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arXiv · 2509.11785

Understanding Quantum Instruments Through the Analysis of $C^*$-Convexity and Their Marginals

B. V. Rajarama Bhat·Arghya Chongdar·Sruthymurali
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Abstract

Quantum instruments are mathematical devices introduced to describe the conditional state change during a quantum process. They are completely positive map valued measures on measurable spaces. We may also view them as non-commutative analogues of joint probability measures. We analyze the $C^*$-convexity structure of spaces of quantum instruments. A complete description of the $C^*$-extreme instruments in finite dimensions has been established. Further, the implications of $C^*$-extremity between quantum instruments and their marginals has been explored.

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B. V. Rajarama Bhat, Arghya Chongdar, Sruthymurali. 2025-09-15. Understanding Quantum Instruments Through the Analysis of $C^*$-Convexity and Their Marginals. https://arxiv.org/abs/2509.11785

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