Staking out the physical sectors of Hilbert spaces

Dmitri Mogilevtsev, Yong-Siah Teo, Jaroslav Rehacek, Zdenek Hradil, Johannes Tiedau, Regina Kruse, Georg Harder, Christine Silberhorn, Luis L. Sánchez-Soto

Published 2016-09-09Version 1

We propose an efficient procedure to confidently identify the subspace that contains all the relevant information about a quantum state that lives in an arbitrarily large-dimensional Hilbert space---its physical sector. This entails only a few simple measurements and does not require performing a full tomography or any additional \emph{ad hoc} assumption. We apply this approach to both discrete- and continuous-variable systems. For the former, this turns out to be a suitable deterministic dimension-testing protocol. For the latter, we experimentally demonstrate the method without the need for ideal photon-number-resolving detectors.