Correlated Noise Estimation with Quantum Sensor Networks

Abstract

We address the metrological problem of estimating collective stochastic properties imprinted on a network of quantum sensors. Canonical examples include center-of-mass quadrature fluctuations in a system of bosonic modes and correlated dephasing in an ensemble of qubits (e.g., spins), bosons, or fermions. We develop a theoretical framework to determine the limits of correlated (weak) noise estimation with quantum sensor networks and reveal the requirements for entanglement advantage. Notably, an advantage emerges from the synergistic interplay between quantum correlations of the sensors and ``classical'' correlations of the noises. We determine optimal entangled probe states and identify a sensing protocol -- reminiscent of a many-body echo -- that achieves the fundamental limits of measurement sensitivity for a broad class of problems, unveiling a route towards entanglement-enhanced metrology of correlated many-body phenomena.

Figures (2)

• Figure 1: Entangled sensors probe an extended reservoir. Quantum correlations of the quantum sensor network (viz., $\bm{\mathcal{H}}$) and "classical" correlations of the reservoir (viz., $\bm V$) collude to enable an entanglement advantage (quantified by the QFI matrix $\bm{\mathcal{F}}_{\mathcal{Q}}$) in estimating aggregate parameters $\Theta=\{\vartheta_I\}$ of the reservoir.
• Figure 2: QSN Echo Protocol. Generate entangled probe, $\ket{\psi}$, by acting with many-body unitary, $\hat{U}$, on local states, $\{\ket{\psi_i}\}$. Quantum channel $\Phi_{\bm V}$ encodes parameter $g$ into probe. Revert the many-body unitary via $\hat{U}^\dagger$. Perform local projective measurements, $\pi_i=\dyad{\psi_i}$, and estimate $g$ from the measurement statistics.

Theorems & Definitions (14)

• Corollary
• Claim
• Lemma 1
• proof
• Lemma 2
• proof
• proof
• Proposition 1
• proof
• Corollary