1 research outputs found
Measuring incompatibility and clustering quantum observables with a quantum switch
The existence of incompatible observables is a cornerstone of quantum
mechanics and a valuable resource in quantum technologies. Here we introduce a
measure of incompatibility, called the mutual eigenspace disturbance (MED),
which quantifies the amount of disturbance induced by the measurement of a
sharp observable on the eigenspaces of another. The MED provides a metric on
the space of von Neumann measurements, and can be efficiently estimated by
letting the measurement processes act in an indefinite order, using a setup
known as the quantum switch, which also allows one to quantify the
noncommutativity of arbitrary quantum processes. Thanks to these features, the
MED can be used in quantum machine learning tasks. We demonstrate this
application by providing an unsupervised algorithm that clusters unknown von
Neumann measurements. Our algorithm is robust to noise can be used to identify
groups of observers that share approximately the same measurement context.Comment: 14 pages, 2 figure