Engineering unsteerable quantum states with active feedback

TL;DR

This paper introduces active feedback protocols for quantum state preparation that can generate entangled states, including unsteerable states, by optimizing local fidelity and using weak measurements, with potential for precise quantum control.

Contribution

It presents novel active steering protocols employing simple couplings and local fidelity measures, capable of preparing complex entangled states including unsteerable ones.

Findings

Active protocols outperform standard fidelity-based methods.

Entanglement can be generated and tuned via Bell measurements.

Protocols can reach passively unsteerable states like the N-qubit W state.

Abstract

We propose active steering protocols for quantum state preparation in quantum circuits where each system qubit is connected to a single detector qubit, employing a simple coupling selected from a small set of steering operators. The decision is made such that the expected cost-function gain in one time step is maximized. We apply these protocols to several many-qubit models. Our results are underlined by three remarkable insights. First, we show that the standard fidelity does not give a useful cost function; instead, successful steering is achieved by including local fidelity terms. Second, although the steering dynamics acts on each system qubit separately, entanglement in the generated target state is introduced, and can be tuned at will, by performing Bell measurements on detector qubit pairs after every time step. This implements a weak-measurement variant of entanglement swapping. Third, numerical simulations suggest that the active steering protocol can reach arbitrarily designated target states, including passively unsteerable states such as the $N$-qubit W state.