Sampling in a Quantum Population, and Applications

We propose a framework for analyzing classical sampling strategies for estimating the Hamming weight of a large string from a few sample positions, when applied to a multi-qubit quantum system instead. The framework shows how to interpret the result of such a strategy and how to define its accuracy when applied to a quantum system. Furthermore, we show how the accuracy of any strategy relates to its accuracy in its classical usage, which is well understood for the important examples. We show the usefulness of our framework by using it to obtain new and simple security proofs for the following quantum-cryptographic schemes: BB84 quantum-key-distribution, and quantum oblivious-transfer from