Quantum Trajectories for a Class of Continuous Matrix Product Input States

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.

17 pages, 2 figures

References in corpus (3)

• Continuous Matrix Product States for Quantum Fields
• Quantum Feedback Networks: Hamiltonian Formulation
• Holographic quantum states

Cited by in corpus (14)

• The SLH framework for modeling quantum input-output networks
• Time-delayed quantum feedback control
• Input-Output Theory with Quantum Pulses
• Quantum interactions with pulses of radiation
• Quantum trajectories for propagating Fock states
• Generating Nonclassical Quantum Input Field States with Modulating Filters
• Particle emission from open-quantum systems
• Quantum trajectories for a system interacting with environment in N-photon state
• Quantum filter for a class of non-Markovian quantum systems
• Mathematical Models of Markovian Dephasing
• Quantum trajectories for environment in superposition of coherent states
• Quantum Stochastic Processes and the Modelling of Quantum Noise
• Markovian Embeddings of Non-Markovian Quantum Systems: Coupled Stochastic and Quantum Master Equations for Non-Markovian Quantum Systems
• Physical Reduced Stochastic Equations for Continuously Monitored Non-Markovian Quantum Systems with a Markovian Embedding