Measurement-induced steering of quantum systems

Abstract

We set out a general protocol for steering the state of a quantum system from an arbitrary initial state toward a chosen target state by coupling it to auxiliary quantum degrees of freedom. The protocol requires multiple repetitions of an elementary step: During each step, the system evolves for a fixed time while coupled to auxiliary degrees of freedom (which we term "detector qubits") that have been prepared in a specified initial state. The detectors are discarded at the end of the step, or equivalently, their state is determined by a projective measurement with an unbiased average over all outcomes. The steering harnesses backaction of the detector qubits on the system, arising from entanglement generated during the coupled evolution. We establish principles for the design of the system-detector coupling that ensure steering of a desired form. We illustrate our general ideas using both few-body examples (including a pair of spins-1/2 steered to the singlet state) and a many-body example (a spin-1 chain steered to the Affleck-Kennedy-Lieb-Tasaki state). We study the continuous time limit in our approach and discuss similarities to (and differences from) drive-and-dissipation protocols for quantum state engineering. Our protocols are amenable to implementations using present-day technology. Obvious extensions of our analysis include engineering of other many-body phases in one and higher spatial dimensions, adiabatic manipulations of the target states, and the incorporation of active error correction steps.

Measurement-induced entanglement transitions in many-body localized systems

“…IV how X-basis measurements with small but nonzero p can actually increase the steady-state entanglement relative to p = 0 for initial states with nonmaximal diagonal entropy, as a consequence of the increase in diagonal entropy induced by X-basis measurements. This may be somewhat counterintuitive, given the usual picture of measurements destroying entanglement, but suggests the possibility that measurements could be used as a tool to produce states with desirable properties [75], such as high entanglement, in systems where simply evolving with random unitaries is not feasible.…”

Engineering two-qubit mixed states with weak measurements

“…We design the protocol such that this steady state is the target state. We first recall a measurement-based protocol whose steady state is an arbitrarily chosen pure state [17]. In order to generate a mixed state, we diagonalize the density matrix of the target state and juxtapose the protocols for stabilizing each of the density matrix's pure eigenstates.…”

“…We now recall the principles of measurement-based steering protocol of Ref. [17], focusing on the two-qubit case, at the center of our analysis. The protocol facilitates stabilizing the system in an arbitrary pure target state |B 1 , corresponding to ρ (T )…”

“…(13). The magnitudes of the density matrix entries in the basis |B i (17) are represented by a color scale. The initial state can be pure (ρ…”

“…An interesting future direction concerns stabilizing N-qubit mixed states. Stabilizing N-qubit pure states in an efficient manner is already a challenging problem, which, however, has been solved for the restricted class of tensor-network states [17,46,60]. Stabilizing N-qubit mixed states turns out to be an even more challenging problem still under research [61].…”