Matrix product states for quantum metrology

TL;DR

This paper shows that optimal states in lossy quantum interferometry can be efficiently simulated with matrix product states, highlighting limitations on Heisenberg scaling due to decoherence in realistic quantum metrology.

Contribution

It introduces the use of low rank matrix product states to simulate optimal quantum metrological states under loss, revealing fundamental constraints imposed by noise.

Findings

Optimal states are efficiently simulatable with matrix product states.

Heisenberg scaling is elusive in the presence of decoherence.

Realistic quantum metrology protocols are limited by uncorrelated noise.

Abstract

We demonstrate that the optimal states in lossy quantum interferometry may be efficiently simulated using low rank matrix product states. We argue that this should be expected in all realistic quantum metrological protocols with uncorrelated noise and is related to the elusive nature of the Heisenberg precision scaling in presence of decoherence.