论文标题
量子不确定性动态
Quantum Uncertainty Dynamics
论文作者
论文摘要
量子不确定性关系对量子力学的形式主义具有根深蒂固的意义。海森伯格的不确定性关系引起了对其在量子信息科学中的应用的重新兴趣。罗伯逊（Robertson）获得了海森堡（Heisenberg）的不确定性关系的一般形式，该关系是由Hermitian操作员代表的一对任意观察到的。在目前的工作中，我们发现了海森伯格 - 罗伯逊的不确定性关系的时间版本，以在两个不同的时间测量两个可观察到的时间，其中动态不确定性至关重要地取决于观测值的时间演变。不确定性不仅取决于可观察物的选择，而且还取决于测量物理观察物的时间。两次换向器的时间与动态不确定性之间的权衡取舍。我们证明了Spin-1/2系统和量子谐波振荡器的这些不确定性关系的动力学。在本工作中发现的时间不确定性关系可以通过当前的量子技术进行实验验证。
Quantum uncertainty relations have deep-rooted significance on the formalism of quantum mechanics. Heisenberg's uncertainty relations attracted a renewed interest for its applications in quantum information science. Robertson derived a general form of Heisenberg's uncertainty relations for a pair of arbitrary observables represented by Hermitian operators. In the present work, we discover a temporal version of the Heisenberg-Robertson uncertainty relations for the measurement of two observables at two different times, where the dynamical uncertainties crucially depend on the time evolution of the observables. The uncertainties not only depend on the choice of observables, but they also depend on the times at which the physical observables are measured. The time correlated two-time commutator dictates the trade-off between the dynamical uncertainties. We demonstrate the dynamics of these uncertainty relations for a spin-1/2 system and for a quantum harmonic oscillator. The temporal uncertainty relations discovered in this work can be experimentally verified with the present quantum technology.
