I Keeping a subspace decoherence free, with the Zeno Effect

[qwertuiop]

I am currently reading papers discussing the Zeno Effect, which discuss how measuring a system at high frequencies can almost freeze the state of a system, or keep the system in a specific subspace of states. This can be easily seen using the projection postulate. Often the topic of decoherence comes up and how limiting the system to evolve in a specific subspace results in protection of information and prevents decoherence. Two things important for quantum computation. I understand that if the system is limited to a certain subspace probability leakage is limited too, protecting information. What I do not understand is how the the subspace is kept decoherence free. How does limiting the system to a specific subspace prevent decoherence?

 

[Strilanc]

Link to the papers you're reading.

 

[Strilanc]

I'm guessing it's a combination of quantum error correcting codes and the zeno effect.

Suppose you can measure "is the system in the QEC subspace?" at a rate significantly higher than the time it takes for an error to accumulate. Since changing any individual qubit pushes the system out of the QEC subspace, and errors tend to happen to individual qubits (i.e. correlated errors are much less likely), the zeno effect caused by the continuous measurements will prevent errors from accumulating.

I'm not sure how practical that approach is. I assume errors can occur over very short time spans, so you'd have to be doing the complicated distributed measurement insanely fast. Also it might get in the way when you do want to operate on the state, since you can't ever stop measuring.

 

[qwertuiop]

http://arxiv.org/pdf/0903.3297v1.pdf

At the moment I'm not too concerned with the applications to Quantum Computation, rather the way in which general decoherence is prevented by restraining the system state to lie in a subspace.

 

[Feeble Wonk]

According to this paper, the quantum Zeno Effect only works in some situations.
https://www.researchgate.net/profile/Gershon_Kurizki/publication/2204834_The_Zeno_and_anti-Zeno_effects_on_decay_in_dissipative_quantum_systems/links/0046352b1b5bfe1fa0000000.pdf?inViewer=0&pdfJsDownload=0&origin=publication_detail

 

[qwertuiop]

http://arxiv.org/pdf/0903.3297v1.pdf

This paper discusses modelling a transition out of the wanted subspace as the onset of 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.