9,069 research outputs found
Factorization and Criticality in the Anisotropic XY Chain via Correlations
In this review, we discuss the zero and finite temperature behavior of
various bipartite quantum and total correlation measures, the skew
information-based quantum coherence, and the local quantum uncertainty in the
thermal ground state of the one-dimensional anisotropic XY model in transverse
magnetic field. We compare the ability of considered measures to correctly
detect or estimate the quantum critical point and the non-trivial factorization
point possessed by the spin chain.Comment: 29 pages, 8 figures. A review paper accepted for publication in the
special issue Entanglement Entropy in the journal Entrop
Bath-induced correlations in an infinite-dimensional Hilbert space
Quantum correlations between two free spinless dissipative distinguishable
particles (interacting with a thermal bath) are studied analytically using the
quantum master equation and tools of quantum information. Bath-induced
coherence and correlations in an infinite-dimensional Hilbert space are shown.
We show that for temperature T > 0 the time-evolution of the reduced density
matrix cannot be written as the direct product of two independent particles. We
have found a time-scale that characterizes the time when the bath-induced
coherence is maximum before being wiped out by dissipation (purity, relative
entropy, spatial dispersion, and mirror correlations are studied). The Wigner
function associated to the Wannier lattice (where the dissipative quantum walks
move) is studied as an indirect measure of the induced correlations among
particles. We have supported the quantum character of the correlations by
analyzing the geometric quantum discord.Comment: 13 pages, 5 figures. arXiv admin note: substantial text overlap with
arXiv:1512.0870
How to quantify coherence: Distinguishing speakable and unspeakable notions
Quantum coherence is a critical resource for many operational tasks.
Understanding how to quantify and manipulate it also promises to have
applications for a diverse set of problems in theoretical physics. For certain
applications, however, one requires coherence between the eigenspaces of
specific physical observables, such as energy, angular momentum, or photon
number, and it makes a difference which eigenspaces appear in the
superposition. For others, there is a preferred set of subspaces relative to
which coherence is deemed a resource, but it is irrelevant which of the
subspaces appear in the superposition. We term these two types of coherence
unspeakable and speakable respectively. We argue that a useful approach to
quantifying and characterizing unspeakable coherence is provided by the
resource theory of asymmetry when the symmetry group is a group of
translations, and we translate a number of prior results on asymmetry into the
language of coherence. We also highlight some of the applications of this
approach, for instance, in the context of quantum metrology, quantum speed
limits, quantum thermodynamics, and NMR. The question of how best to treat
speakable coherence as a resource is also considered. We review a popular
approach in terms of operations that preserve the set of incoherent states,
propose an alternative approach in terms of operations that are covariant under
dephasing, and we outline the challenge of providing a physical justification
for either approach. Finally, we note some mathematical connections that hold
among the different approaches to quantifying coherence.Comment: A non-technical summary of the results and applications is provided
in the first section. V5 close to the published version. Typos correcte
Genuine quantum correlations in quantum many-body systems: a review of recent progress
Quantum information theory has considerably helped in the understanding of
quantum many-body systems. The role of quantum correlations and in particular,
bipartite entanglement, has become crucial to characterise, classify and
simulate quantum many body systems. Furthermore, the scaling of entanglement
has inspired modifications to numerical techniques for the simulation of
many-body systems leading to the, now established, area of tensor networks.
However, the notions and methods brought by quantum information do not end with
bipartite entanglement. There are other forms of correlations embedded in the
ground, excited and thermal states of quantum many-body systems that also need
to be explored and might be utilised as potential resources for quantum
technologies. The aim of this work is to review the most recent developments
regarding correlations in quantum many-body systems focussing on multipartite
entanglement, quantum nonlocality, quantum discord, mutual information but also
other non classical measures of correlations based on quantum coherence.
Moreover, we also discuss applications of quantum metrology in quantum
many-body systems.Comment: Review. Close to published version. Comments are welcome! Please
write an email to g.dechiara[(at)]qub.ac.u
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