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I have found that a qubit has two life times: $T_1$ during which it stays excited and $T_2$ during which it stays "coherent", meaning (from my understanding) that it is in its initial state.

Now I am interested in knowing how long I can keep a pair of entangled qubits alive. Let the pair have an initial fidelity $1$. With time it decreases, partly because of these life times and partly because of other environment interactions.

Let's say I have succeeded in using purification so my fidelity, after some time $\Delta t$, is close to $1$ anew. I have done the math for the simple PBS case ("Advances in quantum entanglement purification" / arXiv 2023 from Pei-Shum Yan et al., chapter II section B) so I understand that after the purification my former, really mixed state, has more probability to be found in the initial wanted state.

Does that mean that the second life time $T_2$ for each qubit has increased? What about $T_1$?

Frederik vom Ende
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Rome
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1 Answers1

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$T_1$ and $T_2$ are properties of a physical system, and so they do not change just because we are doing something specific with that system. For example, in a quantum memory experiment one might try to preserve a logical quantum state for some time $\Delta t$, and show that $\Delta t$ is larger than the time that same state could survive on any of the physical qubits of the system. One could do this by showing that $\Delta t \gg T_1, T_2$, without affecting the decay times themselves.

Similarly, you might argue that the entanglement purification protocol is effective if $\Delta t \gg T_1, T_2$, but this doesn't change the meaning of $T_1$ and $T_2$ - after all, you want something to compare your protocol to!

The decay times describe exponential decay behavior in systems that are not evolving under any external influences other than noise and a few simple pulses. Since this doesn't match the dynamics of your protocol we do not expect that the state is more likely "to die" when $\Delta t$ approaches $T_1$. If you haven't already, it is worth looking at how $T_1$ and $T_2$ are measured experimentally, which can give some intuition as to how they are defined:

Frederik vom Ende
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forky40
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