# Quantum Causal Modelling: Mathematics

• I
• WWCY
In summary, the conversation revolves around the reader struggling to understand the "approach/formalism" used in the paper from page 6 onwards. They are looking for gentle introductions to this topic that can be found online. They are specifically interested in learning about the "Process Matrix Formalism" mentioned in the abstract, as well as the concepts of Completely Positive Trace Preserving maps and Choi–Jamiołkowski isomorphism and how they are used in QM. They ask for recommendations for introductory materials on these topics.
WWCY
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.

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

## 1. What is Quantum Causal Modelling?

Quantum Causal Modelling is a mathematical framework that combines elements of quantum mechanics and causal inference to model complex systems. It aims to understand the causal relationships between variables in a system by using mathematical tools from quantum mechanics.

## 2. How is Quantum Causal Modelling different from traditional causal modelling?

Traditional causal modelling relies on classical probability theory and assumes that variables have definite values. Quantum Causal Modelling, on the other hand, takes into account the uncertainty and indeterminacy inherent in quantum systems, allowing for a more nuanced understanding of causality.

## 3. What are the advantages of using Quantum Causal Modelling?

Quantum Causal Modelling allows for a more comprehensive and accurate understanding of complex systems, especially those involving quantum phenomena. It also provides a more flexible and powerful framework for modelling causality, as it can handle situations where traditional methods fail.

## 4. What are the potential applications of Quantum Causal Modelling?

Quantum Causal Modelling has potential applications in various fields, including quantum computing, quantum biology, and social sciences. It can also be used to study complex systems in physics, such as quantum entanglement and quantum phase transitions.

## 5. Do I need a background in quantum mechanics to understand Quantum Causal Modelling?

While a basic understanding of quantum mechanics can be helpful, it is not necessary to have a background in it to understand Quantum Causal Modelling. The concepts and principles of quantum mechanics used in this framework can be learned as needed, making it accessible to a wider range of researchers and scientists.

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