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To enhance the fidelity of entangled pairs, common methods include error correction and purification. For different channel error rates (corresponding to different initial fidelities), these methods might have their respective advantages, especially considering the Depolarizing channel.

In my assumption, error correction would perform better than purification when the fidelity is low. However, I am unable to prove this assumption mathematically.

I am a newbie who is learning quantum computing, I would be grateful if your explanation can be as detailed as possible.

QIAN
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If you only consider noisy EPR pairs with no local error (meaning noisy operations in Alice and Bob's devices locally), I believe 30 years ago people established an equivalence between one-way entanglement purification and QECC Bennett et. al.
If you have error in local operations, things get trickier and it's hard to establish a definite result. I more or less did this comparison in my Master's project FT Magic Square Game, although I'm distilling/error-correcting to obtain logical EPR pairs, probably a bit different from what you want to achieve. But my experience is that purification is pretty robust, especially when the infidelity of original EPR pair is much greater than error rate of local operations. But it has bottleneck, that is when the infidelity is of the same order as the local error rate, it doesn't purify anymore, you have to use a "stronger" purification scheme. I suspect the same problem occurs with QECC approach.

AndyLiuin
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