Non-negative Wigner functions in prime dimensions
Non-negative Wigner functions in prime dimensions
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DOI：
10.1007/s00340-006-2510-9
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发表时间：
2007-02-01
影响因子：
2.1
通讯作者：
Gross, D.
中科院分区：
文献类型：
--
作者：
Gross, D.
根据Hudson的经典结果，当且仅当态为高斯态时，纯连续变量量子态的Wigner函数是非负的。我们已经证明了有限维量子系统的一个类似陈述。在这种情况下，稳定态承担了高斯态的作用。一般结果已发表在b[1]上。对于奇素数系统，可以采用一种不同的、大大简化的证明方法，它仍然显示了主要思想。本文对这些方法作了一个完整的说明。
According to a classical result due to Hudson, the Wigner function of a pure, continuous-variable quantum state is non-negative if and only if the state is Gaussian. We have proven an analogous statement for finite-dimensional quantum systems. In this context, the role of Gaussian states is taken on by stabilizer states. The general results have been published in [1]. For the case of systems of odd prime dimension, a different, greatly simplified method of proof can be employed which still exhibits the main ideas. The present paper gives a self-contained account of these methods.