Three distributed parties, two transmitters (Txs) and a receiver (Rx), hold one component each of a tripartite quantum state \(ρ^{A_1A_2C}\). The goal is to simulate the action of a separable instrument acting on the \(A_1\) and \(A_2\) components, with the Rx recovering the classical outcome. To enable this, each Tx \(k\) can transfer bits on a noiseless bit pipe and share randomness at rates \(R_k\) and \(C_k\), respectively, with the Rx. Undertaking a Shannon-theoretic study, we characterize two new sets of inner bounds. The first set, derived for the one-shot regime, is based on instrument simulation protocols built using unstructured IID codes, while the second set, derived for the asymptotic regime, relies on coset codes and new decoding POVMs. The first set of bounds recovers current known inner bounds for instrument and measurement simulation in all previously studied scenarios. Our protocols are based on likelihood POVMs, and our analysis leverages Sen's smooth multiparty covering and simultaneous decoding, while handling the distributed-component scenario via a compatible operator sliding trick.

翻译：三个分布式参与方——两个发射端（Txs）和一个接收端（Rx）——各自持有三方量子态 \(ρ^{A_1A_2C}\) 的一个分量。目标是模拟作用于 \(A_1\) 和 \(A_2\) 分量的可分离仪器的行为，并由 Rx 恢复经典结果。为实现此目标，每个发射端 k 可通过无噪声比特管道传输比特，并与 Rx 分别以速率 \(R_k\) 和 \(C_k\) 共享随机性。通过香农理论分析，我们刻画了两组新的内界。第一组内界针对一次性场景推导，基于使用非结构化IID编码的仪器模拟协议；第二组内界针对渐近场景推导，依赖于陪集编码和新的解码POVM。第一组内界在先前研究的所有场景中恢复了当前已知的仪器与测量模拟内界。我们的协议基于似然POVM，分析利用了Sen的光滑多方覆盖与同时解码，并通过兼容算子滑动技巧处理分布式分量场景。