Algebraic characterization of X-states in quantum information

A class of two-qubit states called X-states are increasingly being used to discuss entanglement and other quantum correlations in the field of quantum information. Maximally entangled Bell states and "Werner" states are subsets of them. Apart from being so named because their density matrix looks like the letter X, there is not as yet any characterization of them. The su(2) X su(2) X u(1) subalgebra of the full su(4) algebra of two qubits is pointed out as the underlying invariance of this class of states. X-states are a seven-parameter family associated with this subalgebra of seven operators. This recognition provides a route to preparing such states and also a convenient algebraic procedure for analytically calculating their properties. At the same time, it points to other groups of seven-parameter states that, while not at first sight appearing similar, are also invariant under the same subalgebra. And it opens the way to analyzing invariant states of other subalgebras in bipartite systems.Comment: 4 pages, 1 figur

Are N=1 and N=2 supersymmetric quantum mechanics equivalent?

After recalling different formulations of the definition of supersymmetric quantum mechanics given in the literature, we discuss the relationships between them in order to provide an answer to the question raised in the title.Comment: 15 page

Unusual magnetic properties of the low-dimensional quantum magnet Na2V3O7

We report the results of low-temperature measurements of the specific heat Cp(T), ac susceptibility chi(T) and 23Na nuclear magnetic resonance NMR of Na2V3O7. At liquid He temperatures Cp(T)/T exhibits broad field-dependent maxima, which shift to higher temperatures upon increasing the applied magnetic field H. Below 1.5 K the ac magnetic susceptibility chi(T) follows a Curie-Weiss law and exhibits a cusp at 0.086 mK which indicates a phase transition at very low temperatures. These results support the previous conjecture that Na2V3O7 is close to a quantum critical point (QCP) at mu_{0}H = 0 T. The entire data set, including results of measurements of the NMR spin-lattice relaxation 1/T1(T), reveals a complex magnetic behavior at low temperatures. We argue that it is due to a distribution of singlet-triplet energy gaps of dimerized V moments. The dimerization process evolves over a rather broad temperature range around and below 100 K. At the lowest temperatures the magnetic properties are dominated by the response of only a minor fraction of the V moments.Comment: 10.5 pages, 15 figures. Submitted to Phys. Rev.

Calculation of quantum discord for qubit-qudit or N qubits

Quantum discord, a kind of quantum correlation, is defined as the difference between quantum mutual information and classical correlation in a bipartite system. It has been discussed so far for small systems with only a few independent parameters. We extend here to a much broader class of states when the second party is of arbitrary dimension d, so long as the first, measured, party is a qubit. We present two formulae to calculate quantum discord, the first relating to the original entropic definition and the second to a recently proposed geometric distance measure which leads to an analytical formulation. The tracing over the qubit in the entropic calculation is reduced to a very simple prescription. And, when the d-dimensional system is a so-called X state, the density matrix having non-zero elements only along the diagonal and anti-diagonal so as to appear visually like the letter X, the entropic calculation can be carried out analytically. Such states of the full bipartite qubit-qudit system may be named "extended X states", whose density matrix is built of four block matrices, each visually appearing as an X. The optimization involved in the entropic calculation is generally over two parameters, reducing to one for many cases, and avoided altogether for an overwhelmingly large set of density matrices as our numerical investigations demonstrate. Our results also apply to states of a N-qubit system, where "extended X states" consist of (2^(N+2) - 1) states, larger in number than the (2^(N+1) - 1) of X states of N qubits. While these are still smaller than the total number (2^(2N) - 1) of states of N qubits, the number of parameters involved is nevertheless large. In the case of N = 2, they encompass the entire 15-dimensional parameter space, that is, the extended X states for N = 2 represent the full qubit-qubit system.Comment: 6 pages, 1 figur

Feed-Forward Chains of Recurrent Attractor Neural Networks Near Saturation

We perform a stationary state replica analysis for a layered network of Ising spin neurons, with recurrent Hebbian interactions within each layer, in combination with strictly feed-forward Hebbian interactions between successive layers. This model interpolates between the fully recurrent and symmetric attractor network studied by Amit el al, and the strictly feed-forward attractor network studied by Domany et al. Due to the absence of detailed balance, it is as yet solvable only in the zero temperature limit. The built-in competition between two qualitatively different modes of operation, feed-forward (ergodic within layers) versus recurrent (non- ergodic within layers), is found to induce interesting phase transitions.Comment: 14 pages LaTex with 4 postscript figures submitted to J. Phys.

Efficient second harmonic generation from thin films of V-shaped benzo[b]thiophene based molecules

We have designed an original approach for efficient Second Harmonic Generation of tailored V-shape benzo[b]thiophene molecular systems enabling versatile and flexible one-step, dry and technologically friendly thin film processing. The designed moieties show χ(2) values at least as high as the reference LiNbO3 single crystal, without poling processing and matching the constrains of integrated optical configuration for nonlinear optical devices. This may open the way to a new class of organic materials exploitable for photonic applications

Amplified spontaneous emission of Rhodamine 6G embedded in pure deoxyribonucleic acid

Deoxyribonucleic acid (DNA) is commonly viewed as a genetic information carrier. However, now it is recognized as a nanomaterial, rather than as a biological material, in the research field of nanotechnology. Here, we show that using pure DNA, doped with rhodamine 6G, we are able to observe amplified spontaneous emission (ASE) phenomenon. Moderate ASE threshold, photodegradation, and reasonable gain coefficient observed in this natural host gives some perspectives for practical applications of this system in biophotonics. Obtained results open the way and will be leading to construction of truly bio-lasers using nature made luminophores, such as anthocyanins

Transport theory yields renormalization group equations

We show that dissipative transport and renormalization can be described in a single theoretical framework. The appropriate mathematical tool is the Nakajima-Zwanzig projection technique. We illustrate our result in the case of interacting quantum gases, where we use the Nakajima-Zwanzig approach to investigate the renormalization group flow of the effective two-body interaction.Comment: 11 pages REVTeX, twocolumn, no figures; revised version with additional examples, to appear in Phys. Rev.

Coarse Grainings and Irreversibility in Quantum Field Theory

In this paper we are interested in the studying coarse-graining in field theories using the language of quantum open systems. Motivated by the ideas of Calzetta and Hu on correlation histories we employ the Zwanzig projection technique to obtain evolution equations for relevant observables in self-interacting scalar field theories. Our coarse-graining operation consists in concentrating solely on the evolution of the correlation functions of degree less than $n$, a treatment which corresponds to the familiar from statistical mechanics truncation of the BBKGY hierarchy at the n-th level. We derive the equations governing the evolution of mean field and two-point functions thus identifying the terms corresponding to dissipation and noise. We discuss possible applications of our formalism, the emergence of classical behaviour and the connection to the decoherent histories framework.Comment: 25 pages, Late