Michele Allegra

Quantum Brachistochrone Curves as Geodesics: Obtaining Accurate Minimum-Time Protocols for the Control of Quantum Systems

Most methods of optimal control cannot obtain accurate time-optimal protocols. The quantum brachistochrone equation is an exception, and has the potential to provide accurate time-optimal protocols for a wide range of quantum control problems. So far, this potential has not been realized, however, due to the inadequacy of conventional numerical methods to solve it. Here we show that the quantum brachistochrone problem can be recast as that of finding geodesic paths in the space of unitary operators. We expect this brachistochrone-geodesic connection to have broad applications, as it opens up minimal-time control to the tools of geometry. As one such application, we use it to obtain a fast numerical method to solve the brachistochrone problem, and apply this method to two examples demonstrating its power.

Quantum discord and classical correlations in the bond-charge Hubbard model: Quantum phase transitions, off-diagonal long-range order, and violation of the monogamy property for discord

We study the quantum discord (QD) and the classical correlations (CC) in a reference model for strongly correlated electrons, the one-dimensional bond-charge extended Hubbard model. We show that the comparison of QD and CC and of their derivatives in the direct and reciprocal lattice allows one to efficiently inspect the structure of two-points driven quantum phase transitions, discriminating those at which off diagonal long-range order (ODLRO) is involved. Moreover, we observe that QD between pair of sites is a monotonic function of ODLRO, thus establishing a direct relation between the latter and two point quantum correlations that differ from the entanglement. The study of the ground-state properties allows us to show that for a whole class of permutation invariant (η-pair) states quantum discord can violate the monogamy property, both in presence and in absence of bipartite entanglement. In the thermodynamic limit, due to the presence of ODLRO, the violation for η-pair states is maximal, while, for the purely fermionic ground state, it is finite. From a general perspective, all our results validate the importance of the concepts of QD and CC for the study of critical condensed-matter systems.

Quantum discord for Gaussian states with non-Gaussian measurements

In recent years the paradigm based on entanglement as the unique measure of quantum correlations has been challenged by the rise of new correlation concepts, such as quantum discord, able to reveal quantum correlations that are present in separable states. It is in general difficult to compute quantum discord, because it involves a minimization over all possible local measurements in a bipartition. In the realm of continuous variable (CV) systems, a Gaussian version of quantum discord has been put forward upon restricting to Gaussian measurements. It is natural to ask whether non-Gaussian measurements can lead to a stronger minimization than Gaussian ones. Here we focus on two relevant classes of two-mode Gaussian states: squeezed thermal states (STS) and mixed thermal states (MTS), and allow for a range of experimentally feasible non-Gaussian measurements, comparing the results with the case of Gaussian measurements. We provide evidence that Gaussian measurements are optimal for Gaussian states.

Two-qubit correlations revisited: average mutual information, relevant (and useful) observables and an application to remote state preparation

Understanding how correlations can be used for quantum communication protocols is a central goal of quantum information science. While many authors have linked global measures of correlations such as entanglement or discord to the performance of specific protocols, in general the latter may require only correlations between specific observables. In this work, we first introduce a general measure of correlations for two-qubit states based on the classical mutual information between local observables. We then discuss the role of the symmetry in the states correlations distribution and accordingly provide a classification of maximally mixed marginals states (MMMS). We discuss the complementarity relation between correlations and coherence. By focusing on a simple yet paradigmatic example, i.e., the remote state preparation protocol, we introduce a method to systematically define proper protocol-tailored measures of correlations. The method is based on the identification of those correlations that are relevant (useful) for the protocol. The approach allows on one hand to discuss the role of the symmetry of the correlations distribution in determining the efficiency of the protocol, both for MMMS and general two-qubit quantum states, and on the other hand to devise an optimized protocol for non-MMMS that can have a better efficiency with respect to the standard one. The scheme we propose can be extended to other communication protocols and more general bipartite settings. Overall our findings clarify how the key resources in simple communication protocols are the purity of the state used and the symmetry of correlations distribution.

DECOHERENCE OF GAUSSIAN AND NONGAUSSIAN PHOTON-NUMBER ENTANGLED STATES IN A NOISY CHANNEL

We consider photon-number entangled states (PNES) and study the degradation of their entanglement in a noisy channel, using different separability criteria and a recently proposed measure of nonGaussianity as key tools. Upon comparing Gaussian and nonGaussian states within the class, we collect some evidence that Gaussian states are maximally robust against noise, i.e. the complete loss of entanglement occurs in maximal time. However, the gap with respect to nonGaussian states is negligible for sufficiently high energy of the states.