100 research outputs found
Monogamy, polygamy, and other properties of entanglement of purification
For bipartite pure and mixed quantum states, in addition to the quantum
mutual information, there is another measure of total correlation, namely, the
entanglement of purification. We study the monogamy, polygamy, and additivity
properties of the entanglement of purification for pure and mixed states. In
this paper, we show that, in contrast to the quantum mutual information which
is strictly monogamous for any tripartite pure states, the entanglement of
purification is polygamous for the same. This shows that there can be genuinely
two types of total correlation across any bipartite cross in a pure tripartite
state. Furthermore, we find the lower bound and actual values of the
entanglement of purification for different classes of tripartite and
higher-dimensional bipartite mixed states. Thereafter, we show that if
entanglement of purification is not additive on tensor product states, it is
actually subadditive. Using these results, we identify some states which are
additive on tensor products for entanglement of purification. The implications
of these findings on the quantum advantage of dense coding are briefly
discussed, whereby we show that for tripartite pure states, it is strictly
monogamous and if it is nonadditive, then it is superadditive on tensor product
states.Comment: 12 pages, 2 figures, Published versio
The one-way unlocalizable quantum discord
In this paper, we present the concept of the one-way unlocalizable quantum
discord and investigate its properties. We provide a polygamy inequality for it
in tripartite pure quantum system of arbitrary dimension. Several tradeoff
relations between the one-way unlocalizable quantum discord and other
correlations are given. If the von Neumann measurement is on a part of the
system, we give two expressions of the one-way unlocalizable quantum discord in
terms of partial distillable entanglement and quantum disturbance. Finally, we
also provide a lower bound for bipartite shareability of quantum correlation
beyond entanglement in a tripartite system.Comment: 6 pages, 3 figures. Minor corrections, references adde
Monogamy and polygamy for multi-qubit entanglement using R\'enyi entropy
Using R\'enyi- entropy to quantify bipartite entanglement, we prove
monogamy of entanglement in multi-qubit systems for . We also
conjecture a polygamy inequality of multi-qubit entanglement with strong
numerical evidence for with
.Comment: 19 pages, 2 figure
Strong polygamy of quantum correlations in multi-party quantum systems
We propose a new type of polygamy inequality for multi-party quantum
entanglement. We first consider the possible amount of bipartite entanglement
distributed between a fixed party and any subset of the rest parties in a
multi-party quantum system. By using the summation of these distributed
entanglements, we provide an upper bound of the distributed entanglement
between a party and the rest in multi-party quantum systems. We then show that
this upper bound also plays as a lower bound of the usual polygamy inequality,
therefore the strong polygamy of multi-party quantum entanglement. For the case
of multi-party pure states, we further show that the strong polygamy of
entanglement implies the strong polygamy of quantum discord.Comment: 5 page
Entanglement of purification: from spin chains to holography
Purification is a powerful technique in quantum physics whereby a mixed
quantum state is extended to a pure state on a larger system. This process is
not unique, and in systems composed of many degrees of freedom, one natural
purification is the one with minimal entanglement. Here we study the entropy of
the minimally entangled purification, called the entanglement of purification,
in three model systems: an Ising spin chain, conformal field theories
holographically dual to Einstein gravity, and random stabilizer tensor
networks. We conjecture values for the entanglement of purification in all
these models, and we support our conjectures with a variety of numerical and
analytical results. We find that such minimally entangled purifications have a
number of applications, from enhancing entanglement-based tensor network
methods for describing mixed states to elucidating novel aspects of the
emergence of geometry from entanglement in the AdS/CFT correspondence.Comment: 40 pages, multiple figures. v2: references added, typos correcte
Polygamy of Distributed Entanglement
While quantum entanglement is known to be monogamous (i.e. shared
entanglement is restricted in multi-partite settings), here we show that
distributed entanglement (or the potential for entanglement) is by nature
polygamous. By establishing the concept of one-way unlocalizable entanglement
(UE) and investigating its properties, we provide a polygamy inequality of
distributed entanglement in tripartite quantum systems of arbitrary dimension.
We also provide a polygamy inequality in multi-qubit systems, and several trade
offs between UE and other correlation measures.Comment: 9 pages, 1 figure, few typos correcte
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