Power of One Bit of Quantum Information in Quantum Metrology

TL;DR

This paper introduces a quantum metrology model inspired by DQC1, demonstrating that measurement precision at the standard quantum limit can be achieved with minimal purity, and surpassing it with an extra qubit, linking discord to precision limits.

Contribution

It presents a quantum metrology scheme using one pure qubit and mixed qubits, showing how minimal purity can reach or exceed the standard quantum limit.

Findings

Standard quantum limit achievable with one pure and multiple mixed qubits

Adding one qubit with slight purity improves measurement precision beyond the limit

Discord in the final state vanishes only at infinite measurement precision

Abstract

We construct a model of quantum metrology inspired by the computational model known as deterministic quantum computation with one quantum bit (DQC1). Using only one pure qubit together with $l$ fully-mixed qubits we obtain measurement precision at the standard quantum limit, which is typically obtained using the same number of uncorrelated qubits in fully-pure states. The standard quantum limit can be exceeded using an additional qubit, which adds only a small amount of purity. We show that the discord in the final state vanishes only in the limit of attaining infinite precision for the parameter being estimated.