339 research outputs found
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
Universality in Distribution of Monogamy Scores for Random Multiqubit Pure States
Monogamy of quantum correlations provides a way to study restrictions on
their sharability in multiparty systems. We find the critical exponent of these
measures, above which randomly generated multiparty pure states satisfy the
usual monogamy relation, and show that the critical power decreases with the
increase in the number of parties. For three-qubit pure states, we detect that
W-class states are more prone to being nonmonogamous as compared to the
GHZ-class states. We also observe a different criticality in monogamy power up
to which random pure states remain nonmonogamous. We prove that the "average
monogamy" score asymptotically approaches its maximal value on increasing the
number of parties. Analyzing the monogamy scores of random three-, four-, five-
and six-qubit pure states, we also report that almost all random pure six-qubit
states possess maximal monogamy score, which we confirm by evaluating
statistical quantities like mean, variance and skewness of the distributions.
In particular, with the variation of number of qubits, means of the
distributions of monogamy scores for random pure states approach to unity --
which is the algebraic maximum -- thereby conforming to the known results of
random states having maximal multipartite entanglement in terms of geometric
measures.Comment: 12 pages, 7 figure
Correlation evolution and monogamy of two geometric quantum discords in multipartite systems
We explore two different geometric quantum discords defined respectively via
the trace norm (GQD-1) and Hilbert-Schmidt norm (GQD-2) in multipartite
systems. A rigorous hierarchy relation is revealed for the two GQDs in a class
of symmetric two-qubit -shape states. For multiqubit pure states, it is
found that both GQDs are related to the entanglement concurrence, with the
hierarchy relation being saturated. Furthermore, we look into a four-partite
dynamical system consisting of two cavities interacting with independent
reservoirs. It is found that the GQD-2 can exhibit various sudden change
behaviours, while the GQD-1 only evolves asymptotically, with the two GQDs
exhibiting different monogamous properties.Comment: 5 pages, 3 figure
Monogamous property of generalized W states in three-qubit systems in terms of relative entropy of entanglement
Because of the difficulty in getting the analytic formula of relative entropy
of entanglement, it becomes troublesome to study the monogamy relations of
relative entropy of entanglement for three-qubit pure states. However, we find
that all generalized W states have the monogamous property for relative entropy
of entanglement by calculating the relative entropy of entanglement for the
reduced states of the generalized W states in three-qubit systems.Comment: 9 pages, 1 figur
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