Not all pure entangled states are useful for sub shot-noise interferometry

Details Not all pure entangled states are useful for sub shot-noise interferometry Not all pure entangled states are useful for sub shot-noise interferometry

2009-12-22

arxiv.org/abs/0912.4349v2

Phys. Rev. A 82, 012337 (2010)

Physics

Quantum Physics

Published version, significantly revised according to the referee's comments. Results unchanged

Scientific paper

We investigate the connection between the shot-noise limit in linear interferometers and particle entanglement. In particular, we ask whether or not sub shot-noise sensitivity can be reached with all pure entangled input states of $N$ particles if they can be optimized with local operations. Results on the optimal local transformations allow us to show that for $N=2$ all pure entangled states can be made useful for sub shot-noise interferometry while for $N>2$ this is not the case. We completely classify the useful entangled states available in a bosonic two-mode interferometer. We apply our results to several states, in particular to multi-particle singlet states and to cluster states. The latter turn out to be practically useless for sub shot-noise interferometry. Our results are based on the Cramer-Rao bound and the Fisher information.

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