Sub-shot noise sensitivities without entanglement

TL;DR

This paper demonstrates that non-entangled bosonic states can surpass the shot-noise limit in interferometry using a fluctuating number of bosons, challenging the notion that entanglement is necessary for such sensitivity improvements.

Contribution

It shows that non-entangled bosonic states can beat shot-noise sensitivity without entanglement, and identifies optimal states for given maximum boson numbers.

Findings

Non-entangled states can outperform entangled states in certain interferometric sensitivities.

NOON states are optimal among two-mode bosonic states without losses.

Surpassing shot-noise limit is possible with all bosons in one mode, even without entanglement.

Abstract

It is commonly maintained that entanglement is necessary to beat the shot noise limit in the sensitivity with which certain parameters can be measured in interferometric experiments. Here we show that, with a fluctuating number of two-mode bosons, the shot-noise limit can be beaten by non-entangled bosonic states with all bosons in one mode. For a given finite maximum number of bosons, we calculate the optimal one- and two-mode bosonic states, and show that in the absence of losses, NOON states are the optimal two-mode bosonic states.