Two-mode bosonic quantum metrology with number fluctuations

Antonella De Pasquale*, Paolo Facchi, Giuseppe Florio, Vittorio Giovannetti, Koji Matsuoka, Kazuya Yuasa

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


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 languageEnglish
Article number042115
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number4
Publication statusPublished - 2015 Oct 20

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics


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