Empirical sets

Hirokazu Nishimura

Hirokazu Nishimura

María Luisa Dalla Chiara

Mark Byrd, Daniel A. Lidar

We present an algorithmic approach to identifying the set of “bang-bang” control operations used to eliminate decoherence afflicting a quantum computer. Using empirical quantum tomography data only, an optimal set of operations is determined.

Hui-Xian Meng, Huaixin Cao, Wenhua Wang +2 more

Motivated by the importance of contextuality and a work on the robustness of the entanglement of mixed quantum states, the robustness of contextuality (RoC) R C ( e ) of an empirical model e against non-contextual noises was introduced and discussed in Science China Physics, Mechanics and Astronomy (59(4) and 59(9), 2016). Because noises are not always non-contextual, this paper introduces and discusses the generalized robustness of contextuality (GRoC) R g ( e ) of an empirical model e against general noises. It is proven that R g ( e ) = 0 if and only if e is non-contextual. This means that the quantity R g can be used to distinguish contextual empirical models from non-contextual ones. It is also shown that the function R g is convex on the set of all empirical models and continuous on the set of all no-signaling empirical models. For any two empirical models e and f such that the generalized relative robustness of e with respect to f is finite, a fascinating relationship between the GRoCs of e and f is proven, which reads R g ( e ) R g ( f ) ≤ 1 . Lastly, for any n-cycle contextual box e, a relationship between the GRoC R g ( e ) and the extent Δ e of violating the non-contextual inequalities is established.

Roderich Tumulka

We consider ontological models of a quantum system, assuming that not all probability distributions over the space $Λ$ of ontic states are preparable, only those belonging to a certain set C. We assume further that every POVM with a finite value space can be measured and that for every density matrix there exists a distribution in C whose outcome statistics is given by the density matrix. We show that this mapping from C to the set of density matrices must be many-to-one, that is, that there must be empirically indistinguishable distributions in C. This shows that there must be limitations to knowledge in the sense of facts in nature that cannot be discovered empirically.