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→Relation to estimator error
当且仅当X和Y是独立的时，<math>h(X|Y) \le h(X)</math>才相等。
当且仅当X和Y是独立的时，<math>h(X|Y) \le h(X)</math>才相等。
===Relation to estimator error===
=== Relation to estimator error 与预估误差的关系 ===
The conditional differential entropy yields a lower bound on the expected squared error of an [[estimator]]. For any random variable <math>X</math>, observation <math>Y</math> and estimator <math>\widehat{X}</math> the following holds:<ref name=cover1991 />{{rp|255}}
The conditional differential entropy yields a lower bound on the expected squared error of an [[estimator]]. For any random variable <math>X</math>, observation <math>Y</math> and estimator <math>\widehat{X}</math> the following holds:<ref name=cover1991 />{{rp|255}}
条件微分熵在估计量的期望平方误差上有一个下限。对于任何随机变量<math>X</math>，观察值<math>Y</math>和估计量<math>\widehat{X}</math>，以下条件成立：
:<math display="block">\mathbb{E}\left[\bigl(X - \widehat{X}{(Y)}\bigr)^2\right]
:<math display="block">\mathbb{E}\left[\bigl(X - \widehat{X}{(Y)}\bigr)^2\right]
\ge \frac{1}{2\pi e}e^{2h(X|Y)}</math>
\ge \frac{1}{2\pi e}e^{2h(X|Y)}</math>
This is related to the [[uncertainty principle]] from [[quantum mechanics]].
This is related to the [[uncertainty principle]] from [[quantum mechanics]].
这与来自量子力学的不确定性原理有关。
==Generalization to quantum theory==
==Generalization to quantum theory==