Coherence time for repeated spin measurements

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Discussion Overview

The discussion revolves around the coherence time for repeated spin measurements on the same electron, focusing on how the correlation function, C(t,0), changes over time. Participants explore theoretical implications, noise effects, and the role of the Hamiltonian in determining the behavior of the correlation function.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants propose that for small time intervals, the correlation function C(t,0) equals 1, while for large intervals, it approaches 0.
  • Others argue that the correlation function's dependence on time is influenced by the Hamiltonian of the system, noting that for a free electron, the spin state does not evolve, but it does in a magnetic field.
  • One participant raises a question about the effects of noise on the spin state, suggesting that the spin does not remain unchanged indefinitely.
  • Another participant mentions the standard model of coupling to a bath and anticipates that the time dependence of the correlation function should involve the coherence time, T_coh, possibly following an exponential decay.
  • Some participants express uncertainty about the relevance of coherence time to the discussion, questioning whether it is pertinent to the specific context of the measurements.
  • A later reply suggests that the choice of Hamiltonian may not be crucial, emphasizing the importance of the density matrix and the decay of off-diagonal terms as exp[-t/T_coh].
  • One participant notes a connection to loophole-free Bell tests, indicating a broader context for the discussion.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the exact dependence of the correlation function on time, with multiple competing views regarding the role of the Hamiltonian and the relevance of coherence time. The discussion remains unresolved.

Contextual Notes

There are limitations in the context provided, particularly regarding the specific Hamiltonian and the assumptions underlying the models discussed. The relationship between coherence time and the correlation function is also not fully clarified.

aa2ll2
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TL;DR
"What is the half life of the correlation between repeated spin measurements on the same electron?
Consider repeated spin measurements, along the same axis, on the same electron, at t=0 and at t=t. For small t, the results are identical, so the correlation function, C(t,0)=1, but for large t, C(t,0) -> 0.

Define C(t,0) = P(same) - P(different) = N(same) - N(different) / N(same) + N(different), where N(same) is the number of trials where the measurements at t=0 and at t=t return the same result etc.

How does this correlation function depend on t?
 
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aa2ll2 said:
TL;DR Summary: "What is the half life of the correlation between repeated spin measurements on the same electron?

Consider repeated spin measurements, along the same axis, on the same electron, at t=0 and at t=t. For small t, the results are identical, so the correlation function, C(t,0)=1, but for large t, C(t,0) -> 0.

Define C(t,0) = P(same) - P(different) = N(same) - N(different) / N(same) + N(different), where N(same) is the number of trials where the measurements at t=0 and at t=t return the same result etc.

How does this correlation function depend on t?
It depends on the Hamiltonian for the system. For a free electron, the spin state does not evolve. The spin state would evolve in a magnetic field.
 
It's a noise question. So, the free particle spin evolving in noise, does not remain forever the same, with prob. 1, right? I actually have in mind an NV centre, which I think is free for the purpose to hand.
 
aa2ll2 said:
It's a noise question. So, the free particle spin evolving in noise, does not remain forever the same, with prob. 1, right? I actually have in mind an NV centre, which I think is free for the purpose to hand.
You'll need to specify a Hamiltonian for your "noise".
 
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The standard, coupling to bath, model. A bit of context may help. The single qubit coherence time is T_coh. I'm anticipating the time dependence should involve T_coh, something like C(t,0) = e^[-t/T_coh]. Or, are you saying coherence time is not pertinent?
 
aa2ll2 said:
The standard, coupling to bath, model. A bit of context may help. The single qubit coherence time is T_coh. I'm anticipating the time dependence should involve T_coh, something like C(t,0) = e^[-t/T_coh]. Or, are you saying coherence time is not pertinent?
Is this to do with quantum computing?
 
It is actually something that came up with loophole free Bell tests, but quite similar to computing.
 
Hi Perok,

Looking at some papers, the question of what hamiltonian to use seems a bit of a red herring. The starting point is the density matrix, where off diagonal terms decay as exp[-t/T_coh] In the model used for predicting the Bell violation in noise. My question should then be quite simple . How does the C(t,0) defined above depend on time?
 
aa2ll2 said:
Hi Perok,

Looking at some papers, the question of what hamiltonian to use seems a bit of a red herring. The starting point is the density matrix, where off diagonal terms decay as exp[-t/T_coh] In the model used for predicting the Bell violation in noise. My question should then be quite simple . How does the C(t,0) defined above depend on time?
There's not enough context in this thread for me to comment. Perhaps someone else who is more familiar with the specific subject matter may be able to help. But, in such specific cases, you ought to provide the full background to the question.
 
  • #10
Thanks for your attention to this matter.
 

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