Simulability of High-Dimensional Quantum Measurements

We investigate the compression of quantum information with respect to a given set M of high-dimensional measurements. This leads to a notion of simulability, where we demand that the statistics obtained from M and an arbitrary quantum state p are recovered exactly by first compressing p into a lower-dimensional space, followed by some quantum measurements. A full quantum compression is possible, i.e., leaving only classical information, if and only if the set M is jointly measurable. Our notion of simulability can thus be seen as a quantification of measurement incompatibility in terms of dimension. After defining these concepts, we provide an illustrative example involving mutually unbiased bases, and develop a method based on semidefinite programming for constructing simulation models. In turn we analytically construct optimal simulation models for all projective measurements subjected to white noise or losses. Finally, we discuss how our approach connects with other concepts introduced in the context of quantum channels and quantum correlations.

Automated summary

This article investigates quantum information compression with respect to a given set of high-dimensional measurements. The notion of simulability is introduced, which demands that the statistics obtained from the measurements and an arbitrary quantum state are exactly recovered through compression and subsequent measurements. The article provides an illustrative example and develops a method for constructing simulation models. It also explores the connection between this approach and other concepts in the context of quantum channels and quantum correlations.