Quantum measurement and entropy

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Discussion Overview

The discussion revolves around the relationship between quantum measurement, entropy, and the implications of these concepts within quantum mechanics. Participants explore how measurement affects the entropy of a quantum system, the nature of entropy before and after measurement, and the interpretations of these changes in the context of thermodynamics and information theory.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants propose that a quantum system transitions from an uncertain to a certain state upon measurement, indicating a decrease in entropy, and question whether this decrease is offset by an increase in entropy elsewhere, such as in the environment or observer.
  • Others argue that the comparison of entropy states before and after measurement is problematic, as they belong to different categories (measured vs. unmeasured states), which complicates the application of the second law of thermodynamics.
  • A viewpoint is presented that the notion of entropy depends on the interpretation of quantum mechanics, with some interpretations suggesting that the state before measurement represents possibilities while the measured state represents actual reality.
  • Participants discuss the von Neumann entropy as a relevant concept, noting that it can yield different results depending on the type of measurement performed (ideal vs. non-ideal) and the state of the system (pure vs. non-pure).
  • Some contributions highlight that measurement can lead to an increase in entropy due to the probabilistic nature of outcomes post-measurement, contrasting with deterministic interpretations of quantum mechanics without collapse.
  • There is a suggestion that mutual information gained by the observer during measurement should be distinguished from the entropy of the process itself.
  • The analogy of a coin flip is used to illustrate the difference between uncertainty in knowledge and uncertainty in the state, prompting further discussion on the implications of this analogy for quantum systems.

Areas of Agreement / Disagreement

Participants express multiple competing views regarding the implications of measurement on entropy, with no consensus reached on whether entropy increases or decreases overall or how to appropriately compare entropy states before and after measurement.

Contextual Notes

Limitations in the discussion include varying interpretations of quantum mechanics and the definitions of entropy being used, which affect the conclusions drawn about the relationship between measurement and entropy.

  • #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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