### Abstract

We search for the optimal quantum pure states of identical bosonic particles for applications in quantum metrology, in particular, in the estimation of a single parameter for the generic two-mode interferometric setup. We consider the general case in which the total number of particles is fluctuating around an average N with variance ΔN2. By recasting the problem in the framework of classical probability, we clarify the maximal accuracy attainable and show that it is always larger than the one reachable with a fixed number of particles (i.e., ΔN=0). In particular, for larger fluctuations, the error in the estimation diminishes proportionally to 1/ΔN, below the Heisenberg-like scaling 1/N. We also clarify the best input state, which is a quasi-NOON state for a generic setup and, for some special cases, a two-mode Schrödinger-cat state with a vacuum component. In addition, we search for the best state within the class of pure Gaussian states with a given average N, which is revealed to be a product state (with no entanglement) with a squeezed vacuum in one mode and the vacuum in the other.

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

Article number | 042115 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 92 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2015 Oct 20 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Physical Review A - Atomic, Molecular, and Optical Physics*,

*92*(4), [042115]. https://doi.org/10.1103/PhysRevA.92.042115

**Two-mode bosonic quantum metrology with number fluctuations.** / De Pasquale, Antonella; Facchi, Paolo; Florio, Giuseppe; Giovannetti, Vittorio; Matsuoka, Koji; Yuasa, Kazuya.

Research output: Contribution to journal › Article

*Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 92, no. 4, 042115. https://doi.org/10.1103/PhysRevA.92.042115

}

TY - JOUR

T1 - Two-mode bosonic quantum metrology with number fluctuations

AU - De Pasquale, Antonella

AU - Facchi, Paolo

AU - Florio, Giuseppe

AU - Giovannetti, Vittorio

AU - Matsuoka, Koji

AU - Yuasa, Kazuya

PY - 2015/10/20

Y1 - 2015/10/20

N2 - We search for the optimal quantum pure states of identical bosonic particles for applications in quantum metrology, in particular, in the estimation of a single parameter for the generic two-mode interferometric setup. We consider the general case in which the total number of particles is fluctuating around an average N with variance ΔN2. By recasting the problem in the framework of classical probability, we clarify the maximal accuracy attainable and show that it is always larger than the one reachable with a fixed number of particles (i.e., ΔN=0). In particular, for larger fluctuations, the error in the estimation diminishes proportionally to 1/ΔN, below the Heisenberg-like scaling 1/N. We also clarify the best input state, which is a quasi-NOON state for a generic setup and, for some special cases, a two-mode Schrödinger-cat state with a vacuum component. In addition, we search for the best state within the class of pure Gaussian states with a given average N, which is revealed to be a product state (with no entanglement) with a squeezed vacuum in one mode and the vacuum in the other.

AB - We search for the optimal quantum pure states of identical bosonic particles for applications in quantum metrology, in particular, in the estimation of a single parameter for the generic two-mode interferometric setup. We consider the general case in which the total number of particles is fluctuating around an average N with variance ΔN2. By recasting the problem in the framework of classical probability, we clarify the maximal accuracy attainable and show that it is always larger than the one reachable with a fixed number of particles (i.e., ΔN=0). In particular, for larger fluctuations, the error in the estimation diminishes proportionally to 1/ΔN, below the Heisenberg-like scaling 1/N. We also clarify the best input state, which is a quasi-NOON state for a generic setup and, for some special cases, a two-mode Schrödinger-cat state with a vacuum component. In addition, we search for the best state within the class of pure Gaussian states with a given average N, which is revealed to be a product state (with no entanglement) with a squeezed vacuum in one mode and the vacuum in the other.

UR - http://www.scopus.com/inward/record.url?scp=84946221333&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84946221333&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.92.042115

DO - 10.1103/PhysRevA.92.042115

M3 - Article

AN - SCOPUS:84946221333

VL - 92

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 4

M1 - 042115

ER -