In the field of quantum sensing, quantum resources occupy a core position. Besides the two well-known quantum resources—the number N of quantum entangled probes and the coherent evolution time $T$—the spin quantum number $S$ has also been confirmed as another key quantum resource. This paper focuses on high-spin quantum systems in a general Gaussian noise environment under the assumption that the noise factor in the exponential part of the modulus of the off-diagonal elements of the system's density matrix is $\chi \left(\tau \right)=\alpha {\tau }^{\beta }$ (where $\alpha >0$ and incorporates relevant noise parameters, and $\beta$ is a positive number whose specific value is determined by the detailed characteristics of the noise) and systematically investigates the estimation problem of the noise parameter $\xi$ using the spin quantum number $S$ as the quantum resource. Surprisingly, as $\beta$ increases gradually, the scaling behaviors of the estimation errors of parameters $\omega$ and $\xi$ with respect to $S$ show distinctly opposite trends. Specifically, the estimation precision of parameter $\omega$ satisfies $\delta \omega \propto 1/S^{1-1/\beta }$, while the estimation precision of parameter $\xi$ follows $\delta \xi \propto 1/S^{1/\beta }$. Furthermore, regardless of the value of $\beta$, the estimation precisions of parameters $\omega$ and $\xi$ always exhibit a complementary relationship, i.e., $\delta \omega \delta \xi \propto 1/S$. Subsequently, taking Ornstein-Uhlenbeck noise as a specific example, we further estimate the noise parameters $b$ (noise amplitude), ${\tau }_c$ (noise memory time), and parameter $\omega$; the final conclusions are completely consistent with the estimation conclusions of $\xi$ and $\omega$ in the general Gaussian noise environment.

Close

PrevNext

View figure in article

• Quantum computation
• Quantum sensing