Entanglement-Assisted Multiparameter Estimation with a Solid-State Quantum Sensor

PRX Quantum 7, 020307 (2026) · DOI: 10.1103/kqfr-bbfx · arXiv: 2505.14578

License: CC BY 4.0.

Abstract

Quantum multiparameter estimation promises to extend quantum advantage to the simultaneous high-precision measurements of multiple physical quantities. However, realizing this capability in practical quantum sensors under realistic conditions remains challenging due to intrinsic system imperfections. Here, we experimentally demonstrate multiparameter estimation using a nitrogen-vacancy (NV) center in diamond, a widely adopted solid-state quantum sensor. Leveraging electronic-nuclear spin entanglement and optimized Bell-state measurement at room temperature, we simultaneously estimate the amplitude, detuning, and phase of a microwave drive from a single measurement sequence. Despite practical constraints, our results achieve linear sensitivity scaling for all parameters with respect to interrogation time. This work bridges the gap between foundational quantum estimation theory and real-world quantum sensing, opening pathways toward enhanced multiparameter quantum sensors suitable for diverse scientific and technological applications.

Figures

16 panels with data across 4 figures. Each panel page shows the plot, its columns and its files; each data.csv begins with a header naming the paper, the panel, the source, the license and the provenance route.

Fig. 1

Illustrative figure, no extractable data. Shown in the paper PDF.

Fig. 2

• panel (c): Signals $p_1 = \Pr(\ket{-1,+1})$, $p_2 = \Pr(\ket{-1,0})$ and $p_3 = \Pr(\ket{0,0})$ against rotation-gate pulse duration $T_r$ (ns), without a sensing loop ($N = 0$). Error bars are the standard deviation of the signal. Dashed curves are the model with state preparation and measurement errors; shaded bands are its 95% confidence intervals. data.csv

Fig. 3

• panel (a): Signals $p_1$, $p_2$ and $p_3$ against target amplitude $\Omega_t$ (MHz) for $N = 1$, with error bars (standard deviation of the signal). Dashed curves are the model with state preparation and measurement errors. The black dashed line marks the control value $\Omega_c$; gray dashed lines bound the sweep range of panel (d). The printed connector lines to panel (d) are not drawn. data.csv
• panel (b): Signals $p_1$, $p_2$ and $p_3$ against target detuning $\Delta_t$ (MHz) for $N = 1$, with error bars (standard deviation of the signal). Dashed curves are the model with state preparation and measurement errors. The black dashed line marks the control value $\Delta_c$; gray dashed lines bound the sweep range of panel (e). The printed connector lines to panel (e) are not drawn. data.csv
• panel (c): Signals $p_1$, $p_2$ and $p_3$ against target phase $\Phi_t$ (deg) for $N = 1$, with error bars (standard deviation of the signal). Dashed curves are the model with state preparation and measurement errors. The black dashed line marks the control value $\Phi_c$; gray dashed lines bound the sweep range of panel (f). The printed connector lines to panel (f) are not drawn. data.csv
• panel (d): Signals $p_1$, $p_2$ and $p_3$ against target amplitude $\Omega_t$ (MHz) for $N = 8$, with error bars (standard deviation of the signal). Dashed curves are the model with state preparation and measurement errors. The black dashed line marks the control value $\Omega_c$. data.csv
• panel (e): Signals $p_1$, $p_2$ and $p_3$ against target detuning $\Delta_t$ (MHz) for $N = 8$, with error bars (standard deviation of the signal). Dashed curves are the model with state preparation and measurement errors. The black dashed line marks the control value $\Delta_c$. data.csv
• panel (f): Signals $p_1$, $p_2$ and $p_3$ against target phase $\Phi_t$ (deg) for $N = 8$, with error bars (standard deviation of the signal). Dashed curves are the model with state preparation and measurement errors. The black dashed line marks the control value $\Phi_c$. data.csv

Fig. 4

• panel (a): Minimum measurable amplitude $\delta\Omega_t$ (MHz) against number of repetitions $N$, log-log: experiment (blue open diamonds, error bars are the standard error), simulation (red circles) with its power-law fit (red line), and the ideal-model photon-shot-noise limits for $P=1$ (gray dashed) and $P=0.51$ (gray dotted). data.csv
• panel (b): Minimum measurable detuning $\delta\Delta_t$ (MHz) against number of repetitions $N$, log-log: experiment (blue open diamonds, error bars are the standard error), simulation (red circles) with its power-law fit (red line), and the ideal-model photon-shot-noise limits for $P=1$ (gray dashed) and $P=0.51$ (gray dotted). data.csv
• panel (c): Minimum measurable phase $\delta\Phi_t$ (deg) against number of repetitions $N$, log-log: experiment (blue open diamonds, error bars are the standard error), simulation (red circles) with its power-law fit (red line), and the ideal-model photon-shot-noise limits for $P=1$ (gray dashed) and $P=0.51$ (gray dotted). data.csv

Fig. 5

• panel (a): Simulated sensitivity of the target microwave amplitude, $\eta_{\Omega}$ (kHz$/\sqrt{\mathrm{Hz}}$), against number of sensing repetitions $N$, log-log, for $T_2^e = 10\,\mu$s, with ideal state preparation, readout and $\pi$-pulses. The blue point marks the optimal $N$. data.csv
• panel (b): Simulated sensitivity of the target microwave frequency, $\eta_{\Delta}$ (kHz$/\sqrt{\mathrm{Hz}}$), against number of sensing repetitions $N$, log-log, for $T_2^e = 10\,\mu$s, with ideal state preparation, readout and $\pi$-pulses. The blue point marks the optimal $N$. data.csv
• panel (c): Simulated sensitivity of the target microwave phase, $\eta_{\Phi}$ (mdeg$/\sqrt{\mathrm{Hz}}$), against number of sensing repetitions $N$, log-log, for $T_2^e = 10\,\mu$s, with ideal state preparation, readout and $\pi$-pulses. The blue point marks the optimal $N$. data.csv
• panel (d): Simulated minimum sensitivity of the target microwave amplitude, $\eta_{\Omega}^{\mathrm{min}}$ (kHz$/\sqrt{\mathrm{Hz}}$), against dephasing time $T_2^e$ ($\mu$s), log-log, one point per decade joined by a line. data.csv
• panel (e): Simulated minimum sensitivity of the target microwave frequency, $\eta_{\Delta}^{\mathrm{min}}$ (kHz$/\sqrt{\mathrm{Hz}}$), against dephasing time $T_2^e$ ($\mu$s), log-log, one point per decade joined by a line. data.csv
• panel (f): Simulated minimum sensitivity of the target microwave phase, $\eta_{\Phi}^{\mathrm{min}}$ (mdeg$/\sqrt{\mathrm{Hz}}$), against dephasing time $T_2^e$ ($\mu$s), log-log, one point per decade joined by a line. data.csv

Cite

Takuya Isogawa, Guoqing Wang, Boning Li, Zhiyao Hu, Shunsuke Nishimura, Ayumi Kanamoto, Haidong Yuan, Paola Cappellaro. Entanglement-Assisted Multiparameter Estimation with a Solid-State Quantum Sensor. PRX Quantum 7, 020307 (2026). https://doi.org/10.1103/kqfr-bbfx

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