标题： 强收敛和一致收敛在玻色高斯信道的远距传输模拟中 显示英文标题

标题： Strong and uniform convergence in the teleportation simulation of bosonic Gaussian channels

摘要： 在关于连续变量玻色隐形传态协议的文献中[Braunstein 和 Kimble, Phys. Rev. Lett., 80(4):869, 1998]，通常会粗略地提到该协议在理想压缩和理想探测的极限下收敛到输入态的完美隐形传态，但这种收敛的确切形式通常未被明确阐述。本文中，我明确指出这种收敛是强收敛而非一致收敛，并且进一步证明了这种收敛适用于协议的任意输入态，包括这里定义和讨论的无限能量Basel态。与上述结果相反，我还证明了纯损耗、热态、纯放大器、放大器和加性噪声信道的隐形传态模拟，在理想压缩和探测的极限下，既强收敛又一致收敛于原始信道。对于这些信道，我给出了它们隐形传态模拟精度的显式一致界。随后，我将这些一致收敛的结果推广到特定的多模玻色高斯信道。这些收敛陈述对利用玻色高斯信道的隐形传态模拟进行的数学证明具有重要意义，其中一些与限制其非渐近密钥协商容量有关。作为此处讨论的一个副产品，我确认了我的联合工作[Berta 和 Tomamichel, Wilde, Tomamichel, Berta, IEEE Trans. Inf. Theory 63(3):1792, 三月 2017]中此类界限证明的正确性。此外，我表明为了确认此证明的正确性，并不需要引用能量约束的钻石距离。 显示英文摘要

摘要： In the literature on the continuous-variable bosonic teleportation protocol due to [Braunstein and Kimble, Phys. Rev. Lett., 80(4):869, 1998], it is often loosely stated that this protocol converges to a perfect teleportation of an input state in the limit of ideal squeezing and ideal detection, but the exact form of this convergence is typically not clarified. In this paper, I explicitly clarify that the convergence is in the strong sense, and not the uniform sense, and furthermore, that the convergence occurs for any input state to the protocol, including the infinite-energy Basel states defined and discussed here. I also prove, in contrast to the above result, that the teleportation simulations of pure-loss, thermal, pure-amplifier, amplifier, and additive-noise channels converge both strongly and uniformly to the original channels, in the limit of ideal squeezing and detection for the simulations. For these channels, I give explicit uniform bounds on the accuracy of their teleportation simulations. I then extend these uniform convergence results to particular multi-mode bosonic Gaussian channels. These convergence statements have important implications for mathematical proofs that make use of the teleportation simulation of bosonic Gaussian channels, some of which have to do with bounding their non-asymptotic secret-key-agreement capacities. As a byproduct of the discussion given here, I confirm the correctness of the proof of such bounds from my joint work with Berta and Tomamichel from [Wilde, Tomamichel, Berta, IEEE Trans. Inf. Theory 63(3):1792, March 2017]. Furthermore, I show that it is not necessary to invoke the energy-constrained diamond distance in order to confirm the correctness of this proof.