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Uncertainty Relation for coarse-grained measurements and their use for entanglement detection

Data: Sexta-Feira 21/06/2013 Sala A5-01, 11:00

Palestrante: Fabricio Toscano (UFRJ)

Título: Uncertainty Relation for coarse-grained measurements and their use for entanglement detection

Resumo: In Quantum Mechanics, mathematical inequalities that originate from the fact that measured quantities are directly associated to non-commuting operators are generically called uncertainty relations. In continuos variable (CV) systems the best known of these inequalities is the Heisenberg uncertainty relation (HUR), which sets a bound on the product of the variances of the observables ``position and ``momentum. The second better known uncertainty relation involves the Shannon entropies of the probabilities densities functions of these complementary observables, i.e. the Bialynicki-Birula-Mycielski uncertainty relation (BBM). Uncertainty relations are intrinsic features of quantum states and their fullfillment can be considered as a sufficient criterion for a quantum mechanically permissible state. An experimental test of an uncertainty relation is not only a way to establish the quantum nature of a physical system but is also a way to characterize or identify salient quantum features. Thus, they are used to characterize non-classicality of states of radiation fields, to construct entanglement criteria for the whole class of negative partial-transpose states and to establish the security in certain quantum cryptography protocols. Because the experiments are always performed with finite precision, coarse-grained measurements can lead to a false violation of uncertainty relations. So, the problem that arises is how to evaluate an uncertainty relations with coarse-grained quantities in a reliable way even for detectors of low precision. Here, we derive new uncertainty relations that are valid for any size detector or sampling window. These new relations are always verified by any physical state, and should be relevant in fundamental investigations of quantum physics as well as applications such as entanglement detection and quantum cryptography.


1- Lukasz Rudnicki, Stephen P. Walborn e Fabricio Toscano, Heisenberg uncertainty relation for coarse-grained observables; Europhysics Letters 97, 38003 (2012).

2- Lukasz Rudnicki, Stephen P. Walborn e Fabricio Toscano, Optimal uncertainty relations for extremely coarse-grained measurements; Physical Review A 85 042115 (2012).

3- Daniel. S. Tasca, Lukasz Rudnicki, Rafael. M. Gomes, Fabricio Toscano, and Stephen. P. Walborn, Reliable Entanglement Detection Under Coarse-Grained Measurements, submitted to Physical Review Lettters (2013).


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