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Quantum Error Correction Inapplicable to Really Entangled States

Document Type Expired Internet-Draft (individual)
Expired & archived
Author Dr. Masataka Ohta
Last updated 2021-05-03 (Latest revision 2020-10-30)
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This Internet-Draft is no longer active. A copy of the expired Internet-Draft is available in these formats:


Though quantum error correction assumes localized error model of Shor that errors on a qubit are caused by interaction with its local environment, enabling essentially classical error correction for unentangled states, the model is applied to entangled states improperly without involving local environment states in the entanglement. That is, when an entangled state (Q) is represented as superposition of unentangled terms (Qi) as Q=Q1+Q2+...+Qn, local environment states around qubits are, in general, different term by term. Q will be, with term-specific error operators (Ei), E1*Q1+E2*Q2+...+En*Qn, not, with a common error operator (E) assumed by Shor, E*(Q1+Q2+...+Qn). A complication is that Shor's error model is a little quantum, allowing for two different local environment states around a qubit. As such, quantum error correction is applicable to some trivially entangled states including states used by Shor code but not to really entangled states.


Dr. Masataka Ohta

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