2,527 research outputs found
Quantum mutual information and quantumness vectors for multi-qubit systems
We introduce a new information theoretic measure of quantum correlations for
multiparticle systems. We use a form of multivariate mutual information -- the
interaction information and generalize it to multiparticle quantum systems.
There are a number of different possible generalizations. We consider two of
them. One of them is related to the notion of quantum discord and the other to
the concept of quantum dissension. This new measure, called dissension vector,
is a set of numbers -- quantumness vector. This can be thought of as a
fine-grained measure, as opposed to measures that quantify some average quantum
properties of a system. These quantities quantify/characterize the correlations
present in multiparticle states. We consider some multiqubit states and find
that these quantities are responsive to different aspects of quantumness, and
correlations present in a state. We find that different dissension vectors can
track the correlations (both classical and quantum), or quantumness only. As
physical applications, we find that these vectors might be useful in several
information processing tasks. We consider the role of dissension vectors -- (a)
in deciding the security of BB84 protocol against an eavesdropper and (b) in
determining the possible role of correlations in the performance of Grover
search algorithm. Especially, in the Grover search algorithm, we find that
dissension vectors can detect the correlations and show the maximum
correlations when one expects.Comment: 18 pages 8 figures. Updated. Comments are welcom
Quantumness of correlations and entanglement
Generalized measurement schemes on one part of bipartite states, which would
leave the set of all separable states insensitive are explored here to
understand quantumness of correlations in a more general perspecitve. This is
done by employing linear maps associated with generalized projective
measurements. A generalized measurement corresponds to a quantum operation
mapping a density matrix to another density matrix, preserving its positivity,
hermiticity and traceclass. The Positive Operator Valued Measure (POVM) --
employed earlier in the literature to optimize the measures of
classical/quatnum correlations -- correspond to completely positive (CP) maps.
The other class, the not completely positive (NCP) maps, are investigated here,
in the context of measurements, for the first time. It is shown that that such
NCP projective maps provide a new clue to the understanding the quantumness of
correlations in a general setting. Especially, the separability-classicality
dichotomy gets resolved only when both the classes of projective maps (CP and
NCP) are incorporated as optimizing measurements. An explicit example of a
separable state -- exhibiting non-zero quantumn discord when possible
optimizing measurements are restricted to POVMs -- is re-examined with this
extended scheme incorporating NCP projective maps to elucidate the power of
this approach.Comment: 14 pages, no figures, revision version, Accepted for publication in
the Special Issue of the International Journal of Quantum Information devoted
to "Quantum Correlations: entanglement and beyond
Multipartite quantum and classical correlations in symmetric n-qubit mixed states
We discuss how to calculate genuine multipartite quantum and classical
correlations in symmetric, spatially invariant, mixed -qubit density
matrices. We show that the existence of symmetries greatly reduces the amount
of free parameters to be optimized in order to find the optimal measurement
that minimizes the conditional entropy in the discord calculation. We apply
this approach to the states exhibited dynamically during a thermodynamic
protocol to extract maximum work. We also apply the symmetry criterion to a
wide class of physically relevant cases of spatially homogeneous noise over
multipartite entangled states. Exploiting symmetries we are able to calculate
the nonlocal and genuine quantum features of these states and note some
interesting properties.Comment: Close to published Versio
Frustration, Entanglement, and Correlations in Quantum Many Body Systems
We derive an exact lower bound to a universal measure of frustration in
degenerate ground states of quantum many-body systems. The bound results in the
sum of two contributions: entanglement and classical correlations arising from
local measurements. We show that average frustration properties are completely
determined by the behavior of the maximally mixed ground state. We identify
sufficient conditions for a quantum spin system to saturate the bound, and for
models with twofold degeneracy we prove that average and local frustration
coincide.Comment: 9 pages, 1 figur
All Multiparty Quantum States Can Be Made Monogamous
Monogamy of quantum correlation measures puts restrictions on the sharability
of quantum correlations in multiparty quantum states. Multiparty quantum states
can satisfy or violate monogamy relations with respect to given quantum
correlations. We show that all multiparty quantum states can be made monogamous
with respect to all measures. More precisely, given any quantum correlation
measure that is non-monogamic for a multiparty quantum state, it is always
possible to find a monotonically increasing function of the measure that is
monogamous for the same state. The statement holds for all quantum states,
whether pure or mixed, in all finite dimensions and for an arbitrary number of
parties. The monotonically increasing function of the quantum correlation
measure satisfies all the properties that is expected for quantum correlations
to follow. We illustrate the concepts by considering a thermodynamic measure of
quantum correlation, called the quantum work deficit.Comment: 6.5 pages, 2 figures, RevTeX 4-1, Title in the published version is
"Monotonically increasing functions of any quantum correlation can make all
multiparty states monogamous
Multipartite non-locality in a thermalized Ising spin-chain
We study multipartite correlations and non-locality in an isotropic Ising
ring under transverse magnetic field at both zero and finite temperature. We
highlight parity-induced differences between the multipartite Bell-like
functions used in order to quantify the degree of non-locality within a ring
state and reveal a mechanism for the passive protection of multipartite quantum
correlations against thermal spoiling effects that is clearly related to the
macroscopic properties of the ring model.Comment: 8 pages, 6 figures, RevTeX4, Published versio
The quantumness of correlations revealed in local measurements exceeds entanglement
We analyze a family of measures of general quantum correlations for composite
systems, defined in terms of the bipartite entanglement necessarily created
between systems and apparatuses during local measurements. For every
entanglement monotone , this operational correspondence provides a different
measure of quantum correlations. Examples of such measures are the
relative entropy of quantumness, the quantum deficit, and the negativity of
quantumness. In general, we prove that any so defined quantum correlation
measure is always greater than (or equal to) the corresponding entanglement
between the subsystems, , for arbitrary states of composite quantum
systems. We analyze qualitatively and quantitatively the flow of correlations
in iterated measurements, showing that general quantum correlations and
entanglement can never decrease along von Neumann chains, and that genuine
multipartite entanglement in the initial state of the observed system always
gives rise to genuine multipartite entanglement among all subsystems and all
measurement apparatuses at any level in the chain. Our results provide a
comprehensive framework to understand and quantify general quantum correlations
in multipartite states.Comment: 6 pages, 2 figures; terminology slightly revised, few remarks adde
Generalizations of entanglement based on coherent states and convex sets
Unentangled pure states on a bipartite system are exactly the coherent states
with respect to the group of local transformations. What aspects of the study
of entanglement are applicable to generalized coherent states? Conversely, what
can be learned about entanglement from the well-studied theory of coherent
states? With these questions in mind, we characterize unentangled pure states
as extremal states when considered as linear functionals on the local Lie
algebra. As a result, a relativized notion of purity emerges, showing that
there is a close relationship between purity, coherence and (non-)entanglement.
To a large extent, these concepts can be defined and studied in the even more
general setting of convex cones of states. Based on the idea that entanglement
is relative, we suggest considering these notions in the context of partially
ordered families of Lie algebras or convex cones, such as those that arise
naturally for multipartite systems. The study of entanglement includes notions
of local operations and, for information-theoretic purposes, entanglement
measures and ways of scaling systems to enable asymptotic developments. We
propose ways in which these may be generalized to the Lie-algebraic setting,
and to a lesser extent to the convex-cones setting. One of our original
motivations for this program is to understand the role of entanglement-like
concepts in condensed matter. We discuss how our work provides tools for
analyzing the correlations involved in quantum phase transitions and other
aspects of condensed-matter systems.Comment: 37 page
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