Beyond the Canonical Protocol: Quantum Encrypted Cloning from Secret-Sharing Access Structures

• URL: http://arxiv.org/abs/2606.06552v1
• Date: Thu, 04 Jun 2026 09:23:16 GMT
• Title: Beyond the Canonical Protocol: Quantum Encrypted Cloning from Secret-Sharing Access Structures
• Abstract summary: Quantum encrypted cloning shows that an unknown quantum state can be distributed into multiple encrypted copies.<n>Recent work has related canonical encrypted-cloning protocols to particular forms of quantum secret sharing.<n>We use QSS access structures as a design library from which encrypted-cloning schemes can be extracted.
• Score: 1.8941846253692634
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum encrypted cloning shows that an unknown quantum state can be distributed into multiple encrypted copies without contradicting the no-cloning theorem: each copy is unusable on its own, but can be redeemed together with a suitable quantum key. Recent work has related canonical encrypted-cloning protocols to particular forms of quantum secret sharing. Here we take the converse perspective: instead of mapping a given encrypted-cloning protocol into QSS, we use QSS access structures as a design library from which encrypted-cloning schemes can be extracted. The criterion is access-structural. A QSS scheme supports a quantum encrypted-cloning structure whenever it contains a family of qualified sets with a non-qualified common intersection. The common subsystem is interpreted as the key, while the non-common parts are interpreted as encrypted clones relative to that key. Thus quantum encrypted cloning does not require a new notion of recoverability beyond QSS; what changes is the operational reading of QSS constituents as a mechanism for delayed and alternative redemption opportunities. This viewpoint separates redemption from perfect secrecy. Perfect QSS yields encrypted-cloning schemes with forbidden non-qualified subsystems, whereas ramp QSS naturally allows intermediate, partially informative non-redeeming subsystems. The resulting framework broadens quantum encrypted cloning from a specific protocol to a general access-structure primitive. We illustrate the extraction principle with threshold-like, ramp, hierarchical, and compartmented architectures, showing how encrypted clones may be symmetric or asymmetric, individual or composite, perfectly hidden or leaky. Equivalently, these constructions can be viewed as overlapping erasure-recovery regions of an isometric quantum code. This establishes secret sharing as a systematic design language for encrypted quantum redundancy.

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