94 research outputs found
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
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