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：理想量子隐形传态的实现依赖于获取最大纠缠态，然而在实践中，这种理想态通常不可获得，而只能实现近似量子隐形传态。基于此，我们提出一种方法，用于量化使用任意资源态时近似量子隐形传态的性能。具体而言，在将近似量子隐形传态任务表述为对单路局部操作与经典通信（LOCC）信道上模拟误差的优化后，我们通过将优化范围扩大到更大的两-PPT-可扩展信道集合，建立了该优化任务的半定松弛。本文的主要解析计算在于利用恒等信道的酉协方差对称性，显著降低了后一优化的计算成本。此外，通过利用近似量子隐形传态与量子纠错之间的已知联系，我们将这些概念用于建立给定量子信道上近似量子纠错性能的界限。最后，我们针对各类资源态与信道的实例评估了所提出的界限。