What is the optimal way to prepare a Bell state using measurement and feedback?

TL;DR

This paper identifies optimal measurement and feedback protocols for generating Bell states using parity measurements, enhancing entanglement speed and success rate through rigorous proofs of optimality.

Contribution

It derives and proves globally optimal feedback protocols for entanglement generation with half- and full-parity measurements, advancing quantum control methods.

Findings

Optimal protocol for half-parity measurement maximizing concurrence.

Protocol for rapid entanglement with full-parity measurement.

Full-parity protocol transfers entanglement efficiently among schemes.

Abstract

Recent work has shown that use of quantum feedback can significantly enhance both the speed and success rate of measurement-based remote entanglement generation, but it is generally unknown what feedback protocols are optimal for these tasks. Here we consider two common measurements that are capable of projecting into pairwise entangled states, namely half- and full-parity measurements of two qubits, and determine in each case a globally optimal protocol for generation of entanglement. For the half-parity measurement, we rederive a previously described protocol using more general methods and prove that it is globally optimal for several figures of merit, including maximal concurrence or fidelity, and minimal time to reach a specified concurrence or fidelity. For the full-parity measurement, we derive a protocol for rapid entanglement generation related to that of (C. Hill, J. Ralph, Phys. Rev. A 77, 014305 (2008)), and then map the dynamics of the concurrence of the state to the Bloch vector length of an effective qubit. This mapping allows us to prove several optimality results for feedback protocols with full-parity measurements. We further show that our full-parity protocol transfers entanglement optimally from one qubit to the other amongst all measurement-based schemes. The methods developed here will be useful for deriving feedback protocols and determining their optimality properties in many other quantum systems subject to measurement and unitary operations.