Five Quantum Register Error Correction Code For Higher Spin Systems

Details Five Quantum Register Error Correction Code For Higher Spin Systems Five Quantum Register Error Correction Code For Higher Spin Systems

1997-02-16

arxiv.org/abs/quant-ph/9702033v3

Physics

Quantum Physics

Revised version, to appear in Phys.Rev.A (Rapid Communications). 4 pages in Revtex 3.1, using amssymb.sty

Scientific paper

10.1103/PhysRevA.56.R1

I construct a quantum error correction code (QECC) in higher spin systems using the idea of multiplicative group character. Each $N$ state quantum particle is encoded as five $N$ state quantum registers. By doing so, this code can correct any quantum error arising from any one of the five quantum registers. This code generalizes the well-known five qubit perfect code in spin-1/2 systems and is shown to be optimal for higher spin systems. I also report a simple algorithm for encoding. The importance of multiplicative group character in constructing QECCs will be addressed.

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