Graduate Quantum measurement and entropy

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Quantum measurement transitions a system from an uncertain to a certain state, indicating a decrease in entropy for the measured system. However, this decrease does not imply a corresponding increase in entropy elsewhere, as the second law of thermodynamics holds when comparing measured states. The discussion highlights that the entropy of the universe increases during measurement due to the probabilistic nature of quantum outcomes, distinguishing between mutual information and entropy. The von Neumann entropy is a key concept in this context, with its value depending on the purity of the state post-measurement. Ultimately, the relationship between quantum and classical entropy remains complex, with no definitive answer regarding their comparative magnitudes.
  • #31
vanhees71 said:
Of course, I'm talking about information in the information-theoretical sense, which has nothing to do with consciousness or vague philosophical ideas of this kind.

Maxwell's demon (particularly its quantum realization in cavity QED in recent works) for me is the prime example for the necessity to introduce information-theoretical methods into a full understanding of (quantum) statistical physics. Among other things these investigations clearly show the correctness of the concept of entropy in the sense of the Shannon-Jaynes-von Neumann entropy of statistical physics. Recently one has proven that indeed the maximum entropy of a qubit is ##k_{\text{B}} \ln 2##.

http://www.pnas.org/content/114/29/7561
https://arxiv.org/abs/1702.05161

https://www.nature.com/articles/s41567-018-0250-5
From what I have roughly understood, memory entropy is greater than decrease of entropy of the system:-so,'information about the system/memory entropy' + 'entropy of the system' is constant or increasing--right?
 

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