论文标题
支持量子状态的不确定性关系
Uncertainty relations for the support of quantum states
论文作者
论文摘要
鉴于在实际线路上有狭窄的信号，因此其傅立叶变换的定位限制了。在素数的空间中，道得出了一个与状态无关的不确定性关系，该关系与离散傅立叶变换相关的两个基础上的纯qudit状态的支撑大小。我们将陶的不确定性关系推广到主要维度空间中的完整无偏基碱基集。我们获得的界限似乎仅适用于三个尺寸。最高十九个质子维度的分析和数值结果表明，结合通常不能饱和。对于主要的尺寸，我们在$（d+1）$互公正基础的支撑大小上构建了尖锐的界限，并确定一些实现它们的州。
Given a narrow signal over the real line, there is a limit to the localisation of its Fourier transform. In spaces of prime dimensions, Tao derived a sharp state-independent uncertainty relation which holds for the support sizes of a pure qudit state in two bases related by a discrete Fourier transform. We generalise Tao's uncertainty relation to complete sets of mutually unbiased bases in spaces of prime dimensions. The bound we obtain appears to be sharp for dimension three only. Analytic and numerical results for prime dimensions up to nineteen suggest that the bound cannot be saturated in general. For prime dimensions two to seven we construct sharp bounds on the support sizes in $(d+1)$ mutually unbiased bases and identify some of the states achieving them.
