Bolduc Eliot, Gariepy Genevieve, Leach Jonathan
Institute of Photonics and Quantum Sciences, School of Engineering &Physical Sciences, Heriot-Watt University, David Brewster Building, Edinburgh EH14 4AS, UK.
Nat Commun. 2016 Jan 19;7:10439. doi: 10.1038/ncomms10439.
In quantum mechanics, predictions are made by way of calculating expectation values of observables, which take the form of Hermitian operators. Non-Hermitian operators, however, are not necessarily devoid of physical significance, and they can play a crucial role in the characterization of quantum states. Here we show that the expectation values of a particular set of non-Hermitian matrices, which we call column operators, directly yield the complex coefficients of a quantum state vector. We provide a definition of the state vector in terms of measurable quantities by decomposing these column operators into observables. The technique we propose renders very-large-scale quantum states significantly more accessible in the laboratory, as we demonstrate by experimentally characterizing a 100,000-dimensional entangled state. This represents an improvement of two orders of magnitude with respect to previous phase-and-amplitude characterizations of discrete entangled states.
在量子力学中，预测是通过计算可观测量的期望值来进行的，这些可观测量采用厄米算符的形式。然而，非厄米算符并非一定没有物理意义，它们在量子态的表征中可以发挥关键作用。在此我们表明，一组特定的非厄米矩阵（我们称之为列算符）的期望值直接给出量子态矢量的复系数。通过将这些列算符分解为可观测量，我们根据可测量量给出了态矢量的定义。正如我们通过对一个10万维纠缠态进行实验表征所证明的那样，我们提出的技术使得在实验室中能够更显著地获取超大规模量子态。这相对于之前对离散纠缠态的相位和幅度表征有了两个数量级的提升。
