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 state's 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.Comment: Revised Figures, improved notation and clearer text to better highlight the main finding

Global coherence of quantum evolutions based on decoherent histories: theory and application to photosynthetic quantum energy transport

Assessing the role of interference in natural and artificial quantum dyanamical processes is a crucial task in quantum information theory. To this aim, an appopriate formalism is provided by the decoherent histories framework. While this approach has been deeply explored from different theoretical perspectives, it still lacks of a comprehensive set of tools able to concisely quantify the amount of coherence developed by a given dynamics. In this paper we introduce and test different measures of the (average) coherence present in dissipative (Markovian) quantum evolutions, at various time scales and for different levels of environmentally induced decoherence. In order to show the effectiveness of the introduced tools, we apply them to a paradigmatic quantum process where the role of coherence is being hotly debated: exciton transport in photosynthetic complexes. To spot out the essential features that may determine the performance of the transport we focus on a relevant trimeric subunit of the FMO complex and we use a simplified (Haken-Strobl) model for the system-bath interaction. Our analysis illustrates how the high efficiency of environmentally assisted transport can be traced back to a quantum recoil avoiding effect on the exciton dynamics, that preserves and sustains the benefits of the initial fast quantum delocalization of the exciton over the network. Indeed, for intermediate levels of decoherence, the bath is seen to selectively kill the negative interference between different exciton pathways, while retaining the initial positive one. The concepts and tools here developed show how the decoherent histories approach can be used to quantify the relation between coherence and efficiency in quantum dynamical processes.Comment: 13 papges, 9 figure

Entanglement in extended Hubbard models and quantum phase transitions

The role of two-point and multipartite entanglement at quantum phase transitions (QPTs) in correlated electron systems is investigated. We consider a bond-charge extended Hubbard model exactly solvable in one dimension which displays various QPTs, with two (qubit) as well as more (qudit) on-site degrees of freedom involved. The analysis is carried out by means of appropriate measures of bipartite/multipartite quantum correlations. It is found that all transitions ascribed to two-point correlations are characterized by an entanglement range which diverges at the transition points. The exponent coincides with that of the correlation length at the transitions. We introduce the correlation ratio, namely, the ratio of quantum mutual information and single-site entanglement. We show that at T=0, it captures the relative role of two-point and multipartite quantum correlations at transition points, generalizing to qudit systems the entanglement ratio. Moreover, a finite value of quantum mutual information between infinitely distant sites is seen to quantify the presence of off-diagonal long-range order induced by multipartite entanglement.Comment: 14 pages, 8 figures, 2 table

State independent uncertainty relations from eigenvalue minimization

We consider uncertainty relations that give lower bounds to the sum of variances. Finding such lower bounds is typically complicated, and efficient procedures are known only for a handful of cases. In this paper we present procedures based on finding the ground state of appropriate Hamiltonian operators, which can make use of the many known techniques developed to this aim. To demonstrate the simplicity of the method we analyze multiple instances, both previously known and novel, that involve two or more observables, both bounded and unbounded.Comment: 14 pages, 3 figure

Gaussian quantum discord

We extend the quantum discord to continuous variable systems and evaluate Gaussian quantum discord C(\rho) for bipartite Gaussian states. In particular, for squeezed thermal states (STS), we explicitly maximize the extractable information over Gaussian measurements: C(\rho) 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(\rho)=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.Comment: 4 pages, 2 figures, new version, typos fixe

Quantum phase transitions and quantum fidelity in free fermion graphs

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 finite-size 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.Comment: 14 pages, 5 figure