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International Telecommunications Symposium (ITS)

A Code for Correcting Quantum Erasures

G. Santos, Francisco de Assis, Adriana Silva Lima

Published Jan 1, 2010• 0 citations
Publisher

Abstract

Quantum states are very delicate, so quantum error-correction procedures are believed to be essential for the successful implementation of quantum communications or computations.To erroneous qubits where the position is known, Grassl et al. [Phys.Rev. A 56, 33 (1997)] proposed an error model which they called quantum erasure channel.In this paper we present a quantum code capable of protecting nqubit of information against the occurrence of t erasures.This code is based on GHZ states.

DOI
10.14209/sbrt.2010.106

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Quantum states are very delicate, so quantum error-correction procedures are believed to be essential for the successful implementation of quantum communications or computations.To erroneous qubits where the position is known, Grassl et al. [Phys.Rev. A 56, 33 (1997)] proposed an error model which they called quantum erasure channel.In this paper we present a quantum code capable of protecting nqubit of information against the occurrence of t erasures.This code is based on GHZ states.
We present a quantum error correction code which protects three quantum bits (qubits) of quantum information against one erasure, i.e., a single-qubit arbitrary error at a known position. The present code has a high encoding efficiency, since only one auxiliary qubit is needed for one message qubit on average. In addition, we note that the code can also work even in a worse case that the interaction with the environment causes a leakage out of the qubit space. The code may have some applications in the storage of quantum information for small-scale quantum computing, quantum information processing, and quantum communication.
We present a quantum error correction code which protects three quantum bits (qubits) of quantum information against one erasure, i.e., a single-qubit arbitrary error at a known position. To accomplish this, we encode the original state by distributing quantum information over six qubits which is the minimal number for the present task (see reference [1]). The encoding and error recovery operations for such a code are presented. It is noted that the present code is also a three-qubit quantum hidded information code over each qubit. In addition, an encoding scheme for hiding nnn-qubit quantum information over each qubit is proposed.
We present a description of encoding/decoding for a concatenated quantum code that enables both protection against quantum computational errors and the occurrence of one quantum erasure. For this, it is presented how encoding and decoding for quantum graph codes are done, which will provide the protection against the occurrence of computational errors (external code). As internal code is used encoding and decoding via scheme of GHZ states for protection against the occurrence of one quantum erasure.
We present a quantum error correction code which protects three quantum bits (qubits) of quantum information against one erasure, i.e., a single-qubit arbitrary error at a known position. To accomplish this, we encode the original state by distributing quantum information over six qubits. The encoding and error recovery operations for such a code are presented. We also show that the present code is a three-qubit quantum hidded information code over each qubit. In addition, hiding nnn-qubit quantum information over each qubit is considered.