Relativities between sets and measurements

Yoshio Kinokuniya

u s p a p e r s ， we h a v e o b t a i n e d a c o u r s e o f a x i o 幽 m a t i z a t i o n w h i c h c a n b e s k e t c h e d a s f o l l o w s .* 紀 国 谷 芳 雄 ( 2 9 )

R. Raussendorf, P. Sarvepalli, T.-C. Wei +1 more

We discuss the interdependence of resource state, measurement setting and temporal order in measurement-based quantum computation. The possible temporal orders of measurement events are constrained by the principle that the randomness inherent in quantum measurement should not affect the outcome of the computation. We provide a classification for all temporal relations among measurement events compatible with a given initial stabilizer state and measurement setting, in terms of a matroid. Conversely, we show that classical processing relations necessary for turning the local measurement outcomes into computational output determine the resource state and measurement setting up to local equivalence. Further, we find a symmetry transformation related to local complementation that leaves the temporal relations invariant.

Wolfgang Ernst Friederich Pauli

Per Arve

Holger Friedrich Hofmann

Quantum contextuality describes situations where the statistics observed in different measurement contexts cannot be explained by a measurement of the independent reality of the system. The most simple case is observed in a three-dimensional Hilbert space, with five different measurement contexts related to each other by shared measurement outcomes. The quantum formalism defines the relations between these contexts in terms of well-defined relations between operators, and these relations can be used to reconstruct an unknown quantum state from a finite set of measurement results. Here, I introduce a reconstruction method based on the relations between the five measurement contexts that can violate the bounds of non-contextual statistics. A complete description of an arbitrary quantum state requires only five of the eight elements of a Kirkwood-Dirac quasiprobability, but only an overcomplete set of eleven elements provides an unbiased description of all five contexts. A set of five fundamental relations between the eleven elements reveals a deterministic structure that links the five contexts. As illustrated by a number of examples, these relations provide a consistent description of contextual realities for the measurement outcomes of all five contexts.

Szabó, László