Reversing Unknown Quantum Processes via Virtual Combs: for Channels with Limited Information
arxiv(2024)
摘要
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.
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