This thesis investigates classical models of correlation experiments from a quantum measurement theoretical point of view. Of special interest are the concept of measurement incompatibility and the phenomenon of quantum steering.
As the main result, we establish a one-to-one connection between non-joint measurability, i.e. the impossibility of measuring two or more observables simultaneously, and quantum steering, i.e. the possibility of one party to affect a space-like separated party’s quantum state by the means of local actions and classical communication. The result can be used to translate various results between the relatively new research field of quantum steering and the older field of incompatibility. As examples, we use steering inequalities as incompatibility criteria and map joint observables to local hidden state models.
The main result comes with some possible generalisations. The generalisations discussed here are strongly motivated by quantum measurement theory and they concentrate on continuous variable and channel versions of steering. The resulting formalism not only extends the aforementioned one-to-one connection, but it also has natural applications to Gaussian steering and to temporal correlations.
Whereas the main result focuses on the connection between non-joint measurability and steering-like phenomena, in the process we also derive steering witnesses and bounds on noise tolerance of incompatible observables. As examples, we map certain entropic uncertainty relations to steering inequalities and use known steering techniques to prove the tightness of the aforementioned noise bounds on incompatibility.
On top of the measurement theoretical work, we introduce a technique for witnessing steering in scenarios with one completely uncharacterised and one dimension-bounded observer. The resulting witnesses are motivated by former works on entanglement theory and, despite being more general, they don’t weaken the detection strength of the known steering criteria in typical symmetric scenarios.