Qubit models of weak continuous measurements: markovian conditional and open-system dynamics

Abstract

In this paper we approach the theory of continuous measurements and the associated unconditional and conditional (stochastic) master equations from the perspective of quantum information and quantum computing. We do so by showing how the continuous-time evolution of these master equations arises from discretizing in time the interaction between a system and a probe field and by formulating quantum-circuit diagrams for the discretized evolution. We then reformulate this interaction by replacing the probe field with a bath of qubits, one for each discretized time segment, reproducing all of the standard quantum-optical master equations. This provides an economical formulation of the theory, highlighting its fundamental underlying assumptions.

Collision models in quantum optics

“…It is worth observing that, as recently shown in Ref. [46], quantum optics MEs can be derived as well through a suitably de ned discrete dynamics where the system interacts in succession with qubits.…”

From a posteriori to a priori solutions for a two-level system interacting with a single-photon wavepacket

“…where H S is the Hamiltonian associated with S, L is a bounded operator acting on H S , σ − k = |0 k 1|, σ + k = |1 k 0|, where |0 k and |1 k stand respectively for a ground and excited state of the k-th two-level system of the bath. The derivation the Hamiltonian (3) together with discussion about physical assumptions leading to it one can find, for instance, in [58,61,71]. The interaction between the system and the field is described in the Weisskopf-Wigner approximation.…”

“…The impact of these correlations on the evolution of open systems was analyzed in the framework of the collision model, for instance, in [60,[63][64][65][66]. Discussions about the discrete filtering equations and their continuous limits one can find, for instance, in [54,56,61,67,69,70]. The time discretization procedure leading to the collision model in quantum optics and its connection with the input-output formalism and quantum trajectories are given in [58,60,61].…”

Quantum frequency estimation with conditional states of continuously monitored independent dephasing channels

“…In this work we consider the possibility of continuously measuring the environment causing the dephasing, i.e. sequentially measuring the output modes after the interaction with the system [37][38][39]. This corresponds to a (weak) continuous monitoring of the N local observables σ (j) z [40,41].…”