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.

A vector measure for the intelligence of a question-answering (Q-A) system

The problem of quantification of intelligence of humans, and of intelligent systems, has been a challenging and controversial topic. IQ tests have been traditionally used to quantify human intelligence based on results of test designed by psychologists. It is in general very difficult to quantify intelligence. In this paper the authors consider a simple question-answering (Q-A) system and use this to quantify intelligence. The authors quantify intelligence as a vector with three components. The components consist of a measure of knowledge in asking questions, effectiveness of questions asked, and correctness of deduction. The authors formalize these parameters and have conducted experiments on humans to measure these parameters

Stochastic differential games: Occupation measure based approach

A new approach based on occupation measures is introduced for studying stochastic differential games. For two-person zero-sum games, the existence of values and optimal strategies for both players is established for various payoff criteria. ForN-person games, the existence of equilibria in Markov strategies is established for various cases.

Strength Symmetry Index: A measure of seizure adequacy in ECT

Seizure electroencephalography (EEG) was recorded from two channels-right (Rt) and left (Lt)-during bilateral electroconvulsive therapy (ECT) (n = 12) and unilateral ECT (n = 12). The EEG was also acquired into a microcomputer and was analyzed without knowledge of the clinical details. EEG recordings of both ECT procedures yielded seizures of comparable duration. The Strength Symmetry Index (SSI) was computed from the early- and midseizure phases using the fractal dimension of the EEG. The seizures of unilateral ECT were characterized by significantly smaller SSI in both phases. More unilateral than bilateral ECT seizures had a smaller than median SSI in both phases. The seizures also differed on other measures as reported in the literature. The findings indicate that SSI may be a potential measure of seizure adequacy that remains to be validated in future research.

Structural sensitivity as a measure of redundancy

The conventional definition of redundancy is applicable to skeletal structural systems only, whereas the concept of redundancy has never been discussed in the context of a continuum. Generally, structures in civil engineering constitute a combination of both skeletal and continuum segments. Hence, this gaper presents a generalized definition of redundancy that has been defined in terms of structural response sensitivity, which is applicable to both continuum and discrete structures. In contrast to the conventional definition of redundancy, which is assumed to be fixed for a given structure and is believed to be independent of loading and material properties, the new definition would depend on strength and response of the structure at a given stage of its service life. The redundancy measure proposed in this paper is linked to the structural response sensitivities. Thus, the structure can have different degrees of redundancy during its lifetime, depending on the response sensitivity under consideration It is believed that this new redundancy measure would be more relevant in structural evaluation, damage assessment, and reliability analysis of structures at large.

A Gradient-Based Comparison Measure for Visual analysis of Multifield Data

We introduce a multifield comparison measure for scalar fields that helps in studying relations between them. The comparison measure is insensitive to noise in the scalar fields and to noise in their gradients. Further, it can be computed robustly and efficiently. Results from the visual analysis of various data sets from climate science and combustion applications demonstrate the effective use of the measure.

Speech segmentation using extrema based signal track length measure

We introduce a novel temporal feature of a signal, namely extrema-based signal track length (ESTL) for the problem of speech segmentation. We show that ESTL measure is sensitive to both amplitude and frequency of the signal. The short-time ESTL (ST_ESTL) shows a promising way to capture the significant segments of speech signal, where the segments correspond to acoustic units of speech having distinct temporal waveforms. We compare ESTL based segmentation with ML and STM methods and find that it is as good as spectral feature based segmentation, but with lesser computational complexity.

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.

A high precision instrument to measure angular and binocular deviation introduced by aircraft windscreens by using a shadow casting technique

Objects viewed through transparent sheets with residual non-parallelism and irregularity appear shifted and distorted. This distortion is measured in terms of angular and binocular deviation of an object viewed through the transparent sheet. The angular and binocular deviations introduced are particularly important in the context of aircraft windscreens and canopies as they can interfere with decision making of pilots especially while landing, leading to accidents. In this work, we have developed an instrument to measure both the angular and binocular deviations introduced by transparent sheets. This instrument is especially useful in the qualification of aircraft windscreens and canopies. It measures the deviation in the geometrical shadow cast by a periodic dot pattern trans-illuminated by the distorted light beam from the transparent test specimen compared to the reference pattern. Accurate quantification of the shift in the pattern is obtained by cross-correlating the reference shadow pattern with the specimen shadow pattern and measuring the location of the correlation peak. The developed instrument is handy to use and computes both angular and binocular deviation with an accuracy of less than +/- 0.1 mrad (approximate to 0.036 mrad) and has an excellent repeatability with an error of less than 2%. (C) 2012 American Institute of Physics. http://dx.doi.org/10.1063/1.4769756]

Asymptotics of the invariant measure in mean field models with jumps

We consider the asymptotics of the invariant measure for the process of spatial distribution of N coupled Markov chains in the limit of a large number of chains. Each chain reflects the stochastic evolution of one particle. The chains are coupled through the dependence of transition rates on the spatial distribution of particles in the various states. Our model is a caricature for medium access interactions in wireless local area networks. Our model is also applicable in the study of spread of epidemics in a network. The limiting process satisfies a deterministic ordinary differential equation called the McKean-Vlasov equation. When this differential equation has a unique globally asymptotically stable equilibrium, the spatial distribution converges weakly to this equilibrium. Using a control-theoretic approach, we examine the question of a large deviation from this equilibrium.

Efficient energy transport in photosynthesis: roles of coherence and entanglement

Recently it has been discovered---contrary to expectations of physicists as well as biologists---that the energy transport during photosynthesis, from the chlorophyll pigment that captures the photon to the reaction centre where glucose is synthesised from carbon dioxide and water, is highly coherent even at ambient temperature and in the cellular environment. This process and the key molecular ingredients that it depends on are described. By looking at the process from the computer science view-point, we can study what has been optimised and how. A spatial search algorithmic model based on robust features of wave dynamics is presented.

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.