The manifold of coupling constants parametrizing a quantum Hamiltonian is equipped with a natural Riemannian metric with an operational distinguishability content. We argue that the singularities of this metric are in correspondence with the quantum phase transitions featured by the corresponding system. This approach provides a universal conceptual framework to study quantum critical phenomena which is differential geometric and information theoretic at the same time.

We extend the quantum discord to continuous variable systems and evaluate Gaussian quantum discord C(̺) for bipartite Gaussian states. In particular, for squeezed thermal states (STS), we explicitly maximize the extractable information over Gaussian measurements: C(̺) is minimized by a generalized measurement rather than a projective one. Almost all STS have nonzero Gaussian discord: they may be either separable or entangled if the discord is below the threshold C(̺) = 1, whereas they are all entangled above the threshold. We elucidate the general role of state parameters in determining the discord and discuss its evolution in noisy channels.PACS numbers: 03.67.-a, 03.65.Ta Quantum correlations have been the subject of intensive studies in the last two decades, mainly due to the general belief that they are a fundamental resource for quantum information processing tasks. The first rigorous attempt to address the classification of quantum correlation from has been put forward by Werner [1], who put on firm basis the elusive concept of quantum entanglement. A state of a bipartite system is called entangled if it cannot be written as follows:where ̺ Ak and ̺ Bk are generic density matrices describing the states of the two subsystems. The definition above has an immediate operational interpretation: separable states can be prepared by local operations and classical communication between the two parties, whereas entangled states cannot. One might have thought that such classical information exchange could not bring any quantum character to the correlations in the state. In this sense separability has often been regarded as a synonymous of classicality. However, it has been shown that this is not the case [2,3]. A measure of correlations -quantum discord-has been defined as the mismatch between two quantum analogues of classically equivalent expression of the mutual information. For pure entangled states quantum discord coincides with the entropy of entanglement. However, quantum discord can be different from zero also for some (mixed) separable state. In other words, classical communication can give rise to quantum correlations. This can be understood by considering that the states ̺ Ak and ̺ Bk above may be physically non distinguishable, i.e. non-orthogonal and thus not all the information about them can then be locally retrieved. This phenomenon has no classical counterpart, thus accounting for the quantumness of the correlations in separable state with positive discord. Quantum discord has been shown to be a property hold by almost all quantum states [4] and recently attracted considerable attention [5][6][7][8][9][10]. In particular, the vanishing of quantum discord between two systems has been shown to be a requirement for the complete positivity of the reduced subsystem dynamics [11].While the discord is a fundamental notion allowing for the description of the quantumness of the correlations present in the state of a quantum system, its evaluation requires an optimization procedure over the set of all measurem...

We analyze the Bures metric over the manifold of thermal density matrices for systems featuring a zero temperature quantum phase transition. We show that the quantum critical region can be characterized in terms of the temperature scaling behavior of the metric tensor itself. Furthermore, the analysis of the metric tensor when both temperature and an external field are varied, allows to complement the understanding of the phase diagram including cross-over regions which are not characterized by any singular behavior. These results provide a further extension of the scope of the metric approach to quantum criticality.Comment: 9 pages, 4 figures, LaTeX problems fixed, references adde

In this paper we analyze the ground state phase diagram of a class of fermionic Hamiltonians by looking at the fidelity of ground states corresponding to slightly different Hamiltonian parameters. The Hamiltonians under investigation can be considered as the variable range generalization of the fermionic Hamiltonian obtained by the Jordan-Wigner transformation of the XY spin-chain in a transverse magnetic field. Under periodic boundary conditions, the matrices of the problem become circulant and the models are exactly solvable. Their free-ends counterparts are instead analyzed numerically. In particular, we focus on the long range model corresponding to a fully connected directed graph, providing asymptotic results in the thermodynamic limit, as well as the finitesize scaling analysis of the second order quantum phase transitions of the system. A strict relation between fidelity and single particle spectrum is demonstrated, and a peculiar gapful transition due to the long range nature of the coupling is found. A comparison between fidelity and another transition marker borrowed from quantum information i.e., single site entanglement, is also considered.

We compute the fidelity between the ground states of general quadratic fermionic hamiltonians and analyze its connections with quantum phase transitions. Each of these systems is characterized by a L × L real matrix whose polar decomposition, into a non-negative Λ and a unitary T , contains all the relevant ground state (GS) information. The boundaries between different regions in the GS phase diagram are given by the points of, possibly asymptotic, singularity of Λ. This latter in turn implies a critical drop of the fidelity function. We present general results as well as their exemplification by a model of fermions on a totally connected graph.