Classification of informative subsets in quantum encrypted cloning on qudits

• URL: http://arxiv.org/abs/2605.11642v1
• Date: Tue, 12 May 2026 07:04:10 GMT
• Title: Classification of informative subsets in quantum encrypted cloning on qudits
• Abstract summary: We systematically classify the informative subsets of the storage register in the qudit encrypted-cloning protocol.<n>We show that the presence or absence of information leakage is determined by the solution set of a system of congruences.<n>Our results extend the parity-based classification known for qubits to arbitrary finite dimensions.
• Score: 6.632912569027217
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Encrypted cloning offers a means of introducing redundancy into quantum storage while respecting the no-cloning theorem: an unknown state is encoded into multiple signal-noise pairs, and only authorized subsets can recover the original information. However, the leakage properties of unauthorized subsets particularly for higher-dimensional systems (qudits) have remained unexplored. In this work, we systematically classify the informative subsets of the storage register in the qudit encrypted-cloning protocol. We focus on unauthorized subsets of size $n$ that contain exactly one qudit from each signal-noise pair. We show that the presence or absence of information leakage is determined by the solution set of a system of congruences whose coefficients depend on the dimension $d$ and on the numbers of signal and noise qudits in the subset. The reduced state is completely uninformative if and only if the congruence system admits only the trivial solution; otherwise, it retains a residual dependence on the input state through specific generalized Pauli operators. Low-dimensional examples ($n=1,2,3$) are worked out explicitly, and the complete classification is expressed in terms of a greatest-common-divisor condition. Our results extend the parity-based classification known for qubits ($d=2$) to arbitrary finite dimensions, revealing a dimension-dependent boundary of confidentiality in encrypted cloning.

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