Distributed Quantum Metrology and the Entangling Power of Linear Networks

TL;DR

This paper establishes fundamental limits on the use of linear optical networks for quantum metrology, showing they require concentrated quantum resources to reach the Heisenberg limit and revealing the classical behavior of well-distributed resources.

Contribution

It derives a bound on the entangling power of linear networks in distributed quantum metrology and proposes a scheme to achieve the Heisenberg limit with concentrated input photons.

Findings

Linear networks cannot effectively utilize well-distributed quantum resources for metrology.

Achieving the Heisenberg limit requires input photons to be concentrated in few modes.

Linear networks can reach the Heisenberg limit with input photons hoarded in a small number of modes.

Abstract

We derive a bound on the ability of a linear optical network to estimate a linear combination of independent phase shifts by using an arbitrary non-classical but unentangled input state, thereby elucidating the quantum resources required to obtain the Heisenberg limit with a multi-port interferometer. Our bound reveals that while linear networks can generate highly entangled states, they cannot effectively combine quantum resources that are well distributed across multiple modes for the purposes of metrology: in this sense linear networks endowed with well-distributed quantum resources behave classically. Conversely, our bound shows that linear networks can achieve the Heisenberg limit for distributed metrology when the input photons are hoarded in a small number of input modes, and we present an explicit scheme for doing so. Our results also have implications for measures of non-classicality.