Quantum Trajectories for a Class of Continuous Matrix Product Input States

TL;DR

This paper introduces a new class of continuous matrix product states for bosonic input fields, deriving associated quantum filtering equations, and demonstrating their relevance to single-photon and multi-photon states in quantum systems.

Contribution

The paper defines a novel class of CMP states, derives their quantum filtering equations, and shows their natural emergence from Markovian models, encompassing single and multi-photon states.

Findings

Derived stochastic master equations for the new CMP states.

Showed CMP states include single-photon and multi-photon states.

Established CMP states as outputs of Markovian models.

Abstract

We introduce a new class of continuous matrix product (CMP) states and establish the stochastic master equations (quantum filters) for an arbitrary quantum system probed by a bosonic input field in this class of states. We show that this class of CMP states arise naturally as outputs of a Markovian model, and that input fields in these states lead to master and filtering (quantum trajectory) equations which are matrix-valued. Furthermore, it is shown that this class of continuous matrix product states include the (continuous-mode) single photon and time-ordered multi-photon states.