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Understanding Quantum Instruments Through the Analysis of $C^*$-Convexity and Their Marginals
B. V. Rajarama Bhat, Arghya Chongdar, Sruthymurali·September 15, 2025
math.OAMathematical PhysicsQuantum Physics
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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.