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Entanglement advantage in sensing power-law spatiotemporal noise correlations

Yu-Xin Wang, Anthony J. Brady, Federico Belliardo, Alexey V. Gorshkov

Abstract

Noise sensing underlies many physical applications including tests of non-classicality, thermometry, verification of correlated phases of quantum matter, and characterization of criticality. While previous works have shown that quantum resources such as entanglement and squeezing can enhance the sensitivity in estimating deterministic signals, less is known about the entanglement advantage in sensing correlated stochastic signals (noise). In this work, we compute the fundamental sensitivity limits of quantum sensors in probing spatiotemporally correlated noise. We first prove the fundamental quantum limits in sensing spatially correlated Markovian noise using entangled and unentangled sensors, respectively. Focusing on power-law spatial noise correlations, which naturally arise in condensed matter systems with long-range interactions and/or near criticality, we further derive a scalable entanglement advantage when the power-law decays slowly. Then, considering a target signal with a $1/f^{p}$-type spectrum, we demonstrate that non-Markovianity may entirely modify the nature of entanglement advantage in estimating spatial noise correlations. Our protocols can be implemented using state-of-the-art quantum sensing platforms including solid-state defects, superconducting circuits, and neutral atoms.

Entanglement advantage in sensing power-law spatiotemporal noise correlations

Abstract

Noise sensing underlies many physical applications including tests of non-classicality, thermometry, verification of correlated phases of quantum matter, and characterization of criticality. While previous works have shown that quantum resources such as entanglement and squeezing can enhance the sensitivity in estimating deterministic signals, less is known about the entanglement advantage in sensing correlated stochastic signals (noise). In this work, we compute the fundamental sensitivity limits of quantum sensors in probing spatiotemporally correlated noise. We first prove the fundamental quantum limits in sensing spatially correlated Markovian noise using entangled and unentangled sensors, respectively. Focusing on power-law spatial noise correlations, which naturally arise in condensed matter systems with long-range interactions and/or near criticality, we further derive a scalable entanglement advantage when the power-law decays slowly. Then, considering a target signal with a -type spectrum, we demonstrate that non-Markovianity may entirely modify the nature of entanglement advantage in estimating spatial noise correlations. Our protocols can be implemented using state-of-the-art quantum sensing platforms including solid-state defects, superconducting circuits, and neutral atoms.
Paper Structure (7 sections, 4 theorems, 96 equations, 2 figures)

This paper contains 7 sections, 4 theorems, 96 equations, 2 figures.

Table of Contents

  1. Equivalence between quantum sensor dynamics generated by a pure-dephasing Markovian quantum environment and dynamics due to classical white noise
  2. Optimality of fast-reset protocols in estimating pure-dephasing noise
  3. Extension of the upper bounds on the time-averaged QFI for noise estimation to function estimation
  4. Entanglement advantage in estimating Markovian noise with a power-law spatial noise correlation
  5. Entanglement advantage in estimating non-Markovian noise with power-law spatial and temporal noise correlations
  6. Optimal sensitivity of a single-qubit sensor for estimating non-Markovian noise with a power-law spectrum
  7. Entanglement advantage in estimating non-Markovian noise with power-law spatiotemporal correlations

Key Result

Theorem 1

(Optimality of fast-reset for entangled sensors) Given access to a dephasing Lindbladian $\mathcal{L} _{\xi}$ acting on $N$ quantum sensors for total time $T _{\mathrm{tot}}$ and arbitrary sensor initial state, control, entanglement with ancillae, and readout, the minimal MSE of an unbiased estimato

Figures (2)

  • Figure 1: Schematic illustrating $N$ quantum sensors of correlated noise, equally distributed in a $1$-dimensional lattice. We are interested in estimating the overall strength of power-law noise fluctuations in space and/or time domain. To understand the existence and nature of entanglement advantage in this task, we compare the performance of entangled sensors [initialized in e.g., a GHZ-type state $\ket{\Psi_{\text{GHZ}}}$ in Eq. \ref{['eq:ghz.def']}] versus that of unentangled sensors initialized in $\otimes _{j=1}^{N} \ket{\psi _{j}}$.
  • Figure S1: Plot of function $g(y) = {y ^{\frac{1+2p}{1+p}}} / (e ^{2y} -1)$ [Eq. \ref{['seq:qfiovert.rescale']}] versus $y$ for $p=1/10$, $1/2$, $1$, and $2$. As shown in the plot, the function reaches its maximum at a finite $y _{0} \in (0,1)$.

Theorems & Definitions (4)

  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Theorem 4