886 research outputs found
Superactivation of monogamy relations for nonadditive quantum correlation measures
We investigate the general monogamy and polygamy relations satisfied by
quantum correlation measures. We show that there exist two real numbers
and such that for any quantum correlation measure ,
is monogamous if and polygamous if for a
given multipartite state . For , we show that the
monogamy relation can be superactivated by finite copies
of for nonadditive correlation measures. As a detailed example, we use
the negativity as the quantum correlation measure to illustrate such
superactivation of monogamy properties. A tighter monogamy relation is
presented at last
Monogamy relations of all quantum correlation measures for multipartite quantum systems
The monogamy relations of quantum correlation restrict the sharability of
quantum correlations in multipartite quantum states. We show that all measures
of quantum correlations satisfy some kind of monogamy relations for arbitrary
multipartite quantum states. Moreover, by introducing residual quantum
correlations, we present tighter monogamy inequalities that are better than all
the existing ones. In particular, for multi-qubit pure states, we also
establish new monogamous relations based on the concurrence and concurrence of
assistance under the partition of the first two qubits and the remaining ones.Comment: arXiv admin note: text overlap with arXiv:1206.4029 by other author
Polygamy relations of multipartite entanglement beyond qubits
We investigate the polygamy relations related to the concurrence of
assistance for any multipartite pure states. General polygamy inequalities
given by the th power of concurrence of
assistance is first presented for multipartite pure states in
arbitrary-dimensional quantum systems. We further show that the general
polygamy inequalities can even be improved to be tighter inequalities under
certain conditions on the assisted entanglement of bipartite subsystems. Based
on the improved polygamy relations, lower bound for distribution of bipartite
entanglement is provided in a multipartite system. Moreover, the th
() power of polygamy inequalities are obtained for the
entanglement of assistance as a by-product, which are shown to be tighter than
the existing ones. A detailed example is presented.Comment: arXiv admin note: text overlap with arXiv:1902.0744
Quantifying quantum coherence and non-classical correlation based on Hellinger distance
Quantum coherence and non-classical correlation are key features of quantum
world. Quantifying coherence and non-classical correlation are two key tasks in
quantum information theory. First, we present a bona fide measure of quantum
coherence by utilizing the Hellinger distance. This coherence measure is proven
to fulfill all the criteria of a well defined coherence measure, including the
strong monotonicity in the resource theories of quantum coherence. In terms of
this coherence measure, the distribution of quantum coherence in multipartite
systems is studied and a corresponding polygamy relation is proposed. Its
operational meanings and the relations between the generation of quantum
correlations and the coherence are also investigated. Moreover, we present
Hellinger distance-based measure of non-classical correlation, which not only
inherits the nice properties of the Hellinger distance including contractivity,
and but also shows a powerful analytic computability for a large class of
quantum states. We show that there is an explicit trade-off relation satisfied
by the quantum coherence and this non-classical correlation
Finer Distribution of Quantum Correlations among Multiqubit Systems
We study the distribution of quantum correlations characterized by monogamy
relations in multipartite systems. By using the Hamming weight of the binary
vectors associated with the subsystems, we establish a class of monogamy
inequalities for multiqubit entanglement based on the th () power of concurrence, and a class of polygamy inequalities for multiqubit
entanglement in terms of the th () power of
concurrence and concurrence of assistance. Moveover, we give the monogamy and
polygamy inequalities for general quantum correlations. Application of these
results to quantum correlations like squared convex-roof extended negativity
(SCREN), entanglement of formation and Tsallis- entanglement gives rise to
either tighter inequalities than the existing ones for some classes of quantum
states or less restrictions on the quantum states. Detailed examples are
presented
Invariants for a Class of Nongeneric Three-qubit States
We investigate the equivalence of quantum states under local unitary
transformations. A complete set of invariants under local unitary
transformations is presented for a class of non-generic three-qubit mixed
states. It is shown that two such states in this class are locally equivalent
if and only if all these invariants have equal values for them.Comment: 7 page
Quantum discord and geometry for a class of two-qubit states
We study the level surfaces of quantum discord for a class of two-qubit
states with parallel nonzero Bloch vectors. The dynamic behavior of quantum
discord under decoherence is investigated. It is shown that a class of X states
has sudden transition between classical and quantum correlations under
decoherence. Our results include the ones in M. D. Lang and C. M. Caves [Phys.
Rev. Lett. 105, 150501 (2010)] as a special case and show new pictures and
structures of quantum discord.Comment: 5 pages, 5 figure
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