Southwest Quantum Information and Technology

Determining the effective dimension of a quantum state space

Presenting Author: Travis Scholten, Sandia National Labs
Contributing Author(s): Robin Blume-Kohout

Quantum state tomography of multiple qubits or optical modes usually relies on techniques to reduce the number of parameters being fit. For example, quantum compressed sensing searches for low-rank estimates, and in optical tomography, the (formally infinite-dimensional) Hilbert space is truncated in some physically- motivated manner. Is it possible to reduce the number of parameters in some other way, using maximum likelihood estimation? Under the assumptions of local asymptotic normality, we have found two useful ways of doing so. The first uses model selection based on the loglikelihood ratio statistic, and allows one to choose the best Hilbert space dimension directly. The second uses the idea of the statistical dimension of the quantum state space to calculate its "effective" dimension. Surprisingly, both results imply that tomography of low-rank true states almost always yields estimates whose dimension is small, even when the estimator does not explicitly impose that constraint.

Read this article online: https://arxiv.org/abs/1609.04385

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