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Trapped Ion Quantum Computing
Central Limit Theorem for Bosonic Quantum Channels
arXiv
Authors: Hami Mehrabi, Ludovico Lami, Mark M. Wilde
Year
2026
Paper ID
63871
Status
Preprint
Abstract Read
~2 min
Abstract Words
129
Citations
N/A
Abstract
In this paper, we develop an extension of the Central Limit Theorem (CLT) to the setting of bosonic quantum channels. This extension provides a deeper understanding of Gaussian bosonic channels as extremal objects. Using our CLT for bosonic quantum channels, we recover both the classical CLT and the CLT for bosonic quantum states, thereby offering a unified perspective that connects classical probability theory with continuous-variable quantum systems. Moreover, using our result, we can provide necessary uncertainty relations that every physical (possibly non-Gaussian) bosonic quantum channel must satisfy. As another application of our limit theorems, we derive tight lower bounds on the energy-constrained quantum capacity of linear bosonic channels by relating it to the capacity of their associated Gaussian bosonic channels, further reinforcing the role of Gaussian channels as extremal.
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- This paper contributes to the Trapped-Ion Quantum Computing research area in the Quantum Articles archive.
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- In this paper, we develop an extension of the Central Limit Theorem (CLT) to the setting of bosonic quantum channels.
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