Maccone Lorenzo, Pati Arun K
Dipartimento Fisica and INFN Sez. Pavia, University of Pavia, via Bassi 6, I-27100 Pavia, Italy.
Quantum Information and Computation Group, Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India and Department of mathematics, Zhejiang University, Hangzhou 310027, People's Republic of China.
Phys Rev Lett. 2014 Dec 31;113(26):260401. doi: 10.1103/PhysRevLett.113.260401.
The Heisenberg-Robertson uncertainty relation expresses a limitation in the possible preparations of the system by giving a lower bound to the product of the variances of two observables in terms of their commutator. Notably, it does not capture the concept of incompatible observables because it can be trivial; i.e., the lower bound can be null even for two noncompatible observables. Here we give two stronger uncertainty relations, relating to the sum of variances, whose lower bound is guaranteed to be nontrivial whenever the two observables are incompatible on the state of the system.
海森堡 - 罗伯逊不确定性关系通过给出两个可观测量方差乘积的下限（以它们的对易子表示）来表达系统可能制备过程中的一种限制。值得注意的是，它没有捕捉到不相容可观测量的概念，因为它可能是平凡的；也就是说，即使对于两个不相容的可观测量，下限也可能为零。在此，我们给出两个更强的不确定性关系，与方差之和相关，只要两个可观测量在系统状态上不相容，其下限就保证是非平凡的。
