Southwest Quantum Information and Technology

Quantum tomography under prior information

Presenting Author: Amir Kalev, Center for Quantum Information and Control
Contributing Author(s): Charles H. Baldwin, Ivan H. Deutsch

Quantum-state tomography (QST) is generally expensive to implement experimentally. Nevertheless, in state-of-the-art quantum information experiments the goal is not to produce arbitrary states but states that have very high purity. Including this prior information in QST results in more manageable tomography protocols, for example, by compressed sensing methods. In the context of pure-state tomography, and more generally, of bounded-rank states (states with rank less than or equals to r) tomography, a natural notion of informational completeness emerges, "rank-r completeness." The purpose of this contribution is three fold. First, to prove and emphasize the significance of a less intuitive, yet more powerful, notion of completeness for practical QST, "rank-r strict-completeness." This notion is made possible due to the positive semidefinite property of density matrices. Strictly-complete quantum measurements ensure a robust estimation of the state of the system, regardless of the convex estimator we use. Thus, pragmatically, quantum state tomography should be done using these kind of measurements. Second, to argue, based on strong numerical indication, that it is fairly straightforward to experimentally implement such measurements by measuring only few random orthonormal bases. For example, in our numerical experiments we find that a measurement of six random orthogonal bases are strictly-complete for pure states and allow for a robust estimation of highly-pure states, regardless of the Hilbert space dimension. Finally, we relate the notion of strict-completeness to compressed sensing. We show that all compressed sensing measurements for QST are particular examples of strict-completeness.

Read this article online: http://arxiv.org/abs/1511.01433, http://arxiv.org/abs/1502.00536, http://arxiv.org/abs/1510.02736

(Session 5 : Thursday from 5:00 - 7:00 pm)