Geometric quantum discord with Bures distance: the qubit case

The minimal Bures distance of a quantum state of a bipartite system AB to the set of classical states for subsystem A defines a geometric measure of quantum discord. When A is a qubit, we show that this geometric quantum discord is given in terms of the eigenvalues of a (2 n_B) x (2 n_B) hermitian matrix, n_B being the Hilbert space dimension of the other subsystem B. As a first application, we calculate the geometric discord for the output state of the DQC1 algorithm. We find that it takes its highest value when the unitary matrix from which the algorithm computes the trace has its eigenvalues uniformly distributed on the unit circle modulo a symmetry with respect to the origin. As a second application, we derive an explicit formula for the geometric discord of two-qubit states with maximally mixed marginals and compare it with other measures of quantum correlations. We also determine the closest classical states to such two-qubit states.Comment: This article contains some material from a previous preprint arXiv:1304.3334v1 [quant-ph], which has been split into two parts, as well as new results. Minor changes in the second version with respect to the first version. 14 pages, 5 figure

Paralittératures. Les indispensables (une bibliothèque de référence)

Ces orientations bibliographiques, adressées au lecteur désireux d'en savoir plus sur l'étude du récit paralittéraire, comprennent des ouvrages généraux et de références, quelques collectifs et quelques études théoriques (mais pas d'analyse d'auteurs spécifiques). Elles sont regroupées par genres : la paralittérature en général et les études regroupant plusieurs genres, le fantastique, le roman western, le roman historique, le roman d'aventures maritimes et le roman de guerre, le roman d'amour et le roman érotique, le roman policier et le roman d'espionnage, la science-fiction et la fantasy .Aimed ai nonspecialists, this bibliography comprises reference tools and general studies, as well as collective and theoretical works on popular literature. Some of the works enumerated deal with popular literature in general; others with studies concerning a specific genre or variety of genres including supernatural and horror fiction, the western, historical romance, sea and war stories, love (from romance all the way to s&m fiction), mysteries, thrillers and spy thrillers, science fiction and fantasy

Bures geodesics and quantum metrology

We study the geodesics on the manifold of mixed quantum states for the Bures metric. It is shown that these geodesics correspond to physical non-Markovian evolutions of the system coupled to an ancilla. Furthermore, we argue that geodesics lead to optimal precision in single-parameter estimation in quantum metrology. More precisely, if the unknown parameter is a phase shift proportional to the time parametrizing the geodesic, the estimation error obtained by processing the data of measurements on the system is equal to the smallest error that can be achieved from joint detections on the system and ancilla, meaning that the ancilla does not carry any information on this parameter. The error can saturate the Heisenberg bound. In addition, the measurement on the system bringing most information on the parameter is parameter-independent and can be determined in terms of the intersections of the geodesic with the boundary of quantum states. These results show that geodesic evolutions are of interest for high-precision detections in systems coupled to an ancilla in the absence of measurements on the ancilla.Comment: 20 pages, 3 figure

Mott law as lower bound for a random walk in a random environment

We consider a random walk on the support of a stationary simple point process on $R^d$, $d\geq 2$ which satisfies a mixing condition w.r.t.the translations or has a strictly positive density uniformly on large enough cubes. Furthermore the point process is furnished with independent random bounded energy marks. The transition rates of the random walk decay exponentially in the jump distances and depend on the energies through a factor of the Boltzmann-type. This is an effective model for the phonon-induced hopping of electrons in disordered solids within the regime of strong Anderson localization. We show that the rescaled random walk converges to a Brownian motion whose diffusion coefficient is bounded below by Mott's law for the variable range hopping conductivity at zero frequency. The proof of the lower bound involves estimates for the supercritical regime of an associated site percolation problem

Macroscopic superpositions in Bose-Josephson junctions: Controlling decoherence due to atom losses

We study how macroscopic superpositions of coherent states produced by the nondissipative dynamics of binary mixtures of ultracold atoms are affected by atom losses. We identify different decoherence scenarios for symmetric or asymmetric loss rates and interaction energies in the two modes. In the symmetric case the quantum coherence in the superposition is lost after a single loss event. By tuning appropriately the energies we show that the superposition can be protected, leading to quantum correlations useful for atom interferometry even after many loss events.Comment: 6 pages, 3 figure

Effect of one-, two-, and three-body atom loss processes on superpositions of phase states in Bose-Josephson junctions

In a two-mode Bose-Josephson junction formed by a binary mixture of ultracold atoms, macroscopic superpositions of phase states are produced during the time evolution after a sudden quench to zero of the coupling amplitude. Using quantum trajectories and an exact diagonalization of the master equation, we study the effect of one-, two-, and three-body atom losses on the superpositions by analyzing separately the amount of quantum correlations in each subspace with fixed atom number. The quantum correlations useful for atom interferometry are estimated using the quantum Fisher information. We identify the choice of parameters leading to the largest Fisher information, thereby showing that, for all kinds of loss processes, quantum correlations can be partially protected from decoherence when the losses are strongly asymmetric in the two modes.Comment: 23 pages, 8 figures, to be published in Eur. Phys. J.

Harnessing synthetic gauge fields for maximally entangled state generation

We study the generation of entanglement between two species of neutral cold atoms living on an optical ring lattice, where each group of particles can be described by a $d$-dimensional Hilbert space (qu$d$it). Synthetic magnetic fields are exploited to create an entangled state between the pair of qu$d$its. Maximally entangled eigenstates are found for well defined values of the Aharonov-Bohm phase, which are zero energy eigenstates of both the kinetic and interacting parts of the Bose-Hubbard Hamiltonian, making them quite exceptional and robust against certain non-perturbative fluctuations of the Hamiltonian. We propose a protocol to reach the maximally entangled state (MES) by starting from an initially prepared ground state. Also, an indirect method to detect the MES by measuring the current of the particles is proposed.Comment: 10 pages, 3 figure

Geometric measures of quantum correlations : characterization, quantification, and comparison by distances and operations

We investigate and compare three distinguished geometric measures of bipartite quantum correlations that have been recently introduced in the literature: the geometric discord, the measurement-induced geometric discord, and the discord of response, each one defined according to three contractive distances on the set of quantum states, namely the trace, Bures, and Hellinger distances. We establish a set of exact algebraic relations and inequalities between the different measures. In particular, we show that the geometric discord and the discord of response based on the Hellinger distance are easy to compute analytically for all quantum states whenever the reference subsystem is a qubit. These two measures thus provide the first instance of discords that are simultaneously fully computable, reliable (since they satisfy all the basic Axioms that must be obeyed by a proper measure of quantum correlations), and operationally viable (in terms of state distinguishability). We apply the general mathematical structure to determine the closest classical-quantum state of a given state and the maximally quantum-correlated states at fixed global state purity according to the different distances, as well as a necessary condition for a channel to be quantumness breaking

BOSONS IN A DOUBLE WELL: TWO-MODE APPROXIMATION AND FLUCTUATIONS

We study the ground state for many interacting bosons in a double-well potential, in a joint limit where the particle number and the distance between the potential wells both go to infinity. Two single-particle orbitals (one for each well) are macroscopically occupied, and we are concerned with deriving the corresponding effective Bose–Hubbard Hamiltonian. We prove an energy expansion, including the two-mode Bose–Hubbard energy and two independent Bogoliubov corrections (one for each potential well), and a variance bound for the number of particles falling inside each potential well. The latter is a signature of a correlated ground state in that it violates the central limit theorem