Parity measurements in quantum optical metrology

Abstract

We investigate the utility of parity detection to achieve Heisenberg-limited phase estimation for optical interferometry. We consider the parity detection with several input states that have been shown to exhibit sub-shot-noise interferometry with their respective detection schemes. We show that with parity detection, all these states achieve the sub-shot-noise limited phase uncertainty. Thus making the parity detection a unified detection strategy for quantum optical metrology. We also consider quantum states that are a combination of a NOON state and a dual-Fock state, which gives a great deal of freedom in the preparation of the input state, and is found to surpass the shot-noise limit.

Keywords:

• Heisenberg limit
• interferometry
• uncorrelated and entangled states
• parity measurements
• unified detection

Acknowledgements

This work is supported by the Intelligence Advanced Research Projects Activity, the Army Research Office, and the Defense Advanced Research Projects Agency. We would like to acknowledge J.P. Dowling and Y. Gao for stimulating discussions.

Notes

1. The rotation matrix element:

where is the Jacobi polynomial. These rotation matrix elements further possess symmetric relations:

and a contraction rule: