Rank properties of exposed positive maps

Let \cK and \cH be finite dimensional Hilbert spaces and let \fP denote the cone of all positive linear maps acting from \fB(\cK) into \fB(\cH). We show that each map of the form $\phi(X)=AXA^*$ or $\phi(X)=AX^TA^*$ is an exposed point of \fP. We also show that if a map $\phi$ is an exposed point of \fP then either $\phi$ is rank 1 non-increasing or \rank\phi(P)>1 for any one-dimensional projection P\in\fB(\cK).Comment: 6 pages, last section removed - it will be a part of another pape

Monogamy of Bell's inequality violations in non-signaling theories

We derive monogamy relations (tradeoffs) between strengths of violations of Bell's inequalities from the non-signaling condition. Our result applies to general Bell inequalities with an arbitrary large number of partners, outcomes and measurement settings. The method is simple, efficient and does not require linear programming. The results are used to derive optimal fidelity for asymmetric cloning in nonsignaling theories.Comment: 4 pages, 2 figures, published versio

Efficient bounds on quantum communication rates via their reduced variants

We investigate one-way communication scenarios where Bob manipulating on his parts can transfer some sub-system to the environment. We define reduced versions of quantum communication rates and further, prove new upper bounds on one-way quantum secret key, distillable entanglement and quantum channel capacity by means of their reduced versions. It is shown that in some cases they drastically improve their estimation.Comment: 6 pages, RevTe

κ\kappa-Deformed Statistics and Classical Fourmomentum Addition Law

We consider $\kappa$-deformed relativistic symmetries described algebraically by modified Majid-Ruegg bicrossproduct basis and investigate the quantization of field oscillators for the $\kappa$-deformed free scalar fields on $\kappa$-Minkowski space. By modification of standard multiplication rule, we postulate the $\kappa$-deformed algebra of bosonic creation and annihilation operators. Our algebra permits to define the n-particle states with classical addition law for the fourmomenta in a way which is not in contradiction with the nonsymmetric quantum fourmomentum coproduct. We introduce $\kappa$-deformed Fock space generated by our $\kappa$-deformed oscillators which satisfy the standard algebraic relations with modified $\kappa$-multiplication rule. We show that such a $\kappa$-deformed bosonic Fock space is endowed with the conventional bosonic symmetry properties. Finally we discuss the role of $\kappa$-deformed algebra of oscillators in field-theoretic noncommutative framework.Comment: LaTeX, 12 pages. V2: second part of chapter 4 changed, new references and comments added. V3: formula (14) corrected. Some additional explanations added. V4: further comments about algebraic structure are adde

N-enlarged Galilei Hopf algebra and its twist deformations

The N-enlarged Galilei Hopf algebra is constructed. Its twist deformations are considered and the corresponding twisted space-times are derived.Comment: 8 pages, no figure

Quantum-mechanical machinery for rational decision-making in classical guessing game

In quantum game theory, one of the most intriguing and important questions is, "Is it possible to get quantum advantages without any modification of the classical game?" The answer to this question so far has largely been negative. So far, it has usually been thought that a change of the classical game setting appears to be unavoidable for getting the quantum advantages. However, we give an affirmative answer here, focusing on the decision-making process (we call 'reasoning') to generate the best strategy, which may occur internally, e.g., in the player's brain. To show this, we consider a classical guessing game. We then define a one-player reasoning problem in the context of the decision-making theory, where the machinery processes are designed to simulate classical and quantum reasoning. In such settings, we present a scenario where a rational player is able to make better use of his/her weak preferences due to quantum reasoning, without any altering or resetting of the classically defined game. We also argue in further analysis that the quantum reasoning may make the player fail, and even make the situation worse, due to any inappropriate preferences.Comment: 9 pages, 10 figures, The scenario is more improve

Matter-wave analog of an optical random laser

The accumulation of atoms in the lowest energy level of a trap and the subsequent out-coupling of these atoms is a realization of a matter-wave analog of a conventional optical laser. Optical random lasers require materials that provide optical gain but, contrary to conventional lasers, the modes are determined by multiple scattering and not a cavity. We show that a Bose-Einstein condensate can be loaded in a spatially correlated disorder potential prepared in such a way that the Anderson localization phenomenon operates as a band-pass filter. A multiple scattering process selects atoms with certain momenta and determines laser modes which represents a matter-wave analog of an optical random laser.Comment: 4 pages, 3 figures version accepted for publication in Phys. Rev. A; minor changes, the present title substituted for "Atom Random Laser

N-particle nonclassicality without N-particle correlations

Most of known multipartite Bell inequalities involve correlation functions for all subsystems. They are useless for entangled states without such correlations. We give a method of derivation of families of Bell inequalities for N parties, which involve, e.g., only (N-1)-partite correlations, but still are able to detect proper N-partite entanglement. We present an inequality which reveals five-partite entanglement despite only four-partite correlations. Classes of inequalities introduced here can be put into a handy form of a single non-linear inequality. An example is given of an N qubit state, which strongly violates such an inequality, despite having no N-qubit correlations. This surprising property might be of potential value for quantum information tasks.Comment: 5 page

A simplified implementation of the least squares solution for pairwise comparisons matrices

This is a follow up to "Solution of the least squares method problem of pairwise comparisons matrix" by Bozóki published by this journal in 2008. Familiarity with this paper is essential and assumed. For lower inconsistency and decreased accuracy, our proposed solutions run in seconds instead of days. As such, they may be useful for researchers willing to use the least squares method (LSM) instead of the geometric means (GM) method