Uncertainty Relations for Approximation and Estimation

量子参数估计不确定性关系

Quantum Parameter Estimation Uncertainty Relation

本文针对量子多参数估计问题，推导了双参数情形下由测量不相容性和参数相关性共同限制估计精度的紧致不确定性关系，并开发误差椭圆方法直观展示其应用，揭示了参数空间几何视角的威力。

Uncertainty Relation Revisited from Quantum Estimation Theory

By invoking quantum estimation theory we formulate bounds of errors in quantum measurement for arbitrary quantum states and observables in a finite-dimensional Hilbert space. We prove that the measurement errors of two observables satisfy Heisenberg's uncertainty relation, find the attainable bound, and provide a strategy to achieve it.

Uncertainty and Trade-offs in Quantum Multiparameter Estimation

Uncertainty relations in quantum mechanics express bounds on our ability to simultaneously obtain knowledge about expectation values of non-commuting observables of a quantum system. They quantify trade-offs in accuracy between complementary pieces of information about the system. In Quantum multiparameter estimation, such trade-offs occur for the precision achievable for different parameters characterizing a density matrix: an uncertainty relation emerges between the achievable variances of the different estimators. This is in contrast to classical multiparameter estimation, where simultaneou…

Nonlinear Schrödinger equations and generalized Heisenberg uncertainty principle violating the principle of estimation independence

One of the advantages of a reconstruction of quantum mechanics based on transparent physical axioms is that it may offer insight to naturally generalize quantum mechanics by relaxing the axioms. Here, we discuss possible extensions of quantum mechanics within a general epistemic framework based on an operational scheme of estimation of momentum given positions under epistemic restriction. The epistemic restriction is parameterized by a global-nonseparable random variable on the order of Planck constant, an ontic extension to the separable classical phase space variables. Within the estimation …

Incorporating Heisenberg's Uncertainty Principle into Quantum Multiparameter Estimation

The quantum multiparameter estimation is very different from the classical multiparameter estimation due to Heisenberg's uncertainty principle in quantum mechanics. When the optimal measurements for different parameters are incompatible, they cannot be jointly performed. We find a correspondence relationship between the inaccuracy of a measurement for estimating the unknown parameter with the measurement error in the context of measurement uncertainty relations. Taking this correspondence relationship as a bridge, we incorporate Heisenberg's uncertainty principle into quantum multiparameter es…

利用神经网络集合进行量子参数估计及不确定性量化

Quantum parameter estimation with uncertainty quantification from continuous measurement data using neural network ensembles

本文提出利用深度神经网络集合进行量子参数估计，同时实现不确定性量化，具有更快的推理速度和更好的不确定性校准能力。