Quantum Causal Modelling: Mathematics

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SUMMARY

The discussion centers on understanding the "Process Matrix Formalism" and "Completely Positive Trace Preserving maps" as presented in the paper from IOPscience. The user seeks introductory materials to grasp these concepts, particularly the Choi–Jamiołkowski isomorphism and its application in quantum mechanics (QM). The inquiry highlights the relevance of these mathematical frameworks in contemporary QM literature, indicating their significance in the field.

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  • Concept of trace and its properties in mathematics
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I have been trying to read through the following paper: https://iopscience.iop.org/article/10.1088/1367-2630/18/6/063032/pdf, but am stuck at the parts from page 6 onwards.

What is the "approach/formalism" used in the following sections of the paper, and are there any gentle introductions (available online, preferably) to this topic I can read through that may help me understand what's in the paper? I have seen similar mathematics appear in quite a few QM papers now and can't help but wonder if it's important.

Thanks in advance.
 
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Perhaps I should have been more specific in my question, apologies:

Could anyone recommend some introductory materials to
1. "Process Matrix Formalism" - as mentioned in the abstract
2. Completely Positive Trace Preserving maps, Choi–Jamiołkowski isomorphism, and how they are used in QM

Thanks in advance.
 

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