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

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

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.

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

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

Adiabatic transitions in a two-level system coupled to a free Boson reservoir

We consider a time-dependent two-level quantum system interacting with a free Boson reservoir. The coupling is energy conserving and depends slowly on time, as does the system Hamiltonian, with a common adiabatic parameter $\varepsilon$. Assuming that the system and reservoir are initially decoupled, with the reservoir in equilibrium at temperature $T\ge 0$, we compute the transition probability from one eigenstate of the two-level system to the other eigenstate as a function of time, in the regime of small $\varepsilon$ and small coupling constant $\lambda$. We analyse the deviation from the adiabatic transition probability obtained in absence of the reservoir

Dynamique des systèmes quantiques ouverts décohérence et perte d'intrication

On commence dans le chapitre d'introduction par rappeler les résultats majeurs sur l'intrication et les systèmes quantiques ouverts. Puis en particulier on prouve la désintrication en temps fini pour deux qubits (systèmes quantiques à deux niveaux d'énergie) en interaction avec des bains thermiques distincts à température positive. On propose dans le premier chapitre de cette thèse une méthode pour empêcher la désintrication en temps fini basée sur des mesures continues sur les bains et utilisant la théorie des sauts quantiques et celle des équations différentielles stochastiques. Dans le deuxième chapitre on étudie un sous-ensemble des états de deux qubits : celui des états qu'on peut représenter dans la base canonique pour une matrice ayant une forme de X. Cela nous permet d'obtenir des formules explicites pour la décomposition d'un état X séparable en au plus cinq états purs produits. On généralise ensuite cette étude à l'ensemble des états obtenus à partir d'états X par conjugaison avec des unitaires locaux. Puis on donne un algorithme pour décomposer tout état séparable de cet ensemble en une combinaison convexe de cinq états purs produits. Le troisième chapitre de cette thèse propose l'étude de l'évolution de l'intrication de deux qubits dans un modèle d'interactions répétées avec la même chaîne de spins dans les limites de van Hove et de couplage singulier. En particulier on observe une intrication asymptotique non nulle quand la chaîne est à température infinie et des phénomènes de création d'intrication quand la chaîne est à température nulle.In the introductory chapter we first give the major results about entanglement and open quantum systems. In particular we give the proof of entanglement sudden death (ESD) for two qubits (two level quantum systems) interacting with their own heat bath at positive temperature. We propose in the first chapter a method to protect qubits against ESD, based on continuous measurements of the baths and using the theory of quantum jumps and stochastic differential equations. In the second chapter, we study a subset of two qubits states : the set of states that we can represent in the canonical basis by an X-form matrix. We also give explicit formulas for decompositions of a separable X-state in a convex sum of five pure product states. We generalize this study to the set of states obtained from X-states by a conjugation with local unitary operators. Furthermore, we give an algorithm to decompose a separable state of this set in a convex sum of five pure product states. Finally, in the third chapter we study entanglement of two qubits in a model of repeated interactions with the same spin chain in the van Hove and singular coupling limits. In particular we observe non zero asymptotic entanglement when the chain is at infinite temperature and phenomenons of entanglement sudden birth when the chain is at zero temperature.SAVOIE-SCD - Bib.électronique (730659901) / SudocGRENOBLE1/INP-Bib.électronique (384210012) / SudocGRENOBLE2/3-Bib.électronique (384219901) / SudocSudocFranceF

Semiclassical form factor for spectral and matrix element fluctuations of multi-dimensional chaotic systems

We present a semiclassical calculation of the generalized form factor which characterizes the fluctuations of matrix elements of the quantum operators in the eigenbasis of the Hamiltonian of a chaotic system. Our approach is based on some recently developed techniques for the spectral form factor of systems with hyperbolic and ergodic underlying classical dynamics and f=2 degrees of freedom, that allow us to go beyond the diagonal approximation. First we extend these techniques to systems with f>2. Then we use these results to calculate the generalized form factor. We show that the dependence on the rescaled time in units of the Heisenberg time is universal for both the spectral and the generalized form factor. Furthermore, we derive a relation between the generalized form factor and the classical time-correlation function of the Weyl symbols of the quantum operators.Comment: some typos corrected and few minor changes made; final version in PR