Entanglement under restricted operations: Analogy to mixed-state entanglement

We show that the classification of bipartite pure entangled states when local quantum operations are restricted yields a structure that is analogous in many respects to that of mixed-state entanglement. Specifically, we develop this analogy by restricting operations through local superselection rules, and show that such exotic phenomena as bound entanglement and activation arise using pure states in this setting. This analogy aids in resolving several conceptual puzzles in the study of entanglement under restricted operations. In particular, we demonstrate that several types of quantum optical states that possess confusing entanglement properties are analogous to bound entangled states. Also, the classification of pure-state entanglement under restricted operations can be much simpler than for mixed-state entanglement. For instance, in the case of local Abelian superselection rules all questions concerning distillability can be resolved.

Distillability of Werner states using entanglement witnesses and robust semidefinite programs

We use robust semidefinite programs and entanglement witnesses to study the distillability of Werner states. We perform exact numerical calculations that show two-undistillability in a region of the state space, which was previously conjectured to be undistillable. We also introduce bases that yield interesting expressions for the distillability witnesses and for a tensor product of Werner states with an arbitrary number of copies.

Mixed-state entanglement in the light of pure-state entanglement constrained by superselection rules

We show that the classification of bi-partite pure entangled states when local quantum operations are restricted, e.g., constrained by local superselection rules, yields a structure that is analogous in many respects to that of mixed-state entanglement, including such exotic phenomena as bound entanglement and activation. This analogy aids in resolving several conceptual puzzles in the study of entanglement under restricted operations. Specifically, we demonstrate that several types of quantum optical states that possess confusing entanglement properties are analogous to bound entangled states. Also, the classification of pure-state entanglement under restricted operations can be much simpler than for mixed state entanglement. For instance, in the case of local Abelian superselection rules all questions concerning distillability can be resolved.

Multipartite entanglement and quantum state exchange

We investigate multipartite entanglement in relation to the process of quantum state exchange. In particular, we consider such entanglement for a certain pure state involving two groups of N trapped atoms. The state, which can be produced via quantum state exchange, is analogous to the steady-state intracavity state of the subthreshold optical nondegenerate parametric amplifier. We show that, first, it possesses some 2N-way entanglement. Second, we place a lower bound on the amount of such entanglement in the state using a measure called the entanglement of minimum bipartite entropy.

Entanglement measure for rank-2 mixed states

We provide an easily computable formula for a bipartite mixed-state entanglement measure. Our formula can be applied to readily calculate the entanglement for any rank-2 mixed state of a bipartite system. We use this formula to provide a tight upper bound for the entanglement of formation for rank-2 states of a qubit and a qudit. We also outline situations where our formula could be applied to study the entanglement properties of complex quantum systems.

Robustness of quantum gates in the presence of noise

We define several quantitative measures of the robustness of a quantum gate against noise. Exact analytic expressions for the robustness against depolarizing noise are obtained for all bipartite unitary quantum gates, and it is found that the controlled-NOT gate is the most robust two-qubit quantum gate, in the sense that it is the quantum gate which can tolerate the most depolarizing noise and still generate entanglement. Our results enable us to place several analytic upper bounds on the value of the threshold for quantum computation, with the best bound in the most pessimistic error model being p(th)less than or equal to0.5.

Entanglement induced by spontaneous emission in spatially extended two-atom systems

The role of the collective antisymmetric state in entanglement creation by spontaneous emission in a system of two non-overlapping two-level atoms has been investigated. Populations of the collective atomic states and the Wootters entanglement measure (concurrence) for two sets of initial atomic conditions are calculated and illustrated graphically. Calculations include the dipole-dipole interaction and a spatial separation between the atoms that the antisymmetric state of the system is included throughout even for small interatomic separations. It is shown that spontaneous emission can lead to a transient entanglement between the atoms even if the atoms were prepared initially in an unentangled state. It is found that the ability of spontaneous emission to create transient entanglement relies on the absence of population in the collective symmetric state of the system. For the initial state of only one atom excited, entanglement builds up rapidly in time and reaches a maximum for parameter values corresponding roughly to zero population in the symmetric state. On the other hand, for the initial condition of both atoms excited, the atoms remain unentangled until the symmetric state is depopulated. A simple physical interpretation of these results is given in terms of the diagonal states of the density matrix of the system. We also study entanglement creation in a system of two non-identical atoms of different transition frequencies. It is found that the entanglement between the atoms can be enhanced compared to that for identical atoms, and can decay with two different time scales resulting from the coherent transfer of the population from the symmetric to the antisymmetric state. In addition, it was found that a decaying initial entanglement between the atoms can display a revival behaviour.

Nucleation regime map for liquid bound granules

Nucleation is the first step in granulation where the powder and liquid first contact. Two types of nucleation in wet granulation processes are proposed. Drop controlled nucleation, where one drop forms one nucleus, occurs when drops hitting the powder surface do not overlap (low spray flux Psi(a)) and the drop must wet quickly into the bed (short drop penetration time t(p)). If either criterion is not met, powder mixing characteristics will dominate (mechanical dispersion regime). Granulation experiments were performed with lactose powder, water, PEG200, and 7% HPC solution in a 6 L and a 25 L mixer granulator. Size distributions were measured as the drop penetration time and spray flux were varied. At short penetration times, decreasing Psi(a) caused the nuclei distribution to become narrower. When drop penetration time was high, the nuclei size distribution was broad independent of changes in dimensionless spray flux. Nucleation regime maps were plotted for each set of experiments in each mixer as a function of the dimensionless distribution width delta. The nucleation regime map demonstrates the interaction between drop penetration time and spray flux in nucleation. The narrowest distribution consistently occurred at low spray flux and low penetration time, proving the existence of the drop controlled regime. The nucleation regime map provides a rational basis for design and scale-up of nucleation and wetting in wet granulation.

Entanglement of two-mode Bose-Einstein condensates

We investigate the entanglement characteristics of two general bimodal Bose-Einstein condensates-a pair of tunnel-coupled Bose-Einstein condensates and the atom-molecule Bose-Einstein condensate. We argue that the entanglement is only physically meaningful if the system is viewed as a bipartite system, where the subsystems are the two modes. The indistinguishibility of the particles in the condensate means that the atomic constituents are physically inaccessible and, thus, the degree of entanglement between individual particles, unlike the entanglement between the modes, is not experimentally relevant so long as the particles remain in the condensed state. We calculate the entanglement between the two modes for the exact ground state of the two bimodal condensates and consider the dynamics of the entanglement in the tunnel-coupled case.

Entanglement and spin squeezing in the two-atom Dicke model

We analyse the relation between the entanglement and spin-squeezing parameter in the two-atom Dicke model and identify the source of the discrepancy recently reported by Banerjee (2001 Preprint quant-ph/0110032) and Zhou et al (2002 J. Opt. B. Quantum Semiclass. Opt. 4 425), namely that one can observe entanglement without spin squeezing. Our calculations demonstrate that there are two criteria for entanglement, one associated with the two-photon coherences that create two-photon entangled states, and the other associated with populations of the collective states. We find that the spin-squeezing parameter correctly predicts entanglement in the two-atom Dicke system only if it is associated with two-photon entangled states, but fails to predict entanglement when it is associated with the entangled symmetric state. This explicitly identifies the source of the discrepancy and explains why the system can be entangled without spin squeezing. We illustrate these findings with three examples of the interaction of the system with thermal, classical squeezed vacuum, and quantum squeezed vacuum fields.

Spin squeezing as a measure of entanglement in a two-qubit system

We show that the two definitions of spin squeezing extensively used in the literature [M. Kitagawa and M. Ueda, Phys. Rev. A 47, 5138 (1993) and D.J. Wineland , Phys. Rev. A 50, 67 (1994)] give different predictions of entanglement in the two-atom Dicke system. We analyze differences between the definitions and show that the spin squeezing parameter of Kitagawa and Ueda is a better measure of entanglement than the commonly used spectroscopic spin squeezing parameter. We illustrate this relation by examining different examples of a driven two-atom Dicke system in which spin squeezing and entanglement arise dynamically. We give an explanation of the source of the difference using the negativity criterion for entanglement.

Entanglement of two atoms

We discuss the problem of creation of entangled states in a system of two two-level atoms which are separated by an arbitrary distance r(12) and interact with each other via the dipole-dipole interaction and both are driven by a laser field. The entangled antisymmetric state of the system is included throughout, even for small inter-atomic separations. Different mechanisms leading to effective transfer of population to the antisymmetric state are identified. The steady-state values of concurrence which is a measure of entanglement are calculated showing that perfect entanglement can be reached in case of two non-identical atoms.

Entangled subspaces and quantum symmetries

Entanglement is defined for each vector subspace of the tensor product of two finite-dimensional Hilbert spaces, by applying the notion of operator entanglement to the projection operator onto that subspace. The operator Schmidt decomposition of the projection operator defines a string of Schmidt coefficients for each subspace, and this string is assumed to characterize its entanglement, so that a first subspace is more entangled than a second, if the Schmidt string of the second majorizes the Schmidt string of the first. The idea is applied to the antisymmetric and symmetric tensor products of a finite-dimensional Hilbert space with itself, and also to the tensor product of an angular momentum j with a spin 1/2. When adapted to the subspaces of states of the nonrelativistic hydrogen atom with definite total angular momentum (orbital plus spin), within the space of bound states with a given total energy, this leads to a complete ordering of those subspaces by their Schmidt strings.

The crystal structures of Klebsiella pneumoniae acetolactate synthase with enzyme-bound cofactor and with an unusual intermediate

Acetohydroxyacid synthase (AHAS) and acetolactate synthase (ALS) are thiamine diphosphate (ThDP)-dependent enzymes that catalyze the decarboxylation of pyruvate to give a cofactor-bound hydroxyethyl group, which is transferred to a second molecule of pyruvate to give 2-acetolactate. AHAS is found in plants, fungi, and bacteria, is involved in the biosynthesis of the branched-chain amino acids, and contains non-catalytic FAD. ALS is found only in some bacteria, is a catabolic enzyme required for the butanediol fermentation, and does not contain FAD. Here we report the 2.3-Angstrom crystal structure of Klebsiella pneumoniae ALS. The overall structure is similar to AHAS except for a groove that accommodates FAD in AHAS, which is filled with amino acid side chains in ALS. The ThDP cofactor has an unusual conformation that is unprecedented among the 26 known three-dimensional structures of nine ThDP-dependent enzymes, including AHAS. This conformation suggests a novel mechanism for ALS. A second structure, at 2.0 Angstrom, is described in which the enzyme is trapped halfway through the catalytic cycle so that it contains the hydroxyethyl intermediate bound to ThDP. The cofactor has a tricyclic structure that has not been observed previously in any ThDP-dependent enzyme, although similar structures are well known for free thiamine. This structure is consistent with our proposed mechanism and probably results from an intramolecular proton transfer within a tricyclic carbanion that is the true reaction intermediate. Modeling of the second molecule of pyruvate into the active site of the enzyme with the bound intermediate is consistent with the stereochemistry and specificity of ALS.

Converged quantum calculations of HO2 bound states and resonances for J=6 and 10

Bound and resonance states of HO2 are calculated quantum mechanically using both the Lanczos homogeneous filter diagonalization method and the real Chebyshev filter diagonalization method for nonzero total angular momentum J=6 and 10, using a parallel computing strategy. For bound states, agreement between the two methods is quite satisfactory; for resonances, while the energies are in good agreement, the widths are in general agreement. The quantum nonzero-J specific unimolecular dissociation rates for HO2 are also calculated. (C) 2004 American Institute of Physics.