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The study investigates the emergence of structural primitives in encrypted quantum cloning through coset decomposition.

February 20, 2026Open Access

Encrypted Cloning via Icosahedral Coset Structure: A Binary Polyhedral Correspondence

Key Points

The study investigates the emergence of structural primitives in encrypted quantum cloning through coset decomposition.
Analyzed structural primitives of encrypted quantum cloning using the binary icosahedral group.
Examined the shift in opacity and its implications at specific angles, particularly θ = π/3.
Utilized IBM Quantum data to validate findings through statistical consistency regarding sector hierarchy.
Identified a transition of opacity from a local state to a decryption frame at θ = π/3.
Demonstrated that sector hierarchy aligns with theoretical predictions at > 3.9σ per gap.

Abstract

We show that the structural primitives of encrypted quantum cloning Yamaguchi and Kempf, PRL 136, 010801 (2026)—index-5 copies, one-time key exclusivity, and encrypted-state opacity — emerge from the coset decomposition 2I : 2T = 5 of the binary icosahedral group. At θ = π/3 the opacity shifts from the local state (|r| = 0.937) to the decryption frame, realizing a public-parameter / hidden-frame (label-hiding) structure. IBM Quantum data are consistent with the predicted sector hierarchy at > 3.9σ per gap.

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