The ideal realization of quantum teleportation relies on having access to a maximally entangled state; however, in practice, such an ideal state is typically not available and one can instead only realize an approximate teleportation. With this in mind, we present a method to quantify the performance of approximate teleportation when using an arbitrary resource state. More specifically, after framing the task of approximate teleportation as an optimization of a simulation error over one-way local operations and classical communication (LOCC) channels, we establish a semi-definite relaxation of this optimization task by instead optimizing over the larger set of two-PPT-extendible channels. The main analytical calculations in our paper consist of exploiting the unitary covariance symmetry of the identity channel to establish a significant reduction of the computational cost of this latter optimization. Next, by exploiting known connections between approximate teleportation and quantum error correction, we also apply these concepts to establish bounds on the performance of approximate quantum error correction over a given quantum channel. Finally, we evaluate our bounds for various examples of resource states and channels.
翻译:量子传送的理想实现取决于能否获得一个最深层的混合状态;然而,在实践中,这种理想状态通常是不存在的,人们只能实现大致的传送。考虑到这一点,我们提出了一个方法来量化使用任意资源状态时近似传送的性能。更具体地说,在将近似传送任务作为单向本地操作和传统通信(LOCC)渠道模拟错误的最佳利用之后,我们为这一优化任务建立了半无限期的松绑,办法是优化两个PPPT可扩展的更大频道。我们文件中的主要分析计算包括利用身份渠道的统一共变对称,以大幅度降低这一后一种优化的计算成本。此外,通过利用已知的近似传送和量子错误更正之间的联系,我们还运用这些概念来确定对某一量子频道的近似量差校正效果的界限。最后,我们评估了资源状态和渠道的各种例子的界限。