposite of its own output is used to generate a
time series. We analyse properties of the weight vector and the generated
sequence, like the cycle length and the probability distribution of generated
sequences. A remarkable suppression of the autocorrelation function is
explained, and connections to the Bernasconi model are discussed. If a
continuous transfer function is used, the system displays chaotic and
intermittent behaviour, with the product of the learning rate and amplification
as a control parameter.Comment: 11 pages, 14 figures; slightly expanded and clarified, mistakes
corrected; accepted for publication in PR
Entropy and Quantum Kolmogorov Complexity: A Quantum Brudno's Theorem
In classical information theory, entropy rate and Kolmogorov complexity per
symbol are related by a theorem of Brudno. In this paper, we prove a quantum
version of this theorem, connecting the von Neumann entropy rate and two
notions of quantum Kolmogorov complexity, both based on the shortest qubit
descriptions of qubit strings that, run by a universal quantum Turing machine,
reproduce them as outputs.Comment: 26 pages, no figures. Reference to publication added: published in
the Communications in Mathematical Physics
(http://www.springerlink.com/content/1432-0916/
Optimality of neighbor-balanced designs for total effects
The purpose of this paper is to study optimality of circular
neighbor-balanced block designs when neighbor effects are present in the model.
In the literature many optimality results are established for direct effects
and neighbor effects separately, but few for total effects, that is, the sum of
direct effect of treatment and relevant neighbor effects. We show that circular
neighbor-balanced designs are universally optimal for total effects among
designs with no self neighbor. Then we give efficiency factors of these
designs, and show some situations where a design with self neighbors is
preferable to a neighbor-balanced design.Comment: Published by the Institute of Mathematical Statistics
(http://www.imstat.org) in the Annals of Statistics
(http://www.imstat.org/aos/) at http://dx.doi.org/10.1214/00905360400000048
- …