  This paper establishes single-letter formulas for the exact entanglement cost
of simulating quantum channels under free quantum operations that completely
preserve positivity of the partial transpose (PPT). First, we introduce the
$\kappa$-entanglement measure for point-to-point quantum channels, based on the
idea of the $\kappa$-entanglement of bipartite states, and we establish several
fundamental properties for it, including amortization collapse, monotonicity
under PPT superchannels, additivity, normalization, faithfulness, and
non-convexity. Second, we introduce and solve the exact entanglement cost for
simulating quantum channels in both the parallel and sequential settings, along
with the assistance of free PPT-preserving operations. In particular, we
establish that the entanglement cost in both cases is given by the same
single-letter formula, the $\kappa$-entanglement measure of a quantum channel.
We further show that this cost is equal to the largest $\kappa$-entanglement
that can be shared or generated by the sender and receiver of the channel. This
formula is calculable by a semidefinite program, thus allowing for an
efficiently computable solution for general quantum channels. Noting that the
sequential regime is more powerful than the parallel regime, another notable
implication of our result is that both regimes have the same power for exact
quantum channel simulation, when PPT superchannels are free. For several basic
Gaussian quantum channels, we show that the exact entanglement cost is given by
the Holevo--Werner formula [Holevo and Werner, Phys. Rev. A 63, 032312 (2001)],
giving an operational meaning of the Holevo-Werner quantity for these channels.
