Measurements and Consistent Families of Quantum Channels

Abstract. This article introduces the notion of consistent families (⇤)n 1 of Quantum Channels. These families correspond to simultaneous observation of di↵erent copies of a given quantum system. Here, we are primarily interested in the analysis of measurements connected with them. As usual, the measurement of a quantum system requires the construction of a classical dilation of the corresponding quantum channel. In our case, the quantum systems represented by (⇤)n 1 are supposed to interact through the measurement instrument only. That is, we construct a classical probability space which allows to have a common dilation for all the ⇤’s. Doing this, we introduce and solve a quantum version of the Moment Problem.