Information Theory on Wave Function Collapse

In summary, the conversation discusses the relationship between wave function collapse, superposition, and information theory/entropy. It is noted that both eigenstates and superpositions have zero entropy, but collapse occurs during measurements and introduces additional degrees of freedom. The question of whether there is energy associated with superpositions is raised, with the suggestion that the energy goes to the measurement apparatus during a measurement. There is no definitive answer to this question.
  • #1
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I was trying to understand wave function collapse in terms of superposition, but I ran into some problems when relating back to information theory/entropy. It is given in the definition of information in terms of entropy energy is needed to transfer information. That is something we have always been taught, but if that means information is associated with different eigenstates, what happens to the information associated with different collapse forms of a particle? Is it that there is no energy associated with the information of the superpositions of a particle, but if that were the case, how could those states exist in the first place? Perhaps the answer is in Schrödinger's equation. Any help is welcomed! Thanks.
 
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  • #2
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That is something we have always been taught, but if that means information is associated with different eigenstates, what happens to the information associated with different collapse forms of a particle?
Eigenstates of an observable and superpositions of such eigenstates are not different regarding their (von Neumann) entropy: both are so-called pure states and have zero entropy. When you think about superpositions you should keep in mind that every state can be a superposition of states. This is just a question of which basis you chose. Physically, this corresponds to which observable you are going to measure.

Collapse only occurs during measurements, where additional degrees of freedom are introduced. The interaction with the measurement apparatus leads the initially pure state to a classical probabilistic mixture of states, which has a higher entropy (this is called "decoherence"). However, there is no universally accepted mechanism how a single outcome is chosen from this mixture. So I'm not sure, if there is a satisfying answer to your question.
 
  • #3
Alas I feel the same way, I cannot find definitive answer, however, could you answer this, mathematically, or logically? Is there energy associated with the different superpositions? If so, where does that energy go? I have a thought, but I'd like to hear others opinions first.
 
  • #4
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Is there energy associated with the different superpositions? If so, where does that energy go?
What do you mean by the first question? Arbitrary states |ψ> can be decomposed in a superposition of energy eigenstates. If you have such a superposition, the energy of the state is not well-defined. The best you can do is to talk about average values. During a measurement, this average value changes due to the interaction with the measurement apparatus. So the apparatus is where the "energy goes".
 

1. What is the wave function collapse in information theory?

The wave function collapse is a phenomenon in quantum mechanics where the state of a system changes from a superposition of multiple possible states to a single definite state when it is measured or observed. This collapse is not fully understood and is a topic of ongoing research in information theory.

2. How does information theory explain the wave function collapse?

Information theory explains the wave function collapse as a result of the interaction between the observer and the quantum system. When an observer obtains information about the system, the system's state is updated to reflect that information. This update is known as the collapse of the wave function.

3. What is the role of entropy in information theory and wave function collapse?

In information theory, entropy is a measure of the uncertainty or randomness in a system. In the context of wave function collapse, entropy plays a crucial role in determining the probability of a particular state collapsing. As the system's entropy decreases, the probability of a particular state collapsing increases.

4. Can information be lost during the wave function collapse?

According to the laws of quantum mechanics, information cannot be lost during the wave function collapse. The collapse of the wave function is a deterministic process, meaning that the information obtained by the observer is always consistent with the system's state before the collapse.

5. How does the concept of decoherence relate to information theory and wave function collapse?

Decoherence is a process by which a quantum system becomes entangled with its environment, causing the system's wave function to collapse. In information theory, decoherence is seen as the source of the "noise" that affects the transmission and processing of information. In the context of wave function collapse, decoherence is considered one of the factors that contribute to the collapse of the wave function.

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