Recovering quantum information in a noisy quantum channel

不可逆性似乎是我们日常经验中物理过程的普遍性质。融化的冰淇淋不会自发地冻结成原来的形状，鸡尾酒一旦混合就不会蒸馏成酒。即使在宇宙中最宏观的尺度上也可以观察到可逆性;由于广义相对论原理，落入黑洞的粒子永远不会恢复。另一方面，支配力学的物理定律，如牛顿定律和量子幺正演化，似乎具有时间反演对称性，有时还伴随着其他物理对称性，例如，收费和平价。在量子力学中，封闭量子系统中的所有动力学都是可逆的，这也是所有量子计算算法所假定的特征。然而，在现实世界的情况下，门操作是不完美的，噪声不可避免地被添加到破坏量子相干性和纠缠，并最终这种量子可逆性。该项目提出了一个有趣的方向来解决这个问题，将物理过程视为量子通信信道，传输以量子态编码的有价值的信息。从这个角度来看，量子过程的可逆性可以量化为解码过程可以检索的量子信息量。该研究的主要目标是建立一个理论框架，定量描述在有噪声的量子处理信道中恢复量子信息，通过表征恢复量子信息的基本限制，并确定实现恢复的最小资源。通过采用Petz恢复映射作为恢复/解码量子信道，我们将从多个方面研究从噪声环境中恢复量子信息的精确条件：找到量子通信的量子容量的改进界限，开发量子计算中量子纠错的新方法，以及验证和量化量子存储器在量子反馈控制中的作用。我们的研究旨在减少量子计算中噪声和门操作的不完美性的影响，以便我们可以进行模拟或算法来证明量子的优势。这项研究将打开一个新的范式来理解量子计算中的噪声可逆性条件。与此同时，从拟议研究中获得的资源高效恢复协议有可能对实际应用产生重大影响，包括量子通信和量子计算，其中需要高保真度恢复量子态。

Irreversibility seems to be a universal nature of physical processes in our daily experience. Melted ice cream will not spontaneously freeze into its original shape, and a cocktail will not be distilled into liquors once it is mixed. The reversibility can be observed even in the most macroscopic scale in the universe; a particle fell into a black hole will never be recovered due to the principle of general relativity. On the other hand, the physical laws governing mechanics, such as Newtonian's law and quantum unitary evolutions, seem to have the time-reversal symmetry, sometimes accompanied with other physical symmetries, e.g., charge and parity. In other words, the time-reversed trajectory of a single particle seems as natural as the forward trajectory in time.In quantum mechanics, all the dynamics in a closed quantum system is reversible and this is the feature assumed in all the algorithms for quantum computation. However, in the real-world situation, gate operations are imperfect and noise is inevitably added to destroy quantum coherences and entanglement and ultimately this quantum reversibility. This project proposes an intriguing direction to approach this problem by regarding a physical process as a quantum communication channel, transmitting valuable information encoded in a quantum state. From this viewpoint, the reversibility of quantum processes can be quantified as the amount of quantum information that can be retrieved by the decoding process. The main objective of the research is to establish a theoretical framework towards a quantitative description of the recovery of quantum information in a noisy quantum processing channel, by characterising the fundamental limitation of recovering quantum information and identifying a minimal resource to achieve the recovery. By adopting the Petz recovery map as the recovery / decoding quantum channel, we will investigate a precise condition to recover quantum information from a noisy environment in various aspects: to find an improved bound of the quantum capacity for quantum communication, to develop a new method for quantum error correction in quantum computation, and to characterise and quantify a role of quantum memory in the quantum feedback control. Our research aims to reduce the impact of noise and imperfections of gate operations in quantum computing so that we can perform simulations or algorithms to demonstrate quantum advantages.This research will open a new paradigm to understand the noise-reversibility condition in quantum computing. At the same time, the resource-efficient recovery protocols obtained from the proposed research has potential to deliver a significant impact on practical applications, including quantum communications and quantum computations, where a high-fidelity recovery of a quantum state is necessary.