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arXiv · 2412.14336

On conjugate systems with respect to completely positive maps

Yoonkyeong Lee
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Abstract

We study the operator-valued partial derivative associated with covariance matrices on a von Neumann algebra B. We provide a cumulant characterization for the existence of conjugate variables and study some structure implications of their existence. Namely, we show that the center of the von Neumann algebra generated by B and its relative commutant is the center of B.

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Yoonkyeong Lee. 2024-12-18. On conjugate systems with respect to completely positive maps. https://arxiv.org/abs/2412.14336

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