Speaker
Description
Continuous-variable quantum systems play an important role in quantum
computation, communication, and sensing. Characterizing their quantum
states from experimental measurements, however, remains a challenging
task, particularly for non-Gaussian states, which often exhibit complex
structures that cannot be described by a small number of parameters.
In this talk, I will introduce a statistical approach to quantum state
estimation based on tomographic probability distributions, which
describe the outcomes of experimentally accessible measurements. Unlike
conventional approaches that rely on assumptions about the underlying
quantum state, we develop a nonparametric kernel quantum state
estimation (KQSE) framework that allows us to reconstruct unknown
quantum states directly from noisy measurement data.
The proposed method provides estimates of the density matrix in
different representations, as well as important physical quantities such
as purity, higher moments, overlap, and trace distance. Moreover, it
achieves a near-optimal convergence rate of (\tilde{O}(T^{-1})), where
(T) denotes the total number of measurements.
I will illustrate how this approach can be applied to non-Gaussian
quantum states, including states with complex, multimodal probability
distributions, and discuss its potential for quantum state
characterization without prior knowledge of the state.