Open Systems & Information Dynamics

In this work we study the reduced dynamics of a system embedded in a quantum environment, with the use of correlation functions produced through appropriately defined reduced generating functionals. Our construction is based on expressing these functionals in terms of consistently defined coherent-state path integrals in the framework of the Keldysh-Schwinger out-of-equilibrium formalism.

Suppose that for some unit vectors $b_1,\dots b_n$ in ${ℂ}^d$ we have that for any $j\ne k$   $b_j$ is either orthogonal to $b_k$ or $|〈b_j,b_k〉{|}^2=1/d$ (i.e., $b_j$ and $b_k$ are unbiased). We prove that if $n=d(d+1)$, then these vectors necessarily form a complete system of mutually unbiased bases, that is, they can be arranged into $d+1$ orthonormal bases, all being mutually unbiased with respect to each other.

In this paper, a nonlinear optimal feedback control based on the nonlinear state estimator for a two-level open non-Markovian stochastic quantum system is proposed. The proposed nonlinear state estimator is designed by using the state-dependent differential Riccati equation and constructed to optimally estimate the state. The estimated state is updated by the output data of continuous weak measurement of the controlled quantum system and used to design the nonlinear state feedback controller to track the output of the reference model. The output state of reference model is chosen as the desired performance. The numerical simulation results verify the achievability of the proposed state feedback control strategy, and the capability to steer the state of system from any arbitrary initial state to the final reference target state with high state transfer success rate.

In order to discuss the efficiency of information transmission of the Gaussian communication processes consistently, we introduced an entropy type functional and a mutual entropy type functional in reference [16]. In that study, we used the set of Gaussian input measures with covariance operators of trace one. In this paper, we refine the formulation and modify the entropy type complexity and the mutual entropy type complexity to be able to study the efficiency of information transmission for more general input Gaussian measures and Gaussian channels.