Kumar Gautam
Netaji Subhas Institute of Technology, India
Title: Realizing quantum filtering using deterministic linear algebra
Biography
Biography: Kumar Gautam
Abstract
Belavkin's quantum filtering equations with input Brownian motion as the measurement are formulated and these filtering equations are implemented in MATLAB using basis truncations. If is observable at time zero and it evolves under noisy Schrodinger dynamics to = , then can be described by an infinite dimensional matrix even though is a finite dimensional matrix. The finite dimensional truncaed dynamics of is described as well as its MATLAB implementation. Further if is the Abelian non-demolition Von-Neumann algebra at time t, then the filter =ð”¼( | ) satisfies an infinite dimensional Belavkin equation. This filtering dynamics is also truncated and its dynamics is simulated using MATLAB. The remarkable feature about these MATLAB simulation is that no random process needs to be generated. A random process in quantum probability is simply an operator valued function of time which has different probability distribution in different states.