Entanglement-assisted quantum feedback control

Abstract

The main advantage of quantum metrology relies on the effective use of entanglement, which indeed allows us to achieve strictly better estimation performance over the standard quantum limit. In this paper, we propose an analogous method utilizing entanglement for the purpose of feedback control. The system considered is a general linear dynamical quantum system, where the control goal can be systematically formulated as a linear quadratic Gaussian control problem based on the quantum Kalman filtering method; in this setting, an entangled input probe field is effectively used to reduce the estimation error and accordingly the control cost function. In particular, we show that, in the problem of cooling an opto-mechanical oscillator, the entanglement-assisted feedback control can lower the stationary occupation number of the oscillator below the limit attainable by the controller with a coherent probe field and furthermore beats the controller with an optimized squeezed probe field.

An online optimization algorithm for the real-time quantum state tomography

“…4 depicts the fidelity with respect to the number of samplings in the online estimation process. One can see that, for 1, 2, 3, and 4-qubit systems, the number of sampling times required for different algorithms to reach more than 90% fidelity is QST-OADM (9,19,25,168), LS (17,21,28,256), ML (16,22,30,262), and MEG (10,21,29,206), respectively, which shows that the proposed QST-OADM has the lowest sampling times among the 4 algorithms.…”

“…The process from pure state dissipation to the maximum mixed state corresponds to the decrease of purity from 1 to 1/d (d = 2 n ). In addition, it is noteworthy that in most cases [3-5, 9-11, 13-16, 18], the fidelity is defined as F 2 (ρ k ,ρ k ) := tr( ρ k ρ k ρ k ) [25]. At the same time, there are some other definitions of fidelity, such as the superfidelity, defined as [26]; the A-fidelity, defined as F 4 (ρ k ,ρ k ) := (tr( √ ρ k ρ k )) 2 [27]; and the geometric mean fidelity, defined as F 5 (ρ k ,ρ k ) := tr(ρ kρk )/ tr(ρ 2 k ) tr(ρ 2 k ) [28].…”

Mechanical cooling and squeezing using optimal control

“…It includes a complete quantum-mechanical description of the control system and is often formulated in terms of a master equation for the density matrix representing the system. The formalism includes a real-time estimation algorithm that provides the optimal information about the measured state conditioned on previous measurements and finally produces a conditional state which can be subsequently used to drive the mechanical oscillator into the desired state via feedback [3,4,6,10,12,[17][18][19][20][21][22][23].…”

Mechanical cooling and squeezing using optimal control

“…It includes a complete quantum mechanical description of the control system and is often formulated in terms of a master equation for the density matrix representing the system. The formalism includes a real-time estimation algorithm that provides the optimal information about the measured state conditioned on previous measurements, and finally produces a conditional state which can be subsequently used to drive the mechanical oscillator into the desired state via feedback [3,4,6,10,12,[17][18][19][20][21][22].…”