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- W4316830025 abstract "We present an alternative (constructive) proof of the statement that for every completely positive, trace-preserving map $Phi$ there exists an auxiliary Hilbert space $mathcal K$ in a pure state $|psiranglelanglepsi|$ as well as a unitary operator $U$ on system plus environment such that $Phi$ equals $operatorname{tr}_{mathcal K}(U((cdot)otimes|psiranglelanglepsi|)U^*)$. The main tool of our proof is Sz.-Nagy's dilation theorem applied to isometries defined on a subspace. In our construction, the environment consists of a system of dimension Kraus rank of $Phi$ together with a qubit, the latter only acting as a catalyst. In contrast, the original proof of Hellwig & Kraus given in the 70s yields an auxiliary system of dimension Kraus rank plus one. We conclude by providing an example which illustrates how the constructions differ from each other." @default.
- W4316830025 created "2023-01-17" @default.
- W4316830025 creator A5062883307 @default.
- W4316830025 date "2023-01-13" @default.
- W4316830025 modified "2023-09-23" @default.
- W4316830025 title "From Kraus Operators to the Stinespring Form of Quantum Maps: An Alternative Construction for Infinite Dimensions" @default.
- W4316830025 doi "https://doi.org/10.48550/arxiv.2301.05488" @default.
- W4316830025 hasPublicationYear "2023" @default.
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