Keeping a subspace decoherence free, with the Zeno Effect

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Discussion Overview

The discussion revolves around the Zeno Effect and its implications for preventing decoherence in quantum systems by restricting them to specific subspaces. Participants explore the theoretical underpinnings and practical challenges of maintaining decoherence-free subspaces, particularly in the context of quantum computation.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant notes that measuring a system at high frequencies can freeze its state and keep it in a specific subspace, which may protect information and prevent decoherence.
  • Another suggests that a combination of quantum error correcting codes (QEC) and the Zeno effect could help prevent errors from accumulating by measuring the system's presence in the QEC subspace at a high rate.
  • Concerns are raised about the practicality of continuous measurements and their potential interference with state operations.
  • A participant references a paper indicating that the quantum Zeno Effect is not universally applicable, suggesting limitations in its effectiveness.
  • Another participant questions the model that equates remaining in a subspace with preserved coherence, arguing that environmental effects could still cause decoherence even if the system remains in the subspace.

Areas of Agreement / Disagreement

Participants express differing views on the effectiveness and practicality of using the Zeno Effect to prevent decoherence, with no consensus reached on the mechanisms involved or the applicability of the discussed models.

Contextual Notes

Participants highlight limitations in understanding how decoherence is modeled as a transition out of the subspace, indicating that environmental factors may still influence coherence despite confinement to a subspace.

qwertuiop
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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?
 
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Link to the papers you're reading.
 
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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.
 
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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.
 
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
 
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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.
 

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