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# Decoherence, einselection, and the quantum origins of the classical

Reviews of modern physics

American Physical Society (APS)

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### Most cited references218

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### Quantum Computations with Cold Trapped Ions.

(1995)
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### Mixed State Entanglement and Quantum Error Correction

(1996)
Entanglement purification protocols (EPP) and quantum error-correcting codes (QECC) provide two ways of protecting quantum states from interaction with the environment. In an EPP, perfectly entangled pure states are extracted, with some yield D, from a mixed state M shared by two parties; with a QECC, an arbi- trary quantum state $$|\xi\rangle$$ can be transmitted at some rate Q through a noisy channel $$\chi$$ without degradation. We prove that an EPP involving one- way classical communication and acting on mixed state $$\hat{M}(\chi)$$ (obtained by sharing halves of EPR pairs through a channel $$\chi$$) yields a QECC on $$\chi$$ with rate $$Q=D$$, and vice versa. We compare the amount of entanglement E(M) required to prepare a mixed state M by local actions with the amounts $$D_1(M)$$ and $$D_2(M)$$ that can be locally distilled from it by EPPs using one- and two-way classical communication respectively, and give an exact expression for $$E(M)$$ when $$M$$ is Bell-diagonal. While EPPs require classical communica- tion, QECCs do not, and we prove Q is not increased by adding one-way classical communication. However, both D and Q can be increased by adding two-way com- munication. We show that certain noisy quantum channels, for example a 50% depolarizing channel, can be used for reliable transmission of quantum states if two-way communication is available, but cannot be used if only one-way com- munication is available. We exhibit a family of codes based on universal hash- ing able toachieve an asymptotic $$Q$$ (or $$D$$) of 1-S for simple noise models, where S is the error entropy. We also obtain a specific, simple 5-bit single- error-correcting quantum block code. We prove that {\em iff} a QECC results in high fidelity for the case of no error the QECC can be recast into a form where the encoder is the matrix inverse of the decoder.
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### Scheme for reducing decoherence in quantum computer memory.

(1995)
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### Author and article information

###### Journal
10.1103/RevModPhys.75.715