Augusto J. Roncaglia

Dynamics of the entanglement between two oscillators in the same environment.

We provide a complete characterization of the evolution of entanglement between two resonant oscillators coupled to a common environment. We identify three phases with different qualitative long time behavior. There is a phase where entanglement undergoes a sudden death. Another phase (sudden death and revival) is characterized by an infinite sequence of events of sudden death and revival of entanglement. In the third phase (no sudden death) there is no sudden death of entanglement, which persists for a long time. The phase diagram is described and analytic expressions for the boundary between phases are obtained. These results are applicable to a large variety of non-Markovian environments. The case of nonresonant oscillators is also numerically investigated.

Dynamical phases for the evolution of the entanglement between two oscillators coupled to the same environment

We study the dynamics of the entanglement between two oscillators that are initially prepared in a general two-mode Gaussian state and evolve while coupled to the same environment. In a previous paper we showed that there are three qualitatively different dynamical phases for the entanglement in the long time limit: sudden death, sudden death and revival and no-sudden death [Paz & Roncaglia, Phys. Rev. Lett. 100, 220401 (2008)]. Here we generalize and extend those results along several directions: We analyze the fate of entanglement for an environment with a general spectral density providing a complete characterization of the corresponding phase diagrams for ohmic and sub--ohmic environments (we also analyze the super-ohmic case showing that for such environment the expected behavior is rather different). We also generalize previous studies by considering two different models for the interaction between the system and the environment (first we analyze the case when the coupling is through position and then we examine the case where the coupling is symmetric in position and momentum). Finally, we analyze (both numerically and analytically) the case of non-resonant oscillators. In that case we show that the final entanglement is independent of the initial state and may be non-zero at very low temperatures. We provide a natural interpretation of our results in terms of a simple quantum optics model.

Qubits in phase space: Wigner-function approach to quantum-error correction and the mean-king problem

We analyze and further develop a method to represent the quantum state of a system of n qubits in a phase-space grid of NxN points (where N=2{sup n}). The method, which was recently proposed by Wootters and co-workers (Gibbons et al., Phys. Rev. A 70, 062101 (2004).), is based on the use of the elements of the finite field GF(2{sup n}) to label the phase-space axes. We present a self-contained overview of the method, we give insights into some of its features, and we apply it to investigate problems which are of interest for quantum-information theory: We analyze the phase-space representation of stabilizer states and quantum error-correction codes and present a phase-space solution to the so-called mean king problem.

Work Measurement as a Generalized Quantum Measurement

We present a new method to measure the work w performed on a driven quantum system and to sample its probability distribution P(w). The method is based on a simple fact that remained unnoticed until now: Work on a quantum system can be measured by performing a generalized quantum measurement at a single time. Such measurement, which technically speaking is denoted as a positive operator valued measure reduces to an ordinary projective measurement on an enlarged system. This observation not only demystifies work measurement but also suggests a new quantum algorithm to efficiently sample the distribution P(w). This can be used, in combination with fluctuation theorems, to estimate free energies of quantum states on a quantum computer.

Complexity of energy eigenstates as a mechanism for equilibration

Understanding the mechanisms responsible for the equilibration of isolated quantum many-body systems is a long-standing open problem. In this work we obtain a statistical relationship between the equilibration properties of Hamiltonians and the complexity of their eigenvectors, provided that a conjecture about the incompressibility of quantum circuits holds. We quantify the complexity by the size of the smallest quantum circuit mapping the local basis onto the energy eigenbasis. Specifically, we consider the set of all Hamiltonians having complexity C, and show that almost all such Hamiltonians equilibrate if C is super-quadratic with the system size, which includes the fully random Hamiltonian case in the limit C to infinity, and do not equilibrate if C is sub-linear. We also provide a simple formula for the equilibration time-scale in terms of the Fourier transform of the level density. Our results are statistical and, therefore, do not apply to specific Hamiltonians. Yet, they establish a fundamental link between equilibration and complexity theory.

Redundancy of classical and quantum correlations during decoherence

We analyze the time dependence of entanglement and total correlations between a system and fractions of its environment in the course of decoherence. For the quantum Brownian motion model, we show that the entanglement and total correlations have rather different dependence on the size of the environmental fraction. Redundancy manifests differently in both types of correlations and can be related with induced classicality. To study this, we present a measure of redundancy and compare it to the existing one.

Quantum gate arrays can be programmed to evaluate the expectation value of any operator

A programmable gate array is a circuit whose action is controlled by input data. In this paper we describe a special-purpose quantum circuit that can be programmed to evaluate the expectation value of any operator O acting on a space of states of N dimensions. The circuit has a program register whose state ‖Ψ(O)) P encodes the operator O whose expectation value is to be evaluated. The method requires knowledge of the expansion of O in a basis of the space of operators. We discuss some applications of this circuit and its relation to known instances of quantum state tomography.

Measuring work and heat in ultracold quantum gases

We propose a feasible experimental scheme to direct measure heat and work in cold atomic setups. The method is based on a recent proposal which shows that work is a positive operator valued measure (POVM). In the present contribution, we demonstrate that the interaction between the atoms and the light polarization of a probe laser allows us to implement such POVM. In this way the work done on or extracted from the atoms after a given process is encoded in the light quadrature that can be measured with a standard homodyne detection. The protocol allows one to verify fluctuation theorems and study properties of the non-unitary dynamics of a given thermodynamic process.

Quantum algorithms for phase-space tomography

We present efficient circuits that can be used for the phase-space tomography of quantum states. The circuits evaluate individual values or selected averages of the Wigner, Kirkwood, and Husimi distributions. These quantum gate arrays can be programmed by initializing appropriate computational states. The Husimi circuit relies on a subroutine that is also interesting in its own right: the efficient preparation of a coherent state, which is the ground state of the Harper Hamiltonian.

Using a quantum work meter to test non-equilibrium fluctuation theorems

Work is an essential concept in classical thermodynamics, and in the quantum regime, where the notion of a trajectory is not available, its definition is not trivial. For driven (but otherwise isolated) quantum systems, work can be defined as a random variable, associated with the change in the internal energy. The probability for the different values of work captures essential information describing the behaviour of the system, both in and out of thermal equilibrium. In fact, the work probability distribution is at the core of “fluctuation theorems” in quantum thermodynamics. Here we present the design and implementation of a quantum work meter operating on an ensemble of cold atoms, which are controlled by an atom chip. Our device not only directly measures work but also directly samples its probability distribution. We demonstrate the operation of this new tool and use it to verify the validity of the quantum Jarzynksi identity.Defining and measuring work and heat are non-trivial tasks in the quantum regime. Here, the authors design a scheme to directly sample from the work probability distribution, and use it to verify the validity of the quantum version of the Jarzynksi identity using cold atoms on an atomic chip.