  We consider distillation of secret bits from partially secret noisy
correlations P_ABE, shared between two honest parties and an eavesdropper. The
most studied distillation scenario consists of joint operations on a large
number of copies of the distribution (P_ABE)^N, assisted with public
communication. Here we consider distillation with only one copy of the
distribution, and instead of rates, the 'quality' of the distilled secret bits
is optimized, where the 'quality' is quantified by the secret-bit fraction of
the result. The secret-bit fraction of a binary distribution is the proportion
which constitutes a secret bit between Alice and Bob. With local operations and
public communication the maximal extractable secret-bit fraction from a
distribution P_ABE is found, and is denoted by Lambda[P_ABE]. This quantity is
shown to be nonincreasing under local operations and public communication, and
nondecreasing under eavesdropper's local operations: it is a secrecy monotone.
It is shown that if Lambda[P_ABE]>1/2 then P_ABE is distillable, thus providing
a sufficient condition for distillability. A simple expression for
Lambda[P_ABE] is found when the eavesdropper is decoupled, and when the honest
parties' information is binary and the local operations are reversible.
Intriguingly, for general distributions the (optimal) operation requires local
degradation of the data.
