pith:6LNS7VXO
Central Limit Theorem for Bosonic Quantum Channels
The central limit theorem extends to bosonic quantum channels and establishes Gaussian channels as extremal objects.
arxiv:2605.16782 v1 · 2026-05-16 · quant-ph
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Claims
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.
The extension of the central limit theorem to channels requires that the bosonic channels satisfy technical conditions (such as finite moments or complete positivity) that allow the limit to be taken while preserving the bosonic structure; this premise is invoked when the authors state that the result applies to every physical bosonic quantum channel and when they derive the uncertainty relations and capacity bounds from the Gaussian extremality.
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.
References
Receipt and verification
| First computed | 2026-05-20T00:03:21.702999Z |
|---|---|
| Builder | pith-number-builder-2026-05-17-v1 |
| Signature | Pith Ed25519
(pith-v1-2026-05) · public key |
| Schema | pith-number/v1.0 |
Canonical hash
f2db2fd6eed12982de45f48d51ab55555d1ade7c85c20a37aa99bb62572e99a2
Aliases
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curl -sH 'Accept: application/ld+json' https://pith.science/pith/6LNS7VXO2EUYFXSF6SGVDK2VKV \
| jq -c '.canonical_record' \
| python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: f2db2fd6eed12982de45f48d51ab55555d1ade7c85c20a37aa99bb62572e99a2
Canonical record JSON
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