有限纠缠辅助下量子信道上的经典承诺
Classical Commitment over Quantum Channels with Limited Entanglement Assistance
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中文总结 AI 辅助
该研究针对有限纠缠辅助的量子信道，推导了非交互式及交互式协议下特定信道的经典承诺容量，明确了交互式通信未提升容量的条件，并确定了量子擦除信道交互式协议的容量。
中文摘要 AI 辅助
我们研究在有限预共享纠缠下量子信道上的经典字符串承诺问题。对于非交互式协议，我们确定了一类输入维度为$d$的信道的承诺容量：该信道每次使用时采样一对经典随机变量$(F,Z)$，将由$Z$索引的$d^2$个海森堡-外尔算子之一作用于输入，并将变换后的量子系统与$F$一同发送给接收者。若$E$为每信道使用的可用纠缠速率（单位为比特），则该类信道的容量为$\text{min}\{H(Z|F),\log_2 d + E\}$。这类信道包含量子擦除信道、去极化信道以及各类泡利信道。此外，对于交互式协议，我们证明承诺速率不能超过每信道使用$\log_2 d + E$比特，因此当$H(Z|F)\geq\log_2 d + E$时，交互式通信不会提升容量。由此，我们确定了交互式协议下量子擦除信道的容量。
英文摘要
We study classical string commitment over quantum channels with limited preshared entanglement. For noninteractive protocols, we determine the commitment capacity of a class of channels with input dimension $d$ that, at each use, sample a pair of classical random variables $(F,Z)$, apply one of the $d^2$ Heisenberg--Weyl operators indexed by $Z$ to the input, and deliver the transformed quantum system together with $F$ to the receiver. If $E$ is the available entanglement rate in bits per channel use, then the capacity is $\min\{H(Z|F),\log_2d+E\}$. This class of channels encompasses quantum erasure and depolarizing channels, as well as families of Pauli channels. Additionally, for interactive protocols, we show that the commitment rate cannot exceed $\log_2d+E$ bits per channel use, so that when $H(Z|F)\geq\log_2d+E$, interactive communication does not increase the capacity. As a consequence, for interactive protocols, we determine the capacity of the quantum erasure channel.
