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A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
Published on: September 5, 2019
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How Much Entanglement Is Needed for Quantum Error Correction?
Sergey Bravyi1, Dongjin Lee2,3, Zhi Li2,4
1IBM T. J. Watson Research Center, IBM Quantum, Yorktown Heights, New York 10598, USA.
Physical Review Letters
|June 18, 2025
Summary
Quantum error-correcting codes do not always require high entanglement to correct errors. This study reveals a tradeoff between code distance and entanglement for specific codes, but shows it doesn't hold universally.
Area of Science:
- Quantum Information Science
- Quantum Error Correction
- Quantum Computing
Background:
- A common belief posits that quantum error-correcting codes (QECCs) necessitate high entanglement for error correction.
- This implies that codes correcting more errors inherently require greater entanglement per encoded qubit.
Purpose of the Study:
- To investigate the relationship between entanglement and error correction capabilities in QECCs.
- To challenge the universal assumption of a strict entanglement-error correction tradeoff.
Main Methods:
- Characterization of the tradeoff between code distance (d) and geometric entanglement.
- Geometric entanglement quantifies the maximal overlap of logical states with product or topologically trivial states.
- Analysis of three specific code families: low-density parity-check codes, stabilizer codes, and codes with constant encoding rates.
Main Results:
- A tradeoff exists for specific codes: maximum overlap decreases exponentially with code distance (d).
- Geometric entanglement grows at least linearly with code distance (d) for these codes.
- The distance-entanglement tradeoff is not universally applicable; families of codes exist where entanglement approaches zero for large code lengths.
Conclusions:
- The necessity of high entanglement for robust quantum error correction is code-dependent.
- Geometric entanglement provides a useful measure for characterizing this relationship.
- Further research into diverse code constructions is needed to fully understand entanglement requirements in QECCs.
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