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 CMP states include the (continuous-mode) single photon and time-ordered multi-photon states.
Highlights
Continuous matrix product (CMP) states were introduced by Verstraete and Cirac [1,2,3] as the generalization of finitely correlated states to continuous-variable quantum input processes [4]
We introduce a new class of continuous matrix product (CMP) states and establish the stochastic master equations 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 equations which are matrix-valued
Summary
Continuous matrix product (CMP) states were introduced by Verstraete and Cirac [1,2,3] as the generalization of finitely correlated states to continuous-variable quantum input processes [4]. It is shown that the class of CMP states defined in this paper include the (continuous-mode) single photon and time-ordered multi-photon states, and we derive explicit Markovian generators for these multi-photon states that allow the filtering equations for systems driven by fields in these states to be obtained from the general formulas of this paper. We derive the quantum master equation and quantum filtering (quantum trajectory) equations for an open Markov model driven by a field in the newly defined CMP states, in the form of matrix-valued equations with operator entries Appendix A details a Markovian generator model for time-ordered two-photon states that is generalized to timeordered multi-photon states in appendix B
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