Quantum

Choi-Jamio{\l}kowski isomorphism(s) and channel/state duality, naturally!

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Based on a feed excerpt; full article content has not been acquired. Source evidence retrieved 21/10/2026, 04:13:25 UTC.

Briefings

This article presents a new perspective on the Choi-Jamiolkowski isomorphism, framing it through the lens of naturality in quantum information theory. The authors demonstrate that a unique 'Choi map' exists which produces density operators on the Hilbert-Schmidt inner product space ${\mathsf L}({\mathcal{H}},{\mathcal{K}})$ without requiring an entangled state seed. This construction extends to a unitary map and recovers standard formulas, establishing a canonical correspondence between quantum channels and operators on tensor product spaces.

Key points

• A unique 'Choi map' exists that produces density operators on the Hilbert-Schmidt inner product space ${\mathsf L}({\mathcal{H}},{\mathcal{K}})$ without requiring an entangled state seed.
• The construction extends to a unitary map and recovers standard Choi-Jamiolkowski formulae, expressing naturality in quantum information theory.

Context

The article illuminates the nature of the Choi-Jamiolkowski isomorphism by viewing it through the perspective of naturality, as defined by Eilenberg and MacLane. This approach clarifies the form of associated formulas and explores versions that do not rely on entangled vector seeds, offering a fresh interpretation of channel-state duality.

Limitations

The evidence is limited to the arXiv preprint arXiv:2610.27394v1, which is untrusted data. The study focuses on finite-dimensional Hilbert spaces and does not provide experimental data, numerical results, or specific application cases. The authors do not claim causality or causal claims, and the findings remain theoretical.

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