How Much Entanglement Does a Quantum Code Need?

Abstract

In the setting of entanglement-assisted quantum error-correcting codes (EAQECCs), the sender and the receiver have access to pre-shared entanglement. Such codes promise better information rates or improved error handling properties. Entanglement incurs costs and must be judiciously calibrated in designing quantum codes with good performance, relative to their deployment parameters. Revisiting known constructions, we devise tools from classical coding theory to better understand how the amount of entanglement can be varied. We present three new propagation rules and discuss how each of them affects the error handling. Tables listing the parameters of the best performing qubit and qutrit EAQECCs that we can explicitly construct are supplied for reference and comparison.

References in corpus (19)

• Quantum entanglement
• Mixed State Entanglement and Quantum Error Correction
• Concentrating Partial Entanglement by Local Operations
• Deterministic delivery of remote entanglement on a quantum network
• Correcting Quantum Errors with Entanglement
• On optimal quantum codes
• LCD codes over ${\mathbb{F}}_q$ are as good as linear codes for q at least four
• A Resource Framework for Quantum Shannon Theory
• Entanglement required in achieving entanglement-assisted channel capacities
• Catalytic quantum error correction
• Entanglement-assisted quantum error-correcting codes over arbitrary finite fields
• Entanglement-assisted quantum turbo codes
• Linear Programming Bounds for Entanglement-Assisted Quantum Error-Correcting Codes by Split Weight Enumerators
• Euclidean and Hermitian Hulls of MDS Codes and Their Applications to EAQECCs
• Entropic proofs of Singleton bounds for quantum error-correcting codes
• Entanglement-Assisted Quantum Communication Beating the Quantum Singleton Bound
• Entanglement-Assisted Quantum Error-Correcting Codes with Imperfect Ebits
• Good Stabilizer Codes from Quasi-Cyclic Codes over ${\mathbb{F}}_4$ and ${\mathbb{F}}_9$
• Efficient entanglement generation and detection of generalized stabilizer states

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• Quantum error-correcting codes from projective Reed-Muller codes and their hull variation problem
• MDS, Hermitian Almost MDS, and Gilbert-Varshamov Quantum Codes from Generalized Monomial-Cartesian Codes
• Quasi-cyclic codes of index 2
• On the hull-variation problem of equivalent vector rank metric codes
• Bounds on concatenated entanglement-assisted quantum error-correcting codes