Wu, Re-BingBrif, ConstantinJames, MatthewRabitz, Herschel2018-11-292018-11-291050-2947http://hdl.handle.net/1885/152815In quantum optimal control theory, kinematic bounds are the minimum and maximum values of the control objective achievable for any physically realizable system dynamics. For a given initial state of the system, these bounds depend on the nature and state of the controller. We consider a general situation where the controlled quantum system is coupled to both an external classical field (referred to as a classical controller) and an auxiliary quantum system (referred to as a quantum controller). In this general situation, the kinematic bound is between the classical kinematic bound (CKB), corresponding to the case where only the classical controller is available, and the quantum kinematic bound (QKB), corresponding to the ultimate physical limit of the objective's value. Specifically, when the control objective is the expectation value of a quantum observable (a Hermitian operator on the system's Hilbert space), the QKBs are the minimum and maximum eigenvalues of this operator. We present, both qualitatively and quantitatively, the necessary and sufficient conditions for surpassing the CKB and reaching the QKB, through the use of a quantum controller. The general conditions are illustrated by examples in which the system and controller are initially in thermal states. The obtained results provide a basis for the design of quantum controllers capable of maximizing the control yield and reaching the ultimate physical limit.application/pdfThe authors thank Dr. Mohan Sarovar for useful discussions. R.B.W. acknowledges support from NSFC Grants No. 60904034, No. 61374091, and No. 61134008. C.B. acknowledges support from the Laboratory Directed Research and Development program at Sandia National Laboratories. Sandia National Laboratories is a multiprogram laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the US Department of Energy’s National Nuclear Security Administration under Contract No. DE-AC04-94AL85000. M.R.J. acknowledges support from the Australian Research Council Centre of Excellence for Quantum Computation and Communication Technology (Project No. CE110001027) and AFOSR Grant No. FA2386-12-1-4075. H.R. acknowledges partial support from NSF Grant No. CHE-1058644 and AROMURI Grant No. W911NF-11-1-2068.Keywords: Eigenvalues and eigenfunctions; Kinematics; Quantum electronics; Quantum optics; Quantum theory; Classical controllers; Classical fields; Control objectives; Expectation values; General situation; Hermitian operators; Optimal controls; Quantum optimal con201510.1103/PhysRevA.91.0423272018-11-29