Separability conditions based on local fine-grained uncertainty relations
arXiv:1508.03925 · doi:10.1007/s11128-016-1286-z
Abstract
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.
12 pages, no figures. Minor improvements in the version 2, matches the journal version
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Cited by in corpus (10)
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- Conditional entropic uncertainty relations for Tsallis entropies
- On entropic uncertainty relations for measurements of energy and its "complement"
- Rényi formulation of entanglement criteria for continuous variables
- Generalization of Pauli channels through mutually unbiased measurements
- Relating entropies of quantum channels
- Rényi and Tsallis formulations of separability conditions in finite dimensions
- All classes of informationally complete symmetric measurements in finite dimensions