19 research outputs found
Squashed entanglement for multipartite states and entanglement measures based on the mixed convex roof
New measures of multipartite entanglement are constructed based on two
definitions of multipartite information and different methods of optimizing
over extensions of the states. One is a generalization of the squashed
entanglement where one takes the mutual information of parties conditioned on
the state's extension and takes the infimum over such extensions. Additivity of
the multipartite squashed entanglement is proved for both versions of the
multipartite information which turn out to be related. The second one is based
on taking classical extensions. This scheme is generalized, which enables to
construct measures of entanglement based on the {\it mixed convex roof} of a
quantity, which in contrast to the standard convex roof method involves
optimization over all decompositions of a density matrix rather than just the
decompositions into pure states. As one of the possible applications of these
results we prove that any multipartite monotone is an upper bound on the amount
of multipartite distillable key. The findings are finally related to analogous
results in classical key agreement.Comment: improved version, 13 pages, 1 figur
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
Recoverability in quantum information theory
The fact that the quantum relative entropy is non-increasing with respect to
quantum physical evolutions lies at the core of many optimality theorems in
quantum information theory and has applications in other areas of physics. In
this work, we establish improvements of this entropy inequality in the form of
physically meaningful remainder terms. One of the main results can be
summarized informally as follows: if the decrease in quantum relative entropy
between two quantum states after a quantum physical evolution is relatively
small, then it is possible to perform a recovery operation, such that one can
perfectly recover one state while approximately recovering the other. This can
be interpreted as quantifying how well one can reverse a quantum physical
evolution. Our proof method is elementary, relying on the method of complex
interpolation, basic linear algebra, and the recently introduced Renyi
generalization of a relative entropy difference. The theorem has a number of
applications in quantum information theory, which have to do with providing
physically meaningful improvements to many known entropy inequalities.Comment: v5: 26 pages, generalized lower bounds to apply when supp(rho) is
contained in supp(sigma
Entanglement of Purification for Multipartite States and its Holographic Dual
We introduce a new information-theoretic measure of multipartite
quantum/classical correlations , by generalizing the entanglement of
purification to multipartite states. We provide proofs of its various
properties, focusing on several entropic inequalities, in generic quantum
systems. In particular, it turns out that the multipartite entanglement of
purification gives an upper bound on multipartite mutual information, which is
a generalization of quantum mutual information in the spirit of relative
entropy. After that, motivated by a tensor network description of the AdS/CFT
correspondence, we also define a holographic dual of multipartite entanglement
of purification , as a sum of minimal areas of codimension-2 surfaces
which divide the entanglement wedge into multi-pieces. We prove that this
geometrical quantity satisfies all properties we proved for the multipartite
entanglement of purification. These agreements strongly support the
conjecture. We also show that the multipartite
entanglement of purification gives an upper bound on multipartite squashed
entanglement, which is a promising measure of multipartite quantum
entanglement. We discuss potential saturation of multipartite squashed
entanglement onto multipartite mutual information in holographic CFTs and its
applications.Comment: 30 pages, 11 figures, v2:comments and references added, section 4 is
moved to appendix A, published versio
Multipartite quantum correlations and local recoverability
Characterizing genuine multipartite quantum correlations in quantum physical
systems has historically been a challenging problem in quantum information
theory. More recently however, the total correlation or multipartite
information measure has been helpful in accomplishing this goal, especially
with the multipartite symmetric quantum (MSQ) discord [Piani et al., Phys. Rev.
Lett. 100, 090502, 2008] and the conditional entanglement of multipartite
information (CEMI) [Yang et al., Phys. Rev. Lett. 101, 140501, 2008]. Here we
apply a recent and significant improvement of strong subadditivity of quantum
entropy [Fawzi and Renner, arXiv:1410.0664] in order to develop these
quantities further. In particular, we prove that the MSQ discord is nearly
equal to zero if and only if the multipartite state for which it is evaluated
is approximately locally recoverable after performing measurements on each of
its systems. Furthermore, we prove that the CEMI is a faithful entanglement
measure, i.e., it vanishes if and only if the multipartite state for which it
is evaluated is a fully separable state. Along the way we provide an
operational interpretation of the MSQ discord in terms of the partial state
distribution protocol, which in turn, as a special case, gives an
interpretation for the original discord quantity. Finally, we prove an
inequality that could potentially improve upon the Fawzi-Renner inequality in
the multipartite context, but it remains an open question to determine whether
this is so.Comment: 25 pages, 1 figure; v2: minor changes; v3: minor corrections and
improvement