### Abstract

We study the sensitivity of phase estimation using a generic class of path-symmetric entangled states |φ>|0>> + |0>|φ>, where an arbitrary state |φ> occupies one of two modes in quantum superposition. With this generalization, we identify the fundamental limit of phase estimation under energy constraint that is characterized by the photon statistics of the component state |φ>. We show that quantum Cramer-Rao bound (QCRB) can be indefinitely lowered with super-Poissonianity of the state |φ>. For possible measurement schemes, we demonstrate that a full photon-counting employing the path-symmetric entangled states achieves the QCRB over the entire range [0, 2π] of unknown phase shift Φ whereas a parity measurement does so in a certain confined range of Φ. By introducing a component state of the form |φ> = √q|1> + √1-q|N>, we particularly show that an arbitrarily small QCRB can be achieved even with a finite energy in an ideal situation. This component state also provides the most robust resource against photon loss among considered entangled states over the range of the average input energy N_{av} > 1. Finally we propose experimental schemes to generate these path-symmetric entangled states for phase estimation.

Original language | English |
---|---|

Article number | 30306 |

Journal | Scientific Reports |

Volume | 6 |

DOIs | |

Publication status | Published - 26 Jul 2016 |

### Fingerprint

### ASJC Scopus subject areas

- General

### Cite this

*Scientific Reports*,

*6*, [30306]. https://doi.org/10.1038/srep30306

**Quantum phase estimation using path-symmetric entangled states.** / Lee, Su Yong; Lee, Chang Woo; Lee, Jaehak; Nha, Hyunchul.

Research output: Contribution to journal › Article

*Scientific Reports*, vol. 6, 30306. https://doi.org/10.1038/srep30306

}

TY - JOUR

T1 - Quantum phase estimation using path-symmetric entangled states

AU - Lee, Su Yong

AU - Lee, Chang Woo

AU - Lee, Jaehak

AU - Nha, Hyunchul

PY - 2016/7/26

Y1 - 2016/7/26

N2 - We study the sensitivity of phase estimation using a generic class of path-symmetric entangled states |φ>|0>> + |0>|φ>, where an arbitrary state |φ> occupies one of two modes in quantum superposition. With this generalization, we identify the fundamental limit of phase estimation under energy constraint that is characterized by the photon statistics of the component state |φ>. We show that quantum Cramer-Rao bound (QCRB) can be indefinitely lowered with super-Poissonianity of the state |φ>. For possible measurement schemes, we demonstrate that a full photon-counting employing the path-symmetric entangled states achieves the QCRB over the entire range [0, 2π] of unknown phase shift Φ whereas a parity measurement does so in a certain confined range of Φ. By introducing a component state of the form |φ> = √q|1> + √1-q|N>, we particularly show that an arbitrarily small QCRB can be achieved even with a finite energy in an ideal situation. This component state also provides the most robust resource against photon loss among considered entangled states over the range of the average input energy Nav > 1. Finally we propose experimental schemes to generate these path-symmetric entangled states for phase estimation.

AB - We study the sensitivity of phase estimation using a generic class of path-symmetric entangled states |φ>|0>> + |0>|φ>, where an arbitrary state |φ> occupies one of two modes in quantum superposition. With this generalization, we identify the fundamental limit of phase estimation under energy constraint that is characterized by the photon statistics of the component state |φ>. We show that quantum Cramer-Rao bound (QCRB) can be indefinitely lowered with super-Poissonianity of the state |φ>. For possible measurement schemes, we demonstrate that a full photon-counting employing the path-symmetric entangled states achieves the QCRB over the entire range [0, 2π] of unknown phase shift Φ whereas a parity measurement does so in a certain confined range of Φ. By introducing a component state of the form |φ> = √q|1> + √1-q|N>, we particularly show that an arbitrarily small QCRB can be achieved even with a finite energy in an ideal situation. This component state also provides the most robust resource against photon loss among considered entangled states over the range of the average input energy Nav > 1. Finally we propose experimental schemes to generate these path-symmetric entangled states for phase estimation.

UR - http://www.scopus.com/inward/record.url?scp=84979787295&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84979787295&partnerID=8YFLogxK

U2 - 10.1038/srep30306

DO - 10.1038/srep30306

M3 - Article

AN - SCOPUS:84979787295

VL - 6

JO - Scientific Reports

JF - Scientific Reports

SN - 2045-2322

M1 - 30306

ER -