AI 中文总结
该研究提出稠密编码交换任务，推导三量子比特纯态支持该任务的充要条件，确定最优两量子比特幺正算子，证明其抗噪性及所需真正多体纠缠量随系统规模增大而降低。
AI 中文摘要
我们引入了一种新型的多体纠缠辅助经典通信任务，称为稠密编码交换（dense coding swapping），其中合法各方通过合适的联合幺正操作，协同将一个通信信道的稠密编码能力交换至另一个信道。由于稠密编码（DC）排他原理，该方案可提升目标对的稠密编码能力，同时降低网络中非目标分支的稠密编码能力。这种交换能力具有更广泛的意义，可视为一种过程交换，区别于资源交换，还能在某一接收方受损时提供预防措施。我们推导了三量子比特纯态支持DC交换的充要条件，该条件以施密特系数表示；同时利用混合态的布洛赫关联参数，得到了混合态的充分判据。此外，我们确定了能实现通信信道间稠密编码能力交换的最优两量子比特幺正算子。我们还研究了这些合格态对色噪声和白噪声的容忍度，证明了所提任务在环境扰动下的鲁棒性。我们进一步表明，支持DC交换的多体态仅需少量 genuine multipartite entanglement（真正多体纠缠），且该需求随系统规模增大而降低。
英文摘要
We introduce a novel multipartite entanglement-assisted classical communication task, referred to as dense coding swapping, in which legitimate parties collaboratively swap the dense codeability from one communication channel to another through suitable joint unitary operations. Due to the dense coding (DC) exclusion principle, the scheme enhances the dense codeability of a target pair while simultaneously reducing it for a non-target branch in the network. This swapping capability has broader implications, as it may be viewed as a form of process swapping, distinct from resource swapping, while also providing a prevention measure when one of the receivers is compromised. We derive necessary and sufficient conditions, expressed in terms of the Schmidt coefficients, for three-qubit pure states to support DC swapping, while we obtain a sufficient criterion for mixed states using their Bloch correlation parameters. Furthermore, we identify the optimal two-qubit unitary operators capable of realizing the swapping of dense codeability between communication channels. We further examine the tolerance of these eligible states against both colored and white noise, demonstrating the resilience of the proposed task under environmental perturbations. We also show that multipartite states supporting DC swapping require only a small amount of genuine multipartite entanglement and that this requirement decreases with increasing system size.
Comments17 pages, 8 figures
