论文标题
量子状态的共同随机性和纠缠的多用户蒸馏
Multi-User Distillation of Common Randomness and Entanglement from Quantum States
论文作者
论文摘要
我们为将嘈杂的多部分量子相关性转换为使用本地操作和经典通信（LOCC）的任务的任务构建新协议。对于前者，称为常见的随机性（CR）蒸馏，获得了“可蒸馏的共同随机性”上的两个新的下限，这是量子状态下总真实（经典）相关性的操作度量。我们的证明依赖于《全知的沟通》（CO）[CSISZAR和NARAYAN，IEEE TRANS。 inf。理论50：3047-3061，2004]。我们在这里做出的贡献是一种新型的同时解码器，用于通过在解码器上的量子侧信息随机框架来压缩相关的经典源。对于后者，我们在Greenberger-Horne-Horne-Zeilinger（GHz）状态的速率上得出了两个新的下限，可以从LOCC下的任何给定的纯状态渐近地提炼。我们的方法在于“使拟议的CR蒸馏方案”和资源回收（Devetak等。 IEEE Trans。 inf。理论54（10）：4587-4618，2008]。第一个下限与Vrana和Christandl [IEEE Trans的最新结果相同。 inf。理论65（9）：5945-5958，2019]，基于合并方法以达到相同的速率。我们的第二个下限概括并在此结果上改善，并在GHz蒸馏中统一了许多其他已知的下限。
We construct new protocols for the tasks of converting noisy multipartite quantum correlations into noiseless classical and quantum ones using local operations and classical communications (LOCC). For the former, known as common randomness (CR) distillation, two new lower bounds on the "distillable common randomness", an operational measure of the total genuine (classical) correlations in a quantum state, are obtained. Our proof relies on a generalization of communication for omniscience (CO) [Csiszar and Narayan, IEEE Trans. Inf. Theory 50:3047-3061, 2004]. Our contribution here is a novel simultaneous decoder for the compression of correlated classical sources by random binning with quantum side information at the decoder. For the latter, we derive two new lower bounds on the rate at which Greenberger-Horne-Zeilinger (GHZ) states can be asymptotically distilled from any given pure state under LOCC. Our approach consists in "making coherent" the proposed CR distillation protocols and recycling of resources [Devetak et al. IEEE Trans. Inf. Theory 54(10):4587-4618, 2008]. The first lower bound is identical to a recent result by Vrana and Christandl [IEEE Trans. Inf. Theory 65(9):5945-5958, 2019], which is based on a combinatorial method to achieve the same rate. Our second lower bound generalises and improves upon this result, and unifies a number of other known lower bounds on GHZ distillation.
