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There is one main key point in the description of your question: Is $s$ meant to be a classical secret or a quantum secret? If $s$ is meant to be a classical secret, then the answer is yes, but there is not really much quantum in the positive answer. If $s_A$, $s_B$, and $s_C$ are all $d$-state digits, then there is a simple construction that works in ...

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