Can Entropy Decrease After a Projective Measurement?

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    Coherence Decoherence
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Discussion Overview

The discussion revolves around the implications of projective measurements on entropy in quantum systems, particularly focusing on the relationship between decoherence, measurement, and the potential for entropy to decrease. The scope includes theoretical considerations and conceptual clarifications related to quantum mechanics and entropy.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant questions the implications of decoherence and whether the measured system can regain coherence with the environment, suggesting a potential erasure of measurement effects.
  • Another participant asserts that decoherence cannot be reversed, emphasizing that it must be a proper decoherence process, although they acknowledge that in principle, decoherence is a unitary process.
  • A third participant reiterates the irreversibility of decoherence in practical terms, while also noting the theoretical reversibility due to its unitary nature.
  • A fourth participant references an external source to argue that projective measurements can increase entropy but never decrease it, while generalized measurements may allow for a decrease in entropy, linking this to the concept of wavefunction collapse.

Areas of Agreement / Disagreement

Participants express differing views on the reversibility of decoherence and the effects of projective measurements on entropy. There is no consensus on whether entropy can decrease following a projective measurement, and the discussion remains unresolved.

Contextual Notes

Participants highlight limitations in control over the system's environment and the definitions of decoherence and measurement, which may affect their arguments. The discussion also touches on the nature of pure states versus mixed states in relation to entropy.

StarsRuler
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¿ What´s the matter if after decoherence the measured system coherences again with the bath ¿ Is measure erased
 
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Decoherence cannot be reversed, otherwise it is not a proper decoherence. You can prepare a new system in a coherent state, if you like.
 
mfb said:
Decoherence cannot be reversed, otherwise it is not a proper decoherence.

Well, in practical terms, it cannot. Decoherence is still a unitary process so it's reversible in principle. The point is just that you don't have the necessary control of your system's environment.
 
http://en.wikipedia.org/wiki/Density_matrix#Entropy

"This entropy can increase but never decrease with a projective measurement, however generalized measurements can decrease entropy. The entropy of a pure state is zero, while that of a proper mixture always greater than zero. Therefore a pure state {entropy zero} may be converted into a mixture by a measurement, but a proper mixture can never be converted into a pure state. Thus the act of measurement induces a fundamental irreversible change on the density matrix; this is analogous to the "collapse" of the state vector, or wavefunction collapse."
 

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