论文标题
Haar随机状态的法力
Mana in Haar-random states
论文作者
论文摘要
法力是衡量创建状态所需的非克利福德资源的量度；在$ \ ell $ qudits上以$ \ le \ frac 1 2（\ ell \ ln d -s_2）$限制的混合状态的法力； $ s_2 $该州的第二个Renyi熵。我们计算了Haar-random纯净和混合状态的法术力，发现法力在希尔伯特空间维度上几乎是对数的：也就是说，在Qudit维度中的Qudits和对数数量广泛。尤其是，最大熵的状态平均法力远低于$ \lnπ/2 $。然后，我们将此结果连接到最近在近克利福德大约$ t $ designs上的工作；在此过程中，我们指出的是，法力是对非克利福德资源的有用度量，正是因为它不是可区分的。
Mana is a measure of the amount of non-Clifford resources required to create a state; the mana of a mixed state on $\ell$ qudits bounded by $\le \frac 1 2 (\ell \ln d - S_2)$; $S_2$ the state's second Renyi entropy. We compute the mana of Haar-random pure and mixed states and find that the mana is nearly logarithmic in Hilbert space dimension: that is, extensive in number of qudits and logarithmic in qudit dimension. In particular, the average mana of states with less-than-maximal entropy falls short of that maximum by $\ln π/2$. We then connect this result to recent work on near-Clifford approximate $t$-designs; in doing so we point out that mana is a useful measure of non-Clifford resources precisely because it is not differentiable.
