  Quantum separable operations are defined as those that cannot produce
entanglement from separable states, and it is known that they strictly surpass
local operations and classical communication (LOCC) in a number of tasks, which
is sometimes referred to as "quantum nonlocality without entanglement." Here we
consider a task with such a gap regarding the trade-off between state
discrimination and preservation of entanglement. We show that this task along
with the gap has an analogue in a purely classical setup, indicating that the
quantum properties are not essential in the existence of a nonzero gap between
the separable operations and LOCC.
