Encrypted clones can leak: Classification of informative subsets in Quantum Encrypted Cloning

Abstract

Encrypted cloning enables the redundant storage of an unknown qubit while remaining compatible with the no-cloning theorem, since only one clone can later be recovered through key-consuming decryption. Because encryption in this protocol is introduced to enable cloning-compatible redundancy rather than to guarantee confidentiality by design, its secrecy properties must be assessed explicitly. Here we classify the subsets of the encrypted-clone storage register into authorized, completely non-informative, and partially informative sets. We show that intermediate non-authorized subsets may retain only a restricted residual dependence on the input state, and we characterize exactly when this dependence occurs. The resulting leakage pattern is parity-dependent, revealing a structural confidentiality limitation of encrypted cloning.

v2: added a characterization of the strength and locality of the residual leakage (perfect discrimination on the y-axis; leakage carried by the full-weight Y\otimes^n correlator only, hence accessible only to joint measurements). Corrected a sign inconsistency in the n=3 example of Sec. 3 and minor typographical errors; the general classification is unchanged