2 research outputs found
Concurrence for infinite-dimensional quantum systems
Concurrence is an important entanglement measure for states in
finite-dimensional quantum systems that was explored intensively in the last
decade. In this paper, we extend the concept of concurrence to
infinite-dimensional bipartite systems and show that it is continuous and does
not increase under local operation and classical communication (LOCC).
Moreover, based on the partial Hermitian conjugate (PHC) criterion proposed in
[Chin. Phys. Lett. \textbf{26}, 060305(2009); Chin. Sci. Bull. \textbf{56}(9),
840--846(2011)], we introduce a concept of the PHC measure and show that it
coincides with the concurrence, which provides another perspective on the
concurrence.Comment: 14 page
Separability conditions based on local fine-grained uncertainty relations
Many protocols of quantum information processing use entangled states. Hence,
separability criteria are of great importance. We propose new separability
conditions for a bipartite finite-dimensional system. They are derived by using
fine-grained uncertainty relations. Fine-grained uncertainty relations can be
obtained by consideration of the spectral norms of certain positive matrices.
One of possible approaches to separability conditions is connected with upper
bounds on the sum of maximal probabilities. Separability conditions are often
formulated for measurements that have a special structure. For instance,
mutually unbiased bases and mutually unbiased measurements can be utilized for
such purposes. Using resolution of the identity for each subsystem of a
bipartite system, we construct some resolution of the identity in the product
of Hilbert spaces. Separability conditions are then formulated in terms of
maximal probabilities for a collection of specific outcomes. The presented
conditions are compared with some previous formulations. Our results are
exemplified with entangled states of a two-qutrit system.Comment: 12 pages, no figures. Minor improvements in the version 2, matches
the journal versio