Modelling Decoherence as a Transition Out of Subspace

[qwertuiop]

Modelling the onset of decoherence in a subspace as a transition from this subspace
http://www.ba.infn.it/~pascazio/publications/sudarshan_seven_quests.pdf
(Section 10 is relevant)

I am currently reading papers discussing the Zeno Effect. The linked paper discusses modelling a transition out of a wanted subspace as the onset of decoherence. Thus by frequently projecting back onto the subspace prevents decoherence. I don't quite understand this model. Why does remaining in the subspace mean that coherence must be preserved? Surely environmental effects can decohere the system even if it stays in the subspace. I guess that's what I'm having trouble with, why decoherence is modeled as a transition out of the subspace.

 

[eljose79]

Can someone explain this to me?
Thank you for bringing up this interesting topic. I am a scientist who specializes in quantum mechanics and I would be happy to provide some insight into the model discussed in the paper.

Firstly, let me clarify what is meant by "decoherence" in this context. Decoherence is a process in which a quantum system loses its coherence, or its ability to exist in a superposition of states. This can happen when the system interacts with its environment, causing the different states to become entangled with the environment and lose their individuality.

Now, in the model discussed in the paper, the subspace refers to a set of desired states that the system is supposed to remain in. In other words, the system is confined to this subspace and is not allowed to transition out of it. The authors propose that by frequently projecting the system back onto this subspace, we can prevent decoherence from occurring.

To understand this, let's consider an example of a quantum system confined to a two-state subspace, where one state represents a "0" and the other represents a "1". If the system is allowed to evolve freely, it can transition between these two states and exist in a superposition of both states. However, if we frequently measure the system and project it back onto the subspace, we are essentially forcing it to remain in one of the two states. This prevents it from interacting with the environment and losing its coherence.

Now, you are correct in pointing out that environmental effects can still decohere the system even if it stays in the subspace. However, the key idea here is that by frequently projecting the system back onto the subspace, we are reducing the amount of time it spends interacting with the environment. This effectively reduces the chances of decoherence occurring.

I hope this helps to clarify the model for you. If you have any further questions or would like to discuss this in more detail, please do not hesitate to ask.