Xin Wang

The inherent irreversibility of quantum dynamics for open systems poses a significant barrier to the inversion of unknown quantum processes. To tackle this challenge, we propose the framework of virtual combs that exploit the unknown process iteratively with additional classical post-processing to simulate the process inverse. Our research establishes a path to achieving the exact inverse of unknown channels with certain conditions, accompanied by a no-go theorem that underscores the intrinsic limitations imposed by quantum mechanics on such tasks. Notably, we demonstrate that an n-slot virtual comb can exactly reverse a depolarizing channel with one unknown noise parameter out of n+1 potential candidates, and a 1-slot virtual comb can exactly reverse an arbitrary pair of quantum channels. We further explore the approximate inverse of an unknown channel within a given channel set. For any unknown depolarizing channels within a specified noise region, we unveil a worst-case error decay of O(n^−1) of reversing the channel via virtual combs. Moreover, we show that virtual combs with constant slots can be applied to universally reverse unitary operations and investigate the trade-off between the slot number and the sampling overhead.

The quantum capacity of a noisy quantum channel determines the maximal rate at which we can code reliably over asymptotically many uses of the channel, and it characterizes the channel’s ultimate ability to transmit quantum information coherently. In this paper, we derive single-letter upper bounds on the quantum and private capacities of quantum channels. The quantum capacity of a quantum channel is always no larger than the quantum capacity of its extended channels, since the extensions of the channel can be considered as assistance from the environment. By optimizing the parametrized extended channels with specific structures such as the flag structure, we obtain new upper bounds on the quantum capacity of the original quantum channel. Furthermore, we extend our approach to estimating the fundamental limits of private communication and one-way entanglement distillation. As notable applications, we establish improved upper bounds to the quantum and private capacities for fundamental quantum channels of great interest in quantum information, some of which are also the sources of noise in superconducting quantum computing. In particular, our upper bounds on the quantum capacities of the depolarizing channel and the generalized amplitude damping channel are strictly better than previously best-known bounds.