Quantum Correlations In States Research Articles

Note on a canonical form of matrix product states

A canonical form for a matrix product state representation of a general finitely correlated quantum state on a one-dimensional (finite or infinite) lattice is proposed by exploring the gauge symmetry of the matrix product. This representation is unique in the sense that it is the only one which generates canonical forms for all reduced density matrices of the state.

Ground state correlations in a trapped quasi one-dimensional Bose gas

We review the basic concepts of a non-equilibrium kinetic theory of a trapped bosonic gas. By extending the successful mean-field concept of the Gross–Pitaevskii equation with the effects of non-local, two particle quantum correlations, one obtains a renormalized binary interaction and allows for the dynamic establishment of non-classical many-particle quantum correlations. These concepts are illustrated by self-consistent numerical calculations of the first- and second-order ground state quantum correlations of a harmonically trapped, quasi one-dimensional bosonic gas. We do find a strong suppression of the density fluctuations or, in other words, an enhanced number squeezing with decreasing particle density.

Nature and measure of entanglement in quantum phase transitions

Characterizing and quantifying quantum correlations in states of many-particle systems is at the core of a full understanding of phase transitions in matter. In this work, we continue our investigation of the notion of generalized entanglement [Barnum et al., Phys. Rev. A 68, 032308 (2003)] by focusing on a simple Lie-algebraic measure of purity of a quantum state relative to an observable set. For the algebra of local observables on multi-qubit systems, the resulting local purity measure is equivalent to a recently introduced global entanglement measure [Meyer and Wallach, J. Math. Phys. 43, 4273 (2002)]. In the condensed-matter setting, the notion of Lie-algebraic purity is exploited to identify and characterize the quantum phase transitions present in two exactly solvable models, namely the Lipkin-Meshkov-Glick model and the spin-$\frac{1}{2}$ anisotropic $XY$ model in a transverse magnetic field. For the latter, we argue that a natural fermionic observable set arising after the Jordan-Wigner transformation better characterizes the transition than alternative measures based on qubits. This illustrates the usefulness of going beyond the standard subsystem-based framework while providing a global disorder parameter for this model. Our results show how generalized entanglement leads to useful tools for distinguishing between the ordered and disordered phases in the case of broken symmetry quantum phase transitions. Additional implications and possible extensions of concepts to other systems of interest in condensed-matter physics are also discussed.

Communication Using Quantum States

Abstract Standard information theory deals with alphabets and their transmission over communication channels. Here we examine the novel features introduced by allowing the alphabet symbols to be quantum states. A simple device for communication of one bit of information is discussed and the transition between quantum and classical behaviour is highlighted. A further level of complexity is introduced when we allow the communication to take place with quantum-correlated states. We show, by the simple expedient of constructing a suitable local hidden variable theory, that many of the novel features of such communication are compatible with the concept of local realism. We introduce a convenient parameter for characterizing the contribution of the quantum entanglement to the communication.

Optical quantum nondemolition measurements: experiments

We review the schemes which have been implemented, in order to achieve quantum nondemolition (QND) measurements in the optical domain. The simplest schemes can be obtained using the optical Kerr effect, which yields a crossed-phase modulation coupling between two light beams. Other schemes use either independently generated squeezed light, or coupled-mode parametric amplifiers. These various schemes can be characterized using three criteria, which described respectively the quality of the quantum measurement, the nondestruction of the signal, and the ability of the device to prepare the output beams in a correlated quantum state (“quantum-state preparation”, or QSP criterion). Then we present in more detail an experimental implementation of QND measurements, using three-level atoms inside a doubly resonant optical cavity.

Quantum correlations and squeezing phenomena in lasers

A new principle of laser coherence found recently provides an example of the most correlated quantum state. We discuss the relation between squeezing phenomena and quantum correlations (QC). These new results can be understood only in the framework of a special QC approach.

ChemInform Abstract: Some New Techniques in Nuclear Magnetic Resonance

Abstract Nuclear magnetic resonance (NMR) has undergone a revolution in the last decade with the original slow-passage spectroscopy method being replaced by pulsed methods. Much of pulsed NMR can be understood in terms of a simple classical, or semi-classical, model of precessing spin vectors, but some new techniques are based purely on quantum mechanical physics. One very useful technique described in this paper is the DEPT sequence, which is an example of correlated quantum states of the type invoked in the Einstein, Podolsky and Rosen paradox. These new developments are not only exciting because of their potential applications, but also interesting in terms of their underlying physics.

Some new techniques in nuclear magnetic resonance

Abstract Nuclear magnetic resonance (NMR) has undergone a revolution in the last decade with the original slow-passage spectroscopy method being replaced by pulsed methods. Much of pulsed NMR can be understood in terms of a simple classical, or semi-classical, model of precessing spin vectors, but some new techniques are based purely on quantum mechanical physics. One very useful technique described in this paper is the DEPT sequence, which is an example of correlated quantum states of the type invoked in the Einstein, Podolsky and Rosen paradox. These new developments are not only exciting because of their potential applications, but also interesting in terms of their underlying physics.

Communication and non-communication in Einstein-Rosen experiments

Observers of two particles in correlated quantum states cannot communicate by altering their detection apparatus. We investigate how this result originates from basic assumptions made in quantum mechanics

New method for increase of interaction of gravitational radiation with an antenna

It is shown that there may be a large increase in the interaction of gravitational radiation with an antenna prepared in correlated quantum states.