Optimal O(n^{-1/2}) convergence in trace distance with third moments and O(n^{-1}) in relative entropy with fourth moments for the quantum CLT in m-mode bosonic systems.
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An extension of the central limit theorem to bosonic quantum channels recovers the classical and state versions while supplying uncertainty relations and energy-constrained capacity lower bounds for linear bosonic channels.
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Optimal convergence rates in trace distance and relative entropy for the quantum central limit theorem
Optimal O(n^{-1/2}) convergence in trace distance with third moments and O(n^{-1}) in relative entropy with fourth moments for the quantum CLT in m-mode bosonic systems.
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Central Limit Theorem for Bosonic Quantum Channels
An extension of the central limit theorem to bosonic quantum channels recovers the classical and state versions while supplying uncertainty relations and energy-constrained capacity lower bounds for linear bosonic channels.