## Quantum Error Correction Inapplicable to Really Entangled States

draft-ohta-qec-inapplicable-00

Document | Type | Active Internet-Draft (individual) | |
---|---|---|---|

Author | Masataka Ohta | ||

Last updated | 2020-10-30 | ||

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INTERNET DRAFT M. Ohta draft-ohta-qec-inapplicable-00.txt Tokyo Institute of Technology Intended status: Informational October 30, 2020 Expires: May 3, 2021 Quantum Error Correction Inapplicable to Really Entangled States Status of this Memo This Internet-Draft is submitted in full conformance with the provisions of BCP 78 and BCP 79. Internet-Drafts are working documents of the Internet Engineering Task Force (IETF). Note that other groups may also distribute working documents as Internet-Drafts. The list of current Internet-Drafts is at http://datatracker.ietf.org/drafts/current. Internet-Drafts are draft documents valid for a maximum of six months and may be updated, replaced, or obsoleted by other documents at any time. It is inappropriate to use Internet-Drafts as reference material or to cite them other than as "work in progress." Copyright Notice Copyright (c) 2020 IETF Trust and the persons identified as the document authors. All rights reserved. This document is subject to BCP 78 and the IETF Trust's Legal Provisions Relating to IETF Documents (http://trustee.ietf.org/license-info) in effect on the date of publication of this document. Please review these documents carefully, as they describe your rights and restrictions with respect to this document. Abstract 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). M. Ohta Expires on May 3, 2021 [Page 1] INTERNET DRAFT QEC Inapplicable to Really Entangled States October 2020 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. 1. Introduction An assumption of noise model for quantum error correction by Shor [1] is "The critical assumption here is that decoherence only affects one qubit of our superposition, while the other qubits remain unchanged. It is not clear how reasonable this assumption is physically, but it corresponds to the assumption in classical information theory of the independence of noise.", which means a qubit suffers from error as a result of interaction with local environment around the qubit but no interaction occurs with other qubits or local environment of other qubits. Though some extension to consider certain interaction between a qubit and other qubits or environment of other qubits is possible, some locality is still assumed. The error model is directly applicable to unentangled, that is, essentially classical, states, resulting in localized errors, corrections of which are essentially classical error correction. However, it is unreasonable to expect such localized errors for entangled states, because the states themselves do not have locality. Actually, with a 2 qubit entangled state: |00>+|11>, if the first qubit coherently interacts with its environment to be |0>, the entire state becomes |00>, which means the second qubit is also affected, Though the case is trivial enough to be explained by Shor's error model as superposition of identity (no error) and sign flip (|0> and |1> become |0> and -|1>, correspondingly) error: |00>=((|00>+|11>)+(|00>-|11>))/2, such an explanation dose not deny lack of locality of errors on entangled states. As Shor overlooked the fact that when qubit states are entangled, their environment states are, in general, also entangled, errors on really entangled states are highly non-local to which quantum error correction is not applicable. That is, when an entangled state (Q) is represented as superposition of (minimum number of) unentangled terms (Qi) as Q=Q1+Q2+...+Qn, local environment states around a qubit are, in general, involved in the entanglement and different term by term, resulting in different error operators (Ei). As a result, Q will be disturbed by noise to be E1*Q1+E2*Q2+...+En*Qn, whereas, Shor thought a common error operatorShow full document text