Abstract
The no-cloning theorem is a fundamental principle of quantum mechanics that prohibits the perfect duplication of arbitrary unknown quantum states, thereby ruling out classical redundancy strategies based on direct replication. As a consequence, quantum error correction must rely on structured encodings rather than duplication. In this work, we investigate how no-cloning constraints naturally lead to algebraic frameworks for quantum error-correcting codes. Quantum information is encoded into subspaces of multi-qubit systems, where protection is achieved through entanglement and syndrome-based measurements. We show that this structure can be effectively realized using algebraic coding theory, where self-orthogonality and duality replace classical redundancy.
Status
Graduate
Department
Mathematics
College
College of Arts and Sciences
Campus
Athens
Faculty Mentor
Sergio Lopez-Permouth
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
No-Cloning Constraints and Algebraic Structures in Quantum Error-Correcting Codes
The no-cloning theorem is a fundamental principle of quantum mechanics that prohibits the perfect duplication of arbitrary unknown quantum states, thereby ruling out classical redundancy strategies based on direct replication. As a consequence, quantum error correction must rely on structured encodings rather than duplication. In this work, we investigate how no-cloning constraints naturally lead to algebraic frameworks for quantum error-correcting codes. Quantum information is encoded into subspaces of multi-qubit systems, where protection is achieved through entanglement and syndrome-based measurements. We show that this structure can be effectively realized using algebraic coding theory, where self-orthogonality and duality replace classical redundancy.