= Solution
A <one-time pad> over the <finite additive group> $\mathbb Z_n$ uses a key $K$ that is <uniform distribution>[uniform] on $\mathbb Z_n$, <independent random variables>[independent] of the plaintext $X$, as long as the plaintext, and never reused. Encryption and decryption are
$$
C=X+K\pmod n,
\qquad
X=C-K\pmod n.
$$
For <independent random variables> $X,Y$, <conditioning reduces entropy> and translation by a known element of the <finite additive group> preserves entropy, so
$$
H(X+Y)\geq H(X+Y\mid Y)=H(X\mid Y)=H(X).
$$
Interchanging $X$ and $Y$ gives $H(X+Y)\geq H(Y)$, hence
$$
\boxed{H(X+Y)\geq\max\{H(X),H(Y)\}}.
$$
This is the <entropy of a sum of independent finite-group variables>.
The result explains why adding <independent random variables>[independent pad symbols] cannot reduce uncertainty. For a <uniform distribution>[uniform] pad, $X+K$ is itself uniform and is <independent random variables>[independent] of $X$, which is the <perfect secrecy>[perfect-secrecy property]. Independence is necessary: if $X$ is nonconstant and $Y=-X\pmod n$, then $X+Y=0$ is constant, so
$$
\boxed{H(X+Y)=0<H(X)=H(Y).}
$$
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