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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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