Quantum and classical operational complementarity for single systems (4 pages)

Alfredo Luis

Dénes Petz

Alfredo Luis

We investigate duality relations between conjugate observables after measurements performed on a single realization of the system. The application of standard inference methods implies the existence of duality relations for single systems when using classical as well as quantum physics.

András Szántó

K. M. Fonseca-Romero, J. G. G. de Oliveira, J. G. Peixoto de Faria +1 more

In two-dimensional systems, predictability and visibility satisfy a complementarity relation, which has been generalized to bipartite systems by including the concurrence. We consider systems in which the two alternatives of a which-state experiment are nonorthogonal states and propose generalized measures of predictability and visibility. Criteria like symmetry under exchange of the alternatives, vanishing visibility when only one of the alternatives is present, and clear operational meaning, favor definitions of predictability and visibility which use a three-dimensional basis, previously employed in the unambiguous discrimination of nonorthogonal states. We derive generalized single-partite and bipartite complementarity relations and find that predictability and visibility do not exhaust the single-partite properties for a nonorthogonal basis. A recent experiment on the quantum-classical border is analyzed using generalized complementarity relations.

Raquel Galazo García, Irene Bartolomé, Laura Ares +1 more