Smoothly leaking information over time Say I have a one bit random variable $X \in \{0,1\}$, and let $n$ be a natural number.  I want a sequence of random variables $0 = X_0, X_1, \ldots, X_n = X$ s.t.

$$H\left(X~|~\{X_0,\ldots,X_k\}\right) = 1-\frac{k}{n}$$

That is, each additional $X_k$ provides $1/n$ of the information of $X$, until everything is revealed by $X_n = X$.  Is there a nice construction for this sequence?
Via Michael Kass: let $Y(t)$ be a Wiener process starting at $Y(0) = X$, and define

$$f(t) = H(X~|~Y(t))$$

Then $f(0) = 0$, $f(\infty)=1$, and $f(t)$ is smoothly strictly increasing in between.  Thus, for any $k$ we can find $0 \le t \le \infty$ s.t. $X_k = Y(t)$ has the desired conditional entropy ($t$ will be a decreasing function of $k$).