We characterize and classify quantum correlations in two-fermion systems having 2K single-particle states. For pure states we introduce the Slater decomposition rank (in analogy to Schmidt rank), i.e. decompose state into a combination of elementary determinants formed by mutually orthogonal Mixed can be characterized their number which is minimal required generate them. K=2 give necessary sufficient condition for have 1. correlation measure mixed evaluated analytically K=2. higher K,...

Methods of constructing random matrices typical circular unitary and orthogonal ensembles are presented. We generate numerically show that the statistical properties their spectra (level-spacing distribution, number variance) eigenvectors (entropy, participation ratio, eigenvector statistics) confer to predictions random-matrix theory, for both CUE COE.

We derive a lower bound for the concurrence of mixed bipartite quantum states, valid in arbitrary dimensions. As corollary, weaker, purely algebraic estimate is found, which detects entangled states with positive partial transpose.

We propose generalizations of concurrence for multi-partite quantum systems that can distinguish qualitatively distinct correlations. All introduced quantities be evaluated efficiently arbitrary mixed sates.

Geometric properties of the set quantum entangled states are investigated. We propose an explicit method to compute dimension local orbits for any mixed state general K x M problem and characterize effectively different (which cannot be related by transformations). Thus we generalize earlier results obtained simplest 2 system, which lead a stratification 6D N=4 pure states. define concept absolutely separable states, all globally equivalent separable.

Classical periodic orbits are stationary-phase points in path integral representations of quantum propagators. We show that complex solutions the equation, not corresponding to real classical orbits, give additional contributions propagator which can be important, especially near bifurcations. reveal existence and relevance such ghost for a kicked top.

The famous question of Kac "can one hear the shape a drum?" addressing unique connection between planar region and spectrum corresponding Laplace operator, can be legitimately extended to scattering systems. In modified version, asks whether geometry vibrating system determined by experiments. We present first experimental approach this problem in case microwave graphs (networks) simulating quantum graphs. Our results strongly indicate negative answer. To demonstrate we consider from pair...

Composed ensembles of random unitary matrices are defined via products matrices, each pertaining to a given canonical circular ensemble Dyson. We investigate statistical properties spectra some composed and demonstrate their physical relevance. discuss also the methods generating distributed according invariant Haar measure on orthogonal group.

First results on microwave billiards with broken time reversal symmetry are presented. The quasi two dimensional an attached isolator acting as a unidirectional transmission line. Spectral level dynamics was studied by changing the billiard length. For all spectral properties observed, i.e., nearest-neighbor distance, asymptotic curvature, and closest-approach distance at avoided crossings, we have found behavior characteristic of Gaussian unitary ensemble.

Various problems concerning the geometry of space Hermitian operators on a Hilbert are addressed. In particular, we study canonical Poisson and Riemann–Jordan tensors corresponding foliations into Kähler submanifolds. It is also shown that density states an n-dimensional naturally manifold stratified with stratification induced by rank state. Thus rank-k states, k = 1, ..., n, smooth (real) dimension 2nk − k2 1 this maximal in sense every curve , viewed as subset dual to Lie algebra unitary...

Several statistical properties of the energy levels a two-level atom interacting with one mode quantized electromagnetic field are investigated in connection possible "quantum-chaotic" behavior system.

We introduce detector-level entanglement, a unified entanglement concept for identical particles that takes into account the possible deletion of many-particle which-way information through detection process. The implies measure effective indistinguishability particles, which is controlled by measurement setup and quantifies extent to (anti-)symmetrization wave-function impacts on physical observables. Initially indistinguishable can gain or loose their transition distinguishability, quantum...

This progress report covers recent developments in the area of quantum randomness, which is an extraordinarily interdisciplinary that belongs not only to physics, but also philosophy, mathematics, computer science, and technology. For this reason article contains three parts will be essentially devoted different aspects even directed, although restricted, various audiences: a philosophical part, physical technological part. these reasons written on elementary level, combining very...

Quantum mechanics is already 100 years old, but remains alive and full of challenging open problems. On one hand, the problems encountered at frontiers modern theoretical physics like Gravity, String Theories, etc. concern Theory, are same time related to mathematics. But even within non-relativistic quantum itself there fundamental unresolved that can be formulated in elementary terms. These also questions mathematics; linear algebra functional analysis particular. Two these will discussed...

The authors show that the eigenvectors of Floquet operators periodically kicked tops with orthogonal, unitary and symplectic canonical transformations conform to predictions respective circular ensembles random matrices.

An elementary technique, based on almost degenerate perturbation theory, is used to establish the association between (unitary and antiunitary) symmetries universality classes of level repulsion for autonomous periodically driven quantum systems. For one such class, characterized by Kramers' degeneracy quartic repulsion, we present a simple example, kicked top with half-integer angular momentum, which has antiunitary symmetry (a generalized time reversal) but no unitary symmetry; in...

The authors present a method of obtaining exact isolated solutions for the class quantum optical systems without use rotating wave approximation. generalises results known from literature to case multilevel atomic systems. analytical properties in Bargmann representation radiation field mode are discussed. analogues these interacting with an external constructed.

Non-local properties of ensembles quantum gates induced by the Haar measure on unitary group are investigated. We analyze entropy entanglement a matrix U equal to Shannon vector singular values reshuffled matrix. Averaging over U(N^2) we find its asymptotic behaviour. For two--qubit derive probability distribution interaction content and show that relative volume set perfect entanglers reads 8/3 \pi \approx 0.85. establish explicit conditions under which given one-qubit bistochastic map is...

Majorana representation of quantum states by a constellation $n$ ``stars'' (points on the sphere) can be used to describe any pure state simple system dimension $n+1$ or permutation symmetric composite consisting qubits. We analyze variance distribution stars, which serve as measure degree noncoherence for systems an entanglement composed systems. Dynamics points induced unitary dynamics is investigated.