Entanglement of a Single Spin-1 Object: An Example of Ubiquitous Entanglement

Using a single spin-1 object as an example, we discuss a recent approach to quantum entanglement. The key idea of the approach consists in presetting of basic observables in the very definition of quantum system. Specification of basic observables defines the dynamic symmetry of the system. Entangled states of the system are then interpreted as states with maximal amount of uncertainty of all basic observables. The approach gives purely physical picture of entanglement. In particular, it separates principle physical properties of entanglement from inessential. Within the model example under consideration, we show relativity of entanglement with respect to dynamic symmetry and argue existence of single-particle entanglement. A number of physical examples are considered.Comment: 12 pages, 2 figure : title has been changed, paper is re-organized, new section "Violation of Bell-type condition by single spin-1" is adde

Stable bundles, representation theory and Hermitian operators

We give an interpretation and a solution of the classical problem of the spectrum of the sum of Hermitian matrices in terms of stable bundles on the projective plane. ©Birkhäuser Verlag, Basel, 1998

Random walks on symmetric spaces and inequalities for matrix spectra

Using harmonic analysis on symmetric spaces we reduce the singular spectral problem for products of matrices to the recently solved spectral problem for sums of Hermitian matrices. This proves R.C. Thompson's conjecture [Matrix Spectral Inequalities, Johns Hopkins University Press, Baltimore, MD, 1988]. © 2000 Elsevier Science Inc

Random walks on symmetric spaces and inequalities for matrix spectra

Using harmonic analysis on symmetric spaces we reduce the singular spectral problem for products of matrices to the recently solved spectral problem for sums of Hermitian matrices. This proves R.C. Thompson's conjecture [Matrix Spectral Inequalities, Johns Hopkins University Press, Baltimore, MD, 1988]. © 2000 Elsevier Science Inc

Correlations between the ranks of submatrices and weights of random codes

The results of our study are twofold. From the random matrix theory point of view we obtain results on the rank distribution of column submatrices. We give the moments and the covariances between the ranks (q- rank) of such submatrices. We conjecture the counterparts of these results for arbitrary submatrices. The case of higher correlations gets drastically complicated even in the case of three submatrices. We give a formula for the correlation of ranks of three submatrices and a conjecture for its closed form. From the code theoretical point of view our study yields the covariances of the coefficients of the weight enumerator of a random code. Particularly interesting is that the coefficients of the weight enumerator of a code with random parity check matrix are uncorrelated. We give a conjecture for the triple correlations between the coefficients of the weight enumerator of a random code. © 2009 Elsevier Inc. All rights reserved

General approach to quantum entanglement

We examine quantum entanglement as a physical phenomenon independent of specific problems of quantum information technologies. Within the dynamic symmetry approach, we briefly discuss the role of quantum fluctuations in formation of entangled states, including single-particle entanglement, relativity of entanglement with respect to the choice of basic observables, and stabilization of robust entanglement. © Nauka/Interperiodica 2007

Maximum entanglement and its proper measure

We discuss a definition of maximally entangled states in terms of maximum uncertainty of corresponding measurements. We describe a method of construction of bases of maximally entangled states. The entangled states that can be obtained from the maximally entangled states by means of SLOCC (stochastic local operations assisted by classical communications) we consider as semistable vectors. We discuss a measure of entanglement expressed in terms of a geometric invariant

Spin squeezing and entanglement

We reformulate definition of spin squeezing and spin coherence in terms of the total variance in spin operators. We propose a new measure of spin squeezing. We show equivalence of spin squeezing and spin entanglement. © 2007 Optical Society of America

Entanglement of qutrits

For two types of qutrits specified by the dynamical symmetry SU(3) and SU(2), we consider the difference in entanglement caused by the lack of quantum observables in the latter case. In particular, we show that the SU(2) qutrits can have specific separable entanglement caused by quantum correlations of intrinsic degrees of freedom in a single party without interparty correlations. © Nauka/Interperiodica 2007

Stationary entanglement of atoms induced by classical field

We propose a scheme of stabilization of high-level entanglement through the use of classical driving field in atomic system with dipole-dipole interaction and losses caused by spontaneous radiation processes. © 2005 American Institute of Physics