Alexander A. Klyachko

Simple test for hidden variables in spin-1 systems.

We resolve an old problem about the existence of hidden parameters in a three-dimensional quantum system by constructing an appropriate Bells type inequality. This reveals the nonclassical nature of most spin-1 states. We shortly discuss some physical implications and an underlying cause of this nonclassical behavior, as well as a perspective of its experimental verification.

Quantum marginal problem and N-representability

A fermionic version of the quantum marginal problem was known from the early sixties as N-representability problem. In 1995 it was mentioned by the National Research Council of the USA as one of ten most prominent research challenges in quantum chemistry. In spite of this recognition the progress was very slow, until a couple of years ago the problem came into focus again, now in the framework of quantum information theory. In the paper I give a survey of the recent development.

The Pauli Principle Revisited

By the Pauli exclusion principle, no quantum state can be occupied by more than one electron. One can state this as a constraint on the one electron density matrix that bounds its eigenvalues by 1. Shortly after its discovery, the Pauli principle was replaced by anti-symmetry of the multi-electron wave function. In this paper we solve a longstanding problem about the impact of this replacement on the one electron density matrix, that goes far beyond the original Pauli principle. Our approach uses Berenstein and Sjamaar’s theorem on the restriction of an adjoint orbit onto a subgroup, and allows us to treat any type of permutational symmetry.

Random walks on symmetric spaces and inequalities for matrix spectra

Abstract 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. Thompsons conjecture [Matrix Spectral Inequalities, Johns Hopkins University Press, Baltimore, MD, 1988].

Steady-state entanglement of two atoms created by classical driving field

The stabilization of entanglement caused by action of a classical driving field in the system of two-level atoms with the dipole interaction accompanied by spontaneous emission is discussed. An exact solution shows that the maximum amount of concurrence that can be achieved in the Lamb-Dicke limit is 0.43. Dependence of entanglement on interatomic distance and the classical driving field, beyond the Lamb-Dicke limit, is examined numerically.

Persistent entanglement in three-level atomic systems

We discuss the evolution towards persistent entangled state in an atom–photon system. A maximally entangled state can be stabilized at a local minimum of the system by draining some energy, thus obtaining a persistent entangled state. This scheme can be realized in three-level, Λ type atomic systems since the third level is a meta-stable state. In particular, we compare dynamical description based on the exact and effective models. Some experimental realizations are discussed.

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.

Entanglement and the SU(2) phase states in atomic systems

We show that a system of 2n identical two-level atoms interacting with n cavity photons manifests entanglement and that the set of entangled states coincides with the so-called SU(2) phase states. In particular, violationof classical realism in terms of the Greenberger-Horne-Zeilinger and Clauser-Horne-Shimoni-Holt conditions is proved. We discuss a property of entanglement expressed in terms of local measurements. We also show that generation of entangled states in the atom-photon systems under consideration strongly depends on the choice of initial conditions and that the parasitic influence of cavity detuning can be compensated through the use of Kerr medium.

Robust entanglement in atomic systems via Λ -type processes

It is shown that the system of two three-level atoms in the {lambda} configuration in a cavity can evolve into a long-lived maximum entangled state if the Stokes photons vanish from the cavity by means of either leakage or damping. The difference in the evolution picture corresponding to the general model and effective model with two-photon process in a two-level system is discussed.

Entanglement, local measurements and symmetry

A definition of entanglement in terms of local measurements is discussed. Namely, the maximum entanglement corresponds to the states that cause the highest level of quantum fluctuations in all local measurements determined by the dynamic symmetry group of the system. A number of examples illustrating this definition is considered.