弱退耦对偶与量子识别
Weak Decoupling Duality and Quantum Identification
摘要：
如果量子系统受到噪声的影响，当且仅当没有关于系统的量子态的信息泄漏到环境中时，才有可能执行量子纠错来逆转噪声的作用。在这篇文章中，我们开发了一个类似的对偶性的情况下，环境近似忘记的身份的量子态，一个较弱的条件所满足的ε-随机映射和近似幺正设计。具体地说，我们表明，环境近似忘记量子态当且仅当原始通道近似保持成对的纯输入的连续性，我们称之为弱解耦对偶的观察。使用这个工具，然后，我们继续研究的任务，使用输出的通道，以模拟有限类的测量输入状态的空间。测试输入态是否是任意纯态的模拟测量的情况被称为相等测试或量子识别。弱退耦对偶性的直接后果是无法克隆执行量子识别的能力。我们还建立了量子态可以通过一个嘈杂的量子信道识别的最佳摊销率等于信道的纠缠辅助经典容量，尽管事实上，任务是量子的，而不是经典的，纠缠辅助是不允许的。特别地，对于每个非恒定量子信道，包括经典信道，该速率是严格正的。
英文摘要：
If a quantum system is subject to noise, it is possible to perform quantum error correction reversing the action of the noise if and only if no information about the system's quantum state leaks to the environment. In this article, we develop an analogous duality in the case that the environment approximately forgets the identity of the quantum state, a weaker condition satisfied by epsilon-randomizing maps and approximate unitary designs. Specifically, we show that the environment approximately forgets quantum states if and only if the original channel approximately preserves pairwise fidelities of pure inputs, an observation we call weak decoupling duality. Using this tool, we then go on to study the task of using the output of a channel to simulate restricted classes of measurements on a space of input states. The case of simulating measurements that test whether the input state is an arbitrary pure state is known as equality testing or quantum identification. An immediate consequence of weak decoupling duality is that the ability to perform quantum identification cannot be cloned. We furthermore establish that the optimal amortized rate at which quantum states can be identified through a noisy quantum channel is equal to the entanglement-assisted classical capacity of the channel, despite the fact that the task is quantum, not classical, and entanglement-assistance is not allowed. In particular, this rate is strictly positive for every non-constant quantum channel, including classical channels.
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