Quantum Trajectories and Measurements in Continuous Time

Measurement Uncertainty Relations for Position and Momentum: Relative Entropy Formulation

“…Different names have been used in the literature to refer to the characteristic function of POVMs, or, more generally, quantum instruments, such as characteristic operator or operator characteristic function [3,24,34,44,[58][59][60][61][62]. As a variant, also the symplectic Fourier transform quite often appears [5] (Section 12.4.3).…”

“…The relative entropy S(p q) is an informational quantity which is precisely tailored to quantify the amount of information that is lost by using an approximating probability q in place of the target one p. Although classical and quantum relative entropies have already been used in the evaluation of the performances of quantum measurements [24,27,30,[33][34][35][36][37][38][39][40], their first application to MURs is very recent [41].…”

Principles and applications of quantum control engineering

“…This was extended at the end of the 1980s by Belavkin to the quantum conditionally Markov setting in a series of papers [28][29][30][31][32]. For a general discussion on continual measurement of quantum systems, see Barchielli & Gregoratti [33] and Barchielli & Belavkin [34], as well as Barchielli & Gregoratti [35].…”

Stabilizing Quantum States by Constructive Design of Open Quantum Dynamics

“…From the results in the appendix (Theorem 7), a tridiagonal L in the form (12) has n distinct eigenvalues corresponding to n eigenvectors v k with real entries and the first all different from zero. Without loss of generality, we can assume that the first element of each (unnormalized) eigenvector vj equals 1 for all j.…”

“…In Section III, we illustrate by an example how the Lindblad generator L obtained this way can be implemented by reservoir engineering via direct (Markovian) feedback [9], [10], [11], [12], where the controlled dynamics has the form of a Wiseman-Milburn Markovian Feedback Master Equation (FME) [9], [13]:…”