Abstract
In order to model the most general quantum operation on a d-dimensional system, a d2-dimensional environment is usually needed. We focus on the quantum dephasing process and find that this channel can be modeled by an environment with the size of at most d dimensions. An experimentally accessible matrix D is defined to characterize the dephasing channel and the minimal number of Kraus operators of the channel from the matrix I) for mocking up the dephasing channel is presented in the minimal-sized environment. An experimental simulation of dephasing channels by means of nuclear magnetic resonance techniques is carried out to justify the idea.
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