The Entropy Characterization of Quantum MDS Codes

• URL: http://arxiv.org/abs/2505.19826v2
• Date: Wed, 11 Jun 2025 07:05:42 GMT
• Title: The Entropy Characterization of Quantum MDS Codes
• Authors: Hua Sun,
• Abstract summary: The entropy of the joint state of the reference system of $k$ qudits and the $n$ coded qudits is fully characterized.
• Score: 38.352346029258385
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: An $[[n,k,d]]$ quantum maximum-distance-separable code maps $k$ source qudits to $n$ coded qudits such that any $n-(d-1)$ coded qudits may recover all source qudits and $n = k + 2 (d-1)$. The entropy of the joint state of the reference system of $k$ qudits and the $n$ coded qudits is fully characterized - the joint state must be pure, i.e., has entropy zero; and any sub-system whose number of qudits is at most half of $k+n$, the total number of qudits in the joint state must be maximally mixed, i.e., has entropy equal to its size.

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