I presented this talk as part of my candidacy exam. Given at the Center for Quantum and Information and Control at UNM.
Quantum devices with ill-defined/unknown Hilbert space dimension pose problems for quantum tomography, as the size of the matrix to fit as an estimate needs to be determined. We may begin to address this problem using techniques from classical statistical inference. I will present an approach known as the likelihood ratio test and demonstrate an application to continuous-variable systems. This test relies on the null value of the test statistic - that is, the typical value when increasing the Hilbert space dimension provides no advantage to fitting the data. I will show preliminary numerical results indicating the null value is related to the dimension of the boundary of the Hilbert space, not its bulk dimension.