论文标题
误差指数和量子软覆盖的较强的匡威
Error Exponent and Strong Converse for Quantum Soft Covering
论文作者
论文摘要
我们如何使用具有一定尺寸的随机代码簿近似量子通道输出状态？在这项工作中，我们研究了量子软覆盖问题。也就是说，我们使用一个随机代码簿，该代码簿与从先前的分布中独立采样并通过经典量词通道发送的代码书来近似目标状态。当使用从独立且相同分布的先验中采样的随机代码簿，其速率高于量子互信息时，我们表明，代码书诱导的状态与目标状态衰减之间的预期痕量距离与夹层rényi信息给出的指数。另一方面，当代码书大小的速率低于量子相互信息时，痕量距离会呈指数速度。当使用随机常数构图代码本时，我们获得了类似的结果，而夹杂的奥古斯丁信息表示错误指数。除了上述大偏差分析外，我们的结果还在中等偏差方面。也就是说，我们表明，即使代码簿尺寸的速率接近量子相互信息，痕量距离仍然渐近地消失。
How well can we approximate a quantum channel output state using a random codebook with a certain size? In this work, we study the quantum soft covering problem. Namely, we use a random codebook with codewords independently sampled from a prior distribution and send it through a classical-quantum channel to approximate the target state. When using a random codebook sampled from an independent and identically distributed prior with a rate above the quantum mutual information, we show that the expected trace distance between the codebook-induced state and the target state decays with exponent given by the sandwiched Rényi information. On the other hand, when the rate of the codebook size is below the quantum mutual information, the trace distance converges to one exponentially fast. We obtain similar results when using a random constant composition codebook, whereas the sandwiched Augustin information expresses the error exponent. In addition to the above large deviation analysis, our results also hold in the moderate deviation regime. That is, we show that even when the rate of the codebook size approaches the quantum mutual information moderately quickly, the trace distance still vanishes asymptotically.
