Automated Error Correction For Generalized Bell States

TL;DR

This paper presents an automated method for correcting bit flip and phase errors in Generalized Bell states using ancilla bits and unitary operations, enhancing quantum error correction techniques.

Contribution

It introduces a novel error correction procedure for GBS that encodes error information in ancilla bits without disturbing the state, and generalizes it for higher-dimensional entangled states.

Findings

Error correction via ancilla encoding is effective for GBS.

The method can be extended to higher-dimensional entangled states.

Distributed measurements can identify error syndromes.

Abstract

A procedure is developed to automatically correct the bit flip and the arbitrary phase change errors in Generalized Bell states (GBS). The phase and parity characteristics of the GBS are encoded in ancilla bits without altering the state under consideration. The same information is then used to correct the state at a different point, through appropriate unitrary control operations. It is also shown that the distributed/indirect measurements on ancilla can yield the error syndrome. The restricted error correction circuit obtained for N-qubit entangled states of the Bell type, are generalized for the corresponding higher dimensions, thus opening up the possibility of designing of task specific error correction circuits.