Engineering arbitrary pure and mixed quantum states

Abstract

This work addresses a fundamental problem of controllability of open quantum systems, meaning the ability to steer arbitrary initial system density matrix into any final density matrix. We show that under certain general conditions open quantum systems are completely controllable and propose the first, to the best of our knowledge, deterministic method for a laboratory realization of such controllability which allows for a practical engineering of arbitrary pure and mixed quantum states. The method exploits manipulation by the system with a laser field and a tailored nonequilibrium and time-dependent state of the surrounding environment. As a physical example of the environment we consider incoherent light, where control is its spectral density. The method has two specifically important properties: it realizes the strongest possible degree of quantum state control --- complete density matrix controllability which is the ability to steer arbitrary pure and mixed initial states into any desired pure or mixed final state, and is "all-to-one", i.e. such that each particular control can transfer simultaneously all initial system states into one target state

Review of Some Promising Fractional Physical Models

“…Quantum control is concerned with active manipulation of physical and chemical processes on the atomic and molecular scale. Controlled manipulation by atomic and molecular quantum systems has attracted a lot of research attention in recent years [69,70,71]. Note that the models to control of open quantum system dynamics is a very important subject of nanotechnology.…”

Numerical estimation of reachable and controllability sets for a two-level open quantum system driven by coherent and incoherent controls

“…Coherent control is typically realized by laser radiation. Incoherent control is realized, e.g., using state of incoherent environment in the dissipative part of the master equation ( [11] and [10,12]), back-action of non-selective quantum measurements [13], combining quantum measurements and quantum reinforcement learning [14], in purely dissipative dynamical equation (i.e. without non-dissipative term in the right-hand side of the Gorini-Kossakowski-Lindblad-Sudarshan master equation) with controlled dissipator [15].…”

Engineering two-qubit mixed states with weak measurements

“…By contrast, here we are concerned with stabilizing a predesignated state ("target state"), i.e., finding the evolution protocol (Liouvillian) for which our target state is the steady state. We also note that our approach is distinct from drive-and-dissipation schemes [28,[45][46][47][48][49][50][51][52][53][54][55][56], where environment is employed to relax the system to a desired state. The two crucial distinctions here are that (a) the relaxation is induced by measurements, implying the possibility to use the measurement readouts to confirm the system's desired behavior (and, possibly, hasten the convergence toward the target state), and (b) our system does not have a Hamiltonian (no "drive").…”