Dall'Arno Michele, Brandsen Sarah, Buscemi Francesco
Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore.
Graduate School of Information Science, Nagoya University, Chikusa-ku, Nagoya 464-8601, Japan.
Proc Math Phys Eng Sci. 2017 Mar;473(2199):20160721. doi: 10.1098/rspa.2016.0721. Epub 2017 Mar 15.
We develop a device-independent framework for testing quantum channels. That is, we falsify a hypothesis about a quantum channel based only on an observed set of input-output correlations. Formally, the problem consists of characterizing the set of input-output correlations compatible with any arbitrary given quantum channel. For binary (i.e. two input symbols, two output symbols) correlations, we show that extremal correlations are always achieved by orthogonal encodings and measurements, irrespective of whether or not the channel preserves commutativity. We further provide a full, closed-form characterization of the sets of binary correlations in the case of: (i) any dihedrally covariant qubit channel (such as any Pauli and amplitude-damping channels) and (ii) any universally-covariant commutativity-preserving channel in an arbitrary dimension (such as any erasure, depolarizing, universal cloning and universal transposition channels).
我们开发了一种用于测试量子信道的与设备无关的框架。也就是说，我们仅基于观察到的一组输入 - 输出相关性来证伪关于量子信道的一个假设。形式上，该问题包括刻画与任意给定量子信道兼容的输入 - 输出相关性集合。对于二元（即两个输入符号、两个输出符号）相关性，我们表明，无论信道是否保持可交换性，极值相关性总是通过正交编码和测量来实现。我们进一步在以下两种情况下对二元相关性集合给出了完整的、封闭形式的刻画：(i) 任何二面体协变量子比特信道（例如任何泡利信道和振幅衰减信道）以及 (ii) 任意维度下的任何保持可交换性的全协变信道（例如任何擦除信道、去极化信道、通用克隆信道和通用转置信道）。
