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.

翻译：本文为在自由量子操作下模拟量子频道,完全保存部分转换( PPT) 的假设性( PPT) 的精确纠缠成本建立了单字母公式。 首先, 我们引入了用于点到点量频道的 $kappa 的纠缠度量 。 基于两边国家 $kappa 纠缠的理念, 我们为此设定了几种基本属性, 包括摊销崩溃、 PPPT超级通道下的单调 、 迭代性、 正常化、 忠诚和不调和 。 其次, 我们引入并解决了在平行和相继环境中模拟量子频道( PPPPT) 的精确折叠记成本, 以及自由量频道( PPPT) 的直压值 。 我们提供的量级机制的最大 $\ kappappa- 折叠度成本是最大的, 由可共享的或生成的 直流流流流流流和直流的直流的直流数据显示一个直流的直流数据。, 这个直流的直流流的直流的直流的直流的直流的直流的直径数据是另一个直流的直流的直径流的直方的直方的直方的直方的直方的直方。