Quantum entanglement in a noncommutative system

We explore the effect of two-dimensional position-space noncommutativity on the bipartite entanglement of continuous-variable systems. We first extend the standard symplectic framework for studying entanglement of Gaussian states of commutative systems to the case of noncommutative systems residing in two dimensions. Using the positive partial transpose criterion for separability of bipartite states, we derive a condition on the separability of a noncommutative system that is dependent on the noncommutative parameter theta. We then consider the specific example of a bipartite Gaussian state and show the quantitative reduction in entanglement originating from noncommutative dynamics. We show that such a reduction in entanglement for a noncommutative system arising from the modification of the variances of the phase-space variables (uncertainty relations) is clearly manifested between two particles that are separated by small distances.

Correlations, quantum entanglement and interference in nanoscopic systems

Several of the most interesting quantum effects can or could be observed in nanoscopic systems. For example, the effect of strong correlations between electrons and of quantum interference can be measured in transport experiments through quantum dots, wires, individual molecules and rings formed by large molecules or arrays of quantum dots. In addition, quantum coherence and entanglement can be clearly observed in quantum corrals. In this paper we present calculations of transport properties through Aharonov-Bohm strongly correlated rings where the characteristic phenomenon of charge-spin separation is clearly observed. Additionally quantum interference effects show up in transport through pi-conjugated annulene molecules producing important effects on the conductance for different source-drain configurations, leading to the possibility of an interesting switching effect. Finally, elliptic quantum corrals offer an ideal system to study quantum entanglement due to their focalizing properties. Because of an enhanced interaction between impurities localized at the foci, these systems also show interesting quantum dynamical behaviour and offer a challenging scenario for quantum information experiments.

Entanglement and nonclassicality for multimode radiation-field states

Nonclassicality in the sense of quantum optics is a prerequisite for entanglement in multimode radiation states. In this work we bring out the possibilities of passing from the former to the latter, via action of classicality preserving systems like beam splitters, in a transparent manner. For single-mode states, a complete description of nonclassicality is available via the classical theory of moments, as a set of necessary and sufficient conditions on the photon number distribution. We show that when the mode is coupled to an ancilla in any coherent state, and the system is then acted upon by a beam splitter, these conditions turn exactly into signatures of negativity under partial transpose (NPT) entanglement of the output state. Since the classical moment problem does not generalize to two or more modes, we turn in these cases to other familiar sufficient but not necessary conditions for nonclassicality, namely the Mandel parameter criterion and its extensions. We generalize the Mandel matrix from one-mode states to the two-mode situation, leading to a natural classification of states with varying levels of nonclassicality. For two-mode states we present a single test that can, if successful, simultaneously show nonclassicality as well as NPT entanglement. We also develop a test for NPT entanglement after beam-splitter action on a nonclassical state, tracing carefully the way in which it goes beyond the Mandel nonclassicality test. The result of three-mode beam-splitter action after coupling to an ancilla in the ground state is treated in the same spirit. The concept of genuine tripartite entanglement, and scalar measures of nonclassicality at the Mandel level for two-mode systems, are discussed. Numerous examples illustrating all these concepts are presented.

Exact entanglement studies of strongly correlated systems: role of long-range interactions and symmetries of the system

We study the bipartite entanglement of strongly correlated systems using exact diagonalization techniques. In particular, we examine how the entanglement changes in the presence of long-range interactions by studying the Pariser-Parr-Pople model with long-range interactions. We compare the results for this model with those obtained for the Hubbard and Heisenberg models with short-range interactions. This study helps us to understand why the density matrix renormalization group (DMRG) technique is so successful even in the presence of long-range interactions. To better understand the behavior of long-range interactions and why the DMRG works well with it, we study the entanglement spectrum of the ground state and a few excited states of finite chains. We also investigate if the symmetry properties of a state vector have any significance in relation to its entanglement. Finally, we make an interesting observation on the entanglement profiles of different states (across the energy spectrum) in comparison with the corresponding profile of the density of states. We use isotropic chains and a molecule with non-Abelian symmetry for these numerical investigations.

ENTANGLEMENT IN A 3-SPIN HEISENBERG-XY CHAIN WITH NEAREST-NEIGHBOR INTERACTIONS, SIMULATED IN AN NMR QUANTUM SIMULATOR

The evolution of entanglement in a 3-spin chain with nearest-neighbor Heisenberg-XY interactions for different initial states is investigated here. In an NMR experimental implementation, we generate multipartite entangled states starting from initial separable pseudo-pure states by simulating nearest-neighbor XY interactions in a 3-spin linear chain of nuclear spin qubits. For simulating XY interactions, we follow algebraic method of Zhang et al. Phys. Rev. A 72 (2005) 012331]. Bell state between end qubits has been generated by using only the unitary evolution of the XY Hamiltonian. For generating W-state and GHZ-state a single qubit rotation is applied on second and all the three qubits, respectively after the unitary evolution of the XY Hamiltonian.

Quantum phases of dimerized and frustrated Heisenberg spin chains with s=1/2, 1 and 3/2: an entanglement entropy and fidelity study

We study here different regions in phase diagrams of the spin-1/2, spin-1 and spin-3/2 one-dimensional antiferromagnetic Heisenberg systems with frustration (next-nearest-neighbor interaction J(2)) and dimerization (delta). In particular, we analyze the behaviors of the bipartite entanglement entropy and fidelity at the gapless to gapped phase transitions and across the lines separating different phases in the J(2)-delta plane. All the calculations in this work are based on numerical exact diagonalizations of finite systems.

Minimum uncertainty and entanglement

We address the question, does a system A being entangled with another system B, put any constraints on the Heisenberg uncertainty relation (or the Schrodinger-Robertson inequality)? We find that the equality of the uncertainty relation cannot be reached for any two noncommuting observables, for finite dimensional Hilbert spaces if the Schmidt rank of the entangled state is maximal. One consequence is that the lower bound of the uncertainty relation can never be attained for any two observables for qubits, if the state is entangled. For infinite-dimensional Hilbert space too, we show that there is a class of physically interesting entangled states for which no two noncommuting observables can attain the minimum uncertainty equality.

MINIMUM UNCERTAINTY AND ENTANGLEMENT

We address the question, does a system A being entangled with another system B, put any constraints on the Heisenberg uncertainty relation (or the Schrodinger-Robertson inequality)? We find that the equality of the uncertainty relation cannot be reached for any two noncommuting observables, for finite dimensional Hilbert spaces if the Schmidt rank of the entangled state is maximal. One consequence is that the lower bound of the uncertainty relation can never be attained for any two observables for qubits, if the state is entangled. For infinite-dimensional Hilbert space too, we show that there is a class of physically interesting entangled states for which no two noncommuting observables can attain the minimum uncertainty equality.

Constraining gravity using entanglement in AdS/CFT

We investigate constraints imposed by entanglement on gravity in the context of holography. First, by demanding that relative entropy is positive and using the Ryu-Takayanagi entropy functional, we find certain constraints at a nonlinear level for the dual gravity. Second, by considering Gauss-Bonnet gravity, we show that for a class of small perturbations around the vacuum state, the positivity of the two point function of the field theory stress tensor guarantees the positivity of the relative entropy. Further, if we impose that the entangling surface closes off smoothly in the bulk interior, we find restrictions on the coupling constant in Gauss-Bonnet gravity. We also give an example of an anisotropic excited state in an unstable phase with broken conformal invariance which leads to a negative relative entropy.

Optimal values of bipartite entanglement in a tripartite system

For a general tripartite system in some pure state, an observer possessing any two parts will see them in a mixed state. By the consequence of Hughston-Jozsa-Wootters theorem, each basis set of local measurement on the third part will correspond to a particular decomposition of the bipartite mixed state into a weighted sum of pure states. It is possible to associate an average bipartite entanglement ((S) over bar) with each of these decompositions. The maximum value of (S) over bar is called the entanglement of assistance (E-A) while the minimum value is called the entanglement of formation (E-F). An appropriate choice of the basis set of local measurement will correspond to an optimal value of (S) over bar; we find here a generic optimality condition for the choice of the basis set. In the present context, we analyze the tripartite states W and GHZ and show how they are fundamentally different. (C) 2014 Elsevier B.V. All rights reserved.

SecB binds only to a late native-like intermediate in the folding pathway of barstar and not to the unfolded state

SecB is a cytosolic, tetrameric chaperone of Escherichia coli which maintains precursor proteins in a translocation competent state. We have investigated the effect of SecB on the refolding kinetics of the small protein barstar in I M guanidine hydrochloride at pH 7.0 and 25 degrees C using fluorescence spectroscopy. We show that SecB does not bind either the native or the unfolded states of barstar but binds to a late near-native intermediate along the folding pathway. For barstar, polypeptide collapse and formation of a hydrophobic surface are required for binding to SecB. SecB does not change the apparent rate constant of barstar refolding. The kinetic data for SecB binding to barstar are not consistent with simple kinetic partitioning models.

Electronic Properties of the Vortex State in Cuprate Superconductors

The superconducting state of the cuprates in the presence of a magnetic field has been investigated very actively in the past few years through measurements of electrical and thermal transport, ac conductivity, specific heat, and other quantities. The observed behavior is not well understood; it probes the nature of quasiparticies, vortices, and their interactions in a superconductor with nodes in the pair amplitude. We summarize here experimental results and our attempts to understand the phenomena.

Sizable photocurrent and emission from solid state devices based on CdS nanoparticles

CdS nanoparticles exhibit size dependent optical and electrical properties. We report here the photocurrent and I-V characteristic studies of CdS nanoparticle devices. A sizable short circuit photocurrent was observed in the detection range governed by the size of the clusters. We speculate on the mechanisms leading to the photocurrent and emission in these nanometer scale systems.

Stress-state permeability relationships for clays with coarse fraction

In standard laboratory consolidation tests, only the fraction of soil passing through a particular size of the sieve, called the matrix material, is used. This size is usually restricted to 1/10 of the height of the consolidation ring. Particles larger than this size that are removed before the test may consist of gravel, fragments of rock, or other coarse materials. Hence, it is not possible to estimate the compressibility and permeability of the total material based on the compressibility and permeability behavior obtained from laboratory consolidation tests on the matrix material. In the present investigation an attempt has been made to estimate the compressibility and permeability behavior of the total material based on the compressibility and permeability behavior of the matrix material. The results indicate that the presence of coarse particles will reduce the compressibility of the soil in proportion to the coarse fraction present in the whole soil and will not affect the permeability of the soil for the range investigated. If the coarse fraction exceeds the Limiting percentage, the void ratio-vertical effective stress path will also start to deviate from the predicted path. An expression has been developed to estimate approximately the deviating pressure, and it is found to depend on the soil type as well as the percent clay fraction.

Exact ground state and kink-like excitations of a two-dimensional Heisenberg antiferromagnet

A rare example of a two-dimensional Heisenberg model with an exact dimerized ground state is presented. This model, which can be regarded as a variation on the kagome' lattice, has several features of interest: it has a highly (but not macroscopically) degenerate ground state; it is closely related to spin chains studied by earlier authors; in particular, it exhibits domain-wall-like "kink" excitations normally associated only with one-dimensional systems. In some limits it decouples into noninteracting chains; unusually, this happens in the limit of strong, rather than weak, interchain coupling. [S0163-1829(99)50338-X].