Miguel Orszag

Geometric quantum discord with Bures distance

We define a new measure of quantum correlations in bipartite quantum systems given by the Bures distance of the system state to the set of classical states with respect to one subsystem, that is, to the states with zero quantum discord. Our measure is a geometrical version of the quantum discord. As the latter it quantifies the degree of non-classicality in the system. For pure states it is identical to the geometric measure of entanglement. We show that for mixed states it coincides with the optimal success probability of an ambiguous quantum state discrimination task. Moreover, the closest zero-discord states to a state ρ are obtained in terms of the corresponding optimal measurements.

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 (2nB) × (2nB) Hermitian matrix, nB 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 a two-qubit state ρ with maximally mixed marginals and compare it with other measures of quantum correlations. We also determine the closest classical states to ρ.

Creation of entanglement of two atoms coupled to two distant cavities with losses

We present a model to generate atomic entanglement with atoms located at distant cavities. It consists of two cavities connected by an optical fibre, where each cavity interacts with a single two-level atom. For certain atom–cavity and cavity–fibre coupling parameters, we find a wide time plateau for the concurrence between the atoms. An increase of the atom–cavity detuning gives rise to a linear increase of the width of the plateau, but at the same time, when losses are included in the model, it also decreases the value of the concurrence and increases the response time to reach the maximum.

Stochastic Schrödinger equations in cavity QED: physical interpretation and localization

We propose physical interpretations, also valid for temperatures different from zero, for stochastic methods which have been developed recently to describe the evolution of a quantum system interacting with a reservoir. As opposed to the usual reduced density operator approach, which refers to ensemble averages, these methods deal with the dynamics of single realizations, and involve the solution of stochastic Schr?dinger equations. These procedures have been shown to be completely equivalent to the master equation approach when ensemble averages are taken over many realizations. We show that these techniques are not only convenient mathematical tools for dissipative systems, but may actually correspond to concrete physical processes, for any temperature of the reservoir. We consider a mode of the electromagnetic field in a cavity interacting with a beam of two- or three-level atoms, the field mode playing the role of a small system and the atomic beam standing for a reservoir at finite temperature, the interaction between them being given by the Jaynes-Cummings model. We show that the evolution of the field states, under continuous monitoring of the state of the atoms which leave the cavity, can be described in terms of either the Monte Carlo wavefunction (quantum jump) method or a stochastic Schr?dinger equation, depending on the system configuration. We also show that the Monte Carlo wavefunction approach leads, for finite temperatures, to localization into jumping Fock states, while the diffusion equation method leads to localization into states with a diffusing average photon number, which for sufficiently small temperatures are close approximations to mildly squeezed states. We prove analytically that, in the quantum jump situation, the system evolves in the mean towards a Fock state, even if an infinite number of photon-number amplitudes is present in the initial state.

Thermal effects on sudden changes and freezing of correlations between remote atoms in a cavity quantum electrodynamics network

We investigate thermal effects on sudden changes and freezing of the quantum and classical correlations of remote qubits in a cavity quantum electrodynamics (CQED) network with losses. We find that the detrimental effect of thermal reservoirs on the freezing of correlations can be compensated via an efficient coupling of the fiber connecting the two cavities of the system. Furthermore, for certain initial conditions, we find a double sudden transition in the dynamics of Bures geometrical quantum discord. The second transition tends to disappear at a critical temperature, hence freezing the discord. Finally, we discuss the feasibility of the experimental realization of the present proposal.

Propagation and distribution of quantum correlations in a cavity QED network

We study the propagation and distribution of quantum correlations through two chains of atoms inside cavities joined by optical fibres. This system is interesting because it can be used as a channel for quantum communication or as a network for quantum computation. In order to quantify those correlations, we used two different measurements: entanglement and quantum discord. We also use tangle for multipartite entanglement. We consider an effective Hamiltonian for the system and cavity losses, in the dressed atom picture, using the generalized master equation. We found a case where the quantum discord and the classical correlation are almost constant, and we also found multipartite entanglement, starting with only one excitation per chain. Finally, we propose a way to select the initial condition so that we can optimize the results for different purposes.

Thermally generated long-lived quantum correlations for two atoms trapped in fiber-coupled cavities

A theoretical model for driving a two qubit system to a stable long-lived entanglement is discussed. The entire system is represented by two atoms, initially in ground states and disentangled, each one coupled to a separate cavity with the cavities connected by a fiber. The cavities and fiber exchange energy with their individual thermal environments. Under these conditions, we apply the theory of microscopic master equation developed for the dynamics of the open quantum system. Deriving the density operator of the two-qubit system we found that stable long-lived quantum correlations are generated in the presence of thermal excitation of the environments. To the best of our knowledge, there is no a similar effect observed in a quantum open system described by a generalized microscopic master equation in the approximation of the cavity quantum electrodynamics (CQED).

Coherence and entanglement in a two-qubit system

Entanglement is a fundamental concept in quantum mechanics. In this review, we study various aspects of coherence and entanglement, illustrated by several examples. We relate the concepts of loss of coherence and disentanglement, via a model of two two-level atoms in different types of reservoir, including cases of both independent and common baths. Finally, we relate decoherence and disentanglement, by focusing on the sudden death of the entanglement and the dependence of the death time with the distance of our initial condition from the decoherence-free subspace. In particular, we study the sudden death of the entanglement in a two-atom system with a common reservoir.

Squeezing and bifurcation in the phase probability distribution in a two-photon micromaser

Abstract We derive a master equation for the two-photon micromaser with atomic coherence. We find that the presence of the atomic coherence modifies the threshold condition in the two-photon micromaser, and also produces squeezing and bifurcation in the phase probability distribution. The maximum squeezing is of 36% and it happens below threshold.

Quantum features of a free-electron laser

A nonlinear quantum model of a free-electron laser working in the Compton regime is discussed. Particular emphasis is given to the coherence and squeezing properties of the emitted radiation.