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Title: Quantum entropy and central limit theorem

We introduce a framework to study discrete-variable (DV) quantum systems based on qudits. It relies on notions of a mean state (MS), a minimal stabilizer-projection 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 zero-mean 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.

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Award ID(s):
2037687
NSF-PAR ID:
10482945
Author(s) / Creator(s):
; ;
Publisher / Repository:
Oxford University Press
Date Published:
Journal Name:
Proceedings of the National Academy of Sciences
Volume:
120
Issue:
25
ISSN:
0027-8424
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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