Universal quantum coding
Abstract
Entanglement distillation from noisy bipartite states and reliable quantum communication over noisy channels are fundamental tasks in quantum information theory. Yet existing coding schemes typically require prior knowledge of the underlying state or channel, or assume independent or weakly correlated quantum information sources. Here, using Schur-Weyl duality, we establish a universal quantum error-correction principle that overcomes these limitations. We show that the irreducible permutation spaces arising from the local Schur-Weyl decomposition of multiple copies of an unknown bipartite mixed state form maximally entangled quantum code spaces whose error structure is governed entirely by representation theory. Correcting these symmetry-resolved errors yields protocols for entanglement distillation and quantum communication that achieve coherent-information rates with exponentially vanishing error and optimal second-order corrections, even in the case of almost i.i.d. resources. Our approach also provides sharp finite-copy guarantees that are worst-case optimal at every finite block length, including in the sample-efficient regime, where the number of copies scales only polynomially with the number of qubits. Together, these results establish Schur-Weyl duality as a general mechanism for universal, robust, and optimal quantum coding, unifying entanglement distillation, quantum error correction, and quantum communication within a common representation-theoretic framework.
Related
- High-Dimensional Deterministic Secure Quantum Communication with Reed-Solomon Erasure Coding
- A Spectrum-Based Converse for Quantum State Discrimination and Its Applications to Classical-Quantum Channel Coding
- Communication Advantages from Quantum Dense Network Coding
- A Sum-of-Squares Hierarchy with Quadratic Convergence for Quantum Channel Coding
- Decoherence suppression in quantum dense coding
BibTeX
@misc{rizzo2026universal,
title = {{Universal quantum coding}},
author = {Jacopo Rizzo and Filippo Girardi and Ludovico Lami and Jens Eisert and Lorenzo Leone},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.38038},
eprint = {2609.38038},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38038},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Universal quantum coding
AU - Jacopo Rizzo
AU - Filippo Girardi
AU - Ludovico Lami
AU - Jens Eisert
AU - Lorenzo Leone
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2609.38038
UR - https://arxiv.org/abs/2609.38038
AB - Entanglement distillation from noisy bipartite states and reliable quantum communication over noisy channels are fundamental tasks in quantum information theory. Yet existing coding schemes typically require prior knowledge of the underlying state or channel, or assume independent or weakly correlated quantum information sources. Here, using Schur-Weyl duality, we establish a universal quantum error-correction principle that overcomes these limitations. We show that the irreducible permutation spaces arising from the local Schur-Weyl decomposition of multiple copies of an unknown bipartite mixed state form maximally entangled quantum code spaces whose error structure is governed entirely by representation theory. Correcting these symmetry-resolved errors yields protocols for entanglement distillation and quantum communication that achieve coherent-information rates with exponentially vanishing error and optimal second-order corrections, even in the case of almost i.i.d. resources. Our approach also provides sharp finite-copy guarantees that are worst-case optimal at every finite block length, including in the sample-efficient regime, where the number of copies scales only polynomially with the number of qubits. Together, these results establish Schur-Weyl duality as a general mechanism for universal, robust, and optimal quantum coding, unifying entanglement distillation, quantum error correction, and quantum communication within a common representation-theoretic framework.
ER -