Direct measurement of large-scale quantum states via expectation values of non-Hermitian matrices.
Direct measurement of large-scale quantum states via expectation values of non-Hermitian matrices.
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DOI：
10.1038/ncomms10439
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发表时间：
2016-01-19
影响因子：
16.6
通讯作者：
Leach J
中科院分区：
文献类型：
--
作者：
Bolduc E;Gariepy G;Leach J
在量子力学中，预测是通过计算可见的期望值的方式进行的，这些期望值采用厄米算符的形式。然而，非厄米算符并不一定没有物理意义，它们可以在量子态的表征中发挥关键作用。在这里，我们证明了一组特定的非厄米矩阵的期望值，我们称之为列运算符，直接产生量子态向量的复系数。我们通过将这些列运算符分解成可观测的量，给出了状态向量的定义。我们提出的技术使超大规模量子态在实验室中更容易获得，正如我们通过实验表征100,000维纠缠态所展示的那样。这比之前离散纠缠态的相位和幅度特性提高了两个数量级。量子状态层析成像是检索定义量子系统的值的过程，但通过实验实现它可能是繁重的。在这里，作者提供了另一种方法，通过一组非厄米特矩阵的期望值，刻画了100,000维状态。
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. Quantum state tomography is the process of retrieving the values that define a quantum system, but realizing it experimentally can be burdensome. Here, the authors provide an alternative approach via the expectation values of a set of non-Hermitian matrices, and characterize a 100,000-dimensional state.