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Quantum error correction assisted by two-way noisy communication.

Zhuo Wang1,2, Sixia Yu2,3, Heng Fan1

  • 1Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China.

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This study introduces a new quantum error correction protocol using noisy communication and local entanglement. It purifies entangled pairs during decoding, improving efficiency and enabling novel encoding rates.

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Area of Science:

  • Quantum Information Science
  • Quantum Error Correction
  • Quantum Communication

Background:

  • Entanglement-assisted quantum error-correcting codes (EAQECCs) enhance quantum error correction.
  • Sharing pre-shared non-local entanglement for EAQECCs is hindered by noise and requires resource-intensive distillation.

Purpose of the Study:

  • To propose a more feasible quantum error correction protocol using two-way noisy communication.
  • To overcome limitations of non-local entanglement sharing in EAQECCs.
  • To demonstrate improved performance and novel encoding capabilities.

Main Methods:

  • Developed a protocol utilizing two-way noisy communication, with local entanglement creation and simultaneous purification during decoding.
  • Implemented a simplified version of the EAQECC [[4, 1, 3; 1]].
  • Constructed a novel 1-error-correcting code with 4 physical qudits encoding 1 qubit.

Main Results:

  • The protocol effectively purifies pre-shared noisy entangled pairs within the decoding process.
  • An easier implementation of the [[4, 1, 3; 1]] EAQECC was achieved.
  • A 4-qudit code was constructed, achieving 1-error correction and encoding 1 qubit, a feat impossible in standard quantum error correction.

Conclusions:

  • The proposed protocol offers a practical approach to quantum error correction by mitigating noise in communication and avoiding entanglement distillation.
  • The protocol demonstrates potential for enhanced encoding rates, offering advantages over standard quantum error correction methods.
  • A systematic construction for two-way-noisy-communication-assisted codes was established.