Quantum compression relative to a set of measurements

Understand

In this work, we investigate the possibility of compressing a quantum system to one of smaller dimension in a way that preserves the measurement statistics of a given set of observables.

• In this process, we allow for an arbitrary amount of classical side information.
• We find that the latter can be bounded, which implies that the minimal compression dimension is stable in the sense that it cannot be decreased by allowing for small errors.
• Various bounds on the minimal compression dimension are proven and an SDP-based algorithm for its computation is provided.