Entanglement-assisted Quantum Reed-Muller Tensor Product Codes

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Priya J. Nadkarni¹, Praveen Jayakumar^1,2, Arpit Behera^1,3, and Shayan Srinivasa Garani¹

¹Department of Electronic Systems Engineering, Indian Institute of Science, Bengaluru, India, 560012
²Department of Chemistry, University of Toronto, Toronto, Canada, M5S 3H6
³Department of Complex Systems, Weizmann Institute of Science, Rehovot, Israel, 7610001

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Abstract

We present the construction of standard entanglement-assisted (EA) qubit Reed-Muller (RM) codes and their tensor product variants from classical RM codes. We show that the EA RM codes obtained using the CSS construction have zero coding rate and negative catalytic rate. We further show that EA codes constructed from these same classical RM codes using the tensor product code (TPC) construction have positive coding rate and provide a subclass of EA RM TPCs that have positive catalytic rate, thus establishing the coding analog of superadditivity for this family of codes, useful towards quantum communications. We also generalize this analysis to obtain conditions for EA TPCs from classical codes to have positive catalytic rate when their corresponding EA CSS codes have zero rate.

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Popular summary

The phenomenon of superadditivity of quantum channel capacity involving two zero-capacity quantum channels that achieve a positive quantum capacity does not have a classical bearing. A coding analog of this phenomenon was first demonstrated for quantum CSS codes. Two classical codes individually yielding zero-rate quantum codes were combined to obtain a positive rate quantum code using the quantum tensor product construction. The present study further demonstrates that the coding analog of superadditivity is applicable for constructing quantum codes from well-studied Reed-Muller codes that individually yield zero-rate quantum codes. Conditions for observing this phenomena with polar codes and other classical codes are provided. Our findings enable the construction of many algebraic quantum codes with good properties, useful towards quantum communications.

► BibTeX data

@article{Nadkarni2024entanglement, doi = {10.22331/q-2024-05-02-1329}, url = {https://doi.org/10.22331/q-2024-05-02-1329}, title = {Entanglement-assisted {Q}uantum {R}eed-{M}uller {T}ensor {P}roduct {C}odes}, author = {Nadkarni, Priya J. and Jayakumar, Praveen and Behera, Arpit and Garani, Shayan Srinivasa}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {8}, pages = {1329}, month = may, year = {2024} }

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Source: https://quantum-journal.org/papers/q-2024-05-02-1329/

Time Stamp: May 2, 2024

Time Stamp: Jan 4, 2024

Entanglement-assisted Quantum Reed-Muller Tensor Product Codes

Republished By Plato

Abstract

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