论文标题
将海森堡的不确定性原理纳入量子多参数估计
Incorporating Heisenberg's Uncertainty Principle into Quantum Multiparameter Estimation
论文作者
论文摘要
由于海森伯格在量子力学中的不确定性原理，量子多参数估计与经典多参数估计非常不同。当不同参数的最佳测量不兼容时，无法共同执行它们。我们发现在测量不确定性关系的情况下，测量值的测量误差估算未知参数的不准确性之间的对应关系。以这种对应关系为桥梁，我们将海森堡的不确定性原理纳入量子多参数估计中，通过给出估计不同参数的测量不准确性之间的权衡关系。对于纯量子状态，这种权衡关系很紧，因此在这种情况下，它可以揭示个人估计错误的真实量子限制。我们采用我们的方法来得出在估计相干状态中编码的复杂信号的真实和虚构部分的可达到的错误之间的权衡，并获得了达到权衡关系的联合测量。我们还表明，我们的方法很容易被用来得出共同估计相移和相扩散的误差，而无需明确的参数化量子测量。
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 estimation by giving a tradeoff relation between the measurement inaccuracies for estimating different parameters. For pure quantum states, this tradeoff relation is tight, so it can reveal the true quantum limits on individual estimation errors in such cases. We apply our approach to derive the tradeoff between attainable errors of estimating the real and imaginary parts of a complex signal encoded in coherent states and obtain the joint measurements attaining the tradeoff relation. We also show that our approach can be readily used to derive the tradeoff between the errors of jointly estimating the phase shift and phase diffusion without explicitly parameterizing quantum measurements.
