Why does tracing out help in averaging over unobserved degrees of freedom?

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In summary, "Tracing out" is a method used to obtain the density matrix of a particle after an interaction by averaging over unobserved degrees of freedom. This is similar to the concept of marginal probability and does not come from a specific axiom, as seen in Ballentine's work. It is a useful tool for dividing a system into observed and unobserved parts.
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naima
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Hi Pf
I am looking for the reason why after an interaction "tracing out" the external dof of the system gives the density matrix of the particle.
I looked in Ballentine if it comes from an axiom but i did not find (one occurence for partial trace)
I have the tool but i have not the reason why it is a good tool.
 
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Let the whole system S be divided into A and B, where we observe A and trace out B. You write the observable on the whole system ##O_{S} = O_{A} \otimes I_{B}##, and apply the Born rule to the whole system, and the reduced density matrix should pop out.
 
  • #3
naima said:
Hi Pf
I am looking for the reason why after an interaction "tracing out" the external dof of the system gives the density matrix of the particle.
I looked in Ballentine if it comes from an axiom but i did not find (one occurence for partial trace)
I have the tool but i have not the reason why it is a good tool.
Think of tracing out as averaging over unobserved degrees of freedom, which is akin to the concept of marginal probability:
http://en.wikipedia.org/wiki/Marginal_distribution
 

1. Why is "tracing out" important in scientific research?

"Tracing out" is a crucial step in scientific research as it allows us to identify and isolate specific variables or factors that may be influencing the outcome of an experiment. By tracing out these variables, we can better understand their impact and control for them, leading to more accurate and reliable results.

2. How does "tracing out" help in data analysis?

Tracing out helps in data analysis by allowing us to identify and eliminate any confounding variables that may be affecting our results. This helps us to draw more accurate conclusions and make more informed decisions based on the data.

3. What is the process of "tracing out" in scientific research?

The process of "tracing out" involves identifying and controlling for all relevant variables that may be influencing the outcome of an experiment. This can include using control groups, randomization, and statistical techniques to isolate the effects of specific variables.

4. How can "tracing out" improve the validity of a study?

By tracing out potential confounding variables, researchers can reduce the influence of these variables on the results of a study. This can improve the validity of the study by allowing for more accurate and reliable conclusions to be drawn.

5. What are some challenges of "tracing out" in scientific research?

One challenge of "tracing out" in scientific research is that it can be difficult to identify and control for all potential variables that may be affecting the outcome of an experiment. Additionally, some variables may be interconnected, making it challenging to isolate their effects. This requires careful planning and design of experiments to minimize these challenges.

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