We advance the characterization of complexity in quantum manybody systems by examining
We introduce a framework to study discretevariable (DV) quantum systems based on qudits. It relies on notions of a mean state (MS), a minimal stabilizerprojection state (MSPS), and a new convolution. Some interesting consequences are: The MS is the closest MSPS to a given state with respect to the relative entropy; the MS is extremal with respect to the von Neumann entropy, demonstrating a “maximal entropy principle in DV systems.” We obtain a series of inequalities for quantum entropies and for Fisher information based on convolution, giving a “second law of thermodynamics for quantum convolutions.” We show that the convolution of two stabilizer states is a stabilizer state. We establish a central limit theorem, based on iterating the convolution of a zeromean quantum state, and show this converges to its MS. The rate of convergence is characterized by the “magic gap,” which we define in terms of the support of the characteristic function of the state. We elaborate on two examples: the DV beam splitter and the DV amplifier.
more » « less Award ID(s):
 2037687
 NSFPAR ID:
 10482945
 Publisher / Repository:
 Oxford University Press
 Date Published:
 Journal Name:
 Proceedings of the National Academy of Sciences
 Volume:
 120
 Issue:
 25
 ISSN:
 00278424
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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