Two-Mode Bosonic Quantum Metrology with Number Fluctuations

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 $\Delta N^2$. 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., $\Delta N=0$). In particular, for larger fluctuations, the error in the estimation diminishes proportionally to $1/\Delta N$, 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.

13 pages, 4 figures

References in corpus (4)

• Beating the Standard Quantum Limit with Four Entangled Photons
• Generation of Large Number-Path Entanglement Using Linear Optics and Feed-Forward
• Optimal Quantum-Enhanced Interferometry
• Phase sensitivity bounds for two-mode interferometers

Cited by in corpus (15)

• Quantum Fisher information matrix and multiparameter estimation
• Quantum enhanced measurements without entanglement
• Intramode correlations enhanced phase sensitivities in an SU(1,1) interferometer
• Designing quantum experiments with a genetic algorithm
• "Photonic" cat states from strongly interacting matter waves
• Optimal Gaussian Metrology for Generic Multimode Interferometric Circuit
• Phase estimation of phase shifts in two arms for an SU(1,1) interferometer with coherent and squeezed vacuum states
• Heisenberg scaling precision in the estimation of functions of parameters
• Quantum-enhanced metrology with the single-mode coherent states of an optical cavity inside a quantum feedback loop
• Quantum Jump Metrology
• Quantum metrology with a continuous-variable system
• Typicality of Heisenberg scaling precision in multi-mode quantum metrology
• Non-adaptive Heisenberg-limited metrology with multi-channel homodyne measurements
• Gaussian phase sensitivity of boson-sampling-inspired strategies
• Optimal finite-dimensional probe states for quantum phase estimation