Recovering quantum information in a noisy quantum channel

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.