# Precise Phase Measurements using an Entangled Coherent State

### P. A. Knott, J. A. Dunningham

#### Abstract

Quantum entanglement offers the possibility of making measurements beyond the classical limit, however some issues still need to be overcome before it can be applied in realistic lossy systems. Recent work has used quantum Fisher information (QFI) to show that entangled coherent states (ECSs) may be useful for this purpose as they combine sub-classical phase precision capabilities with robustness (Joo et al., 2011). However, to date no effective scheme for measuring a phase in lossy systems using an ECS has been devised. Here we present a scheme that does just this. We show how one could measure a phase to a precision significantly better than that attainable by both unentangled ‘classical’ states and highly-entangled NOON states over a wide range of different losses. This brings quantum metrology closer to being a realistic and practical technology.

#### References

- Boixo, S., Datta, A., Davis, M., Shaji, A., Tacla, A., and Caves, C. (2009). Quantum-limited metrology and Bose-Einstein condensates. Physical Review A, 80(3):032103.
- Braunstein, S. and Caves, C. (1994). Statistical distance and the geometry of quantum states. Physical Review Letters, 72(22):3439-3443.
- Demkowicz-Dobrzanski, R., Dorner, U., Smith, B., Lundeen, J., Wasilewski, W., Banaszek, K., and Walmsley, I. (2009). Quantum phase estimation with lossy interferometers. Physical Review A, 80(1):013825.
- Dorner, U., Demkowicz-Dobrzanski, R., Smith, B., Lundeen, J., Wasilewski, W., Banaszek, K., and Walmsley, I. (2009). Optimal quantum phase estimation. Physical review letters, 102(4):40403.
- Dowling, J. (2008). Quantum optical metrology-the lowdown on high-N00N states. Contemporary physics, 49(2):125-143.
- Dunningham, J. and Kim, T. (2006). Using quantum interferometers to make measurements at the Heisenberg limit. Journal of Modern Optics, 53(4):557-571.
- Gerrits, T., Glancy, S., Clement, T., Calkins, B., Lita, A., Miller, A., Migdall, A., Nam, S., Mirin, R., and Knill, E. (2010). Generation of optical coherentstate superpositions by number-resolved photon subtraction from the squeezed vacuum. Physical Review A, 82(3):031802.
- Gkortsilas, N., Cooper, J., and Dunningham, J. (2012). Measuring a completely unknown phase with subshot-noise precision in the presence of loss. Physical Review A, 85(6):063827.
- Hirota, O., Kato, K., and Murakami, D. (2011). Effectiveness of entangled coherent state in quantum metrology. arXiv preprint arXiv:1108.1517.
- Joo, J., Munro, W., and Spiller, T. (2011). Quantum metrology with entangled coherent states. Physical Review Letters, 107(8):83601.
- Nagata, T., Okamoto, R., O'Brien, J., Sasaki, K., and Takeuchi, S. (2007). Beating the standard quantum limit with four-entangled photons. Science, 316(5825):726-729.
- Sanders, B. (2012). Review of entangled coherent states. Journal of Physics A: Mathematical and Theoretical, 45(24):244002.
- Zhang, Y., Li, X., Yang, W., and Jin, G. (2013). Quantum fisher information of entangled coherent state in the presence of photon losses: exact solution. arXiv preprint arXiv:1307.7353.

#### Paper Citation

#### in Harvard Style

Knott P. and Dunningham J. (2014). **Precise Phase Measurements using an Entangled Coherent State** . In *Proceedings of 2nd International Conference on Photonics, Optics and Laser Technology - Volume 1: PHOTOPTICS,* ISBN 978-989-758-008-6, pages 205-211. DOI: 10.5220/0004734902050211

#### in Bibtex Style

@conference{photoptics14,

author={P. A. Knott and J. A. Dunningham},

title={Precise Phase Measurements using an Entangled Coherent State},

booktitle={Proceedings of 2nd International Conference on Photonics, Optics and Laser Technology - Volume 1: PHOTOPTICS,},

year={2014},

pages={205-211},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0004734902050211},

isbn={978-989-758-008-6},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of 2nd International Conference on Photonics, Optics and Laser Technology - Volume 1: PHOTOPTICS,

TI - Precise Phase Measurements using an Entangled Coherent State

SN - 978-989-758-008-6

AU - Knott P.

AU - Dunningham J.

PY - 2014

SP - 205

EP - 211

DO - 10.5220/0004734902050211