We present a number of schemes that use quantum mechanics to preserve privacy, in particular, we show that entangled quantum states can be useful in maintaining privacy. We further develop our original proposal [see Phys. Lett. A 349, 75 (2006)] for protecting privacy in voting, and examine its security under certain types of attacks, in particular dishonest voters and external eavesdroppers. A variation of these quantum-based schemes can be used for multi-party function evaluation. We consider functions corresponding to group multiplication of $N$ group elements, with each element chosen by a different party. We show how quantum mechanics can be useful in maintaining the privacy of the choices group elements.Comment: 11 pages, no figure

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We discuss three applications of efficient quantum algorithms to determining properties of permutations and group automorphisms. The first uses the Bernstein-Vazirani algorithm to determine an unknown homomorphism from Z p−1 m to Aut͑Z p ͒ where p is prime. The remaining two make use of modifications of the Grover search algorithm. The first finds the fixed point of a permutation or an automorphism ͑assuming it has only one besides the identity͒. It can be generalized to find cycles of a specified size for permutations or orbits of a specified size for automorphisms. The second finds which of a set of permutations or automorphisms maps one particular element of a set or group onto another. This has relevance to the conjugacy problem for groups. We show how two of these algorithms can be implemented via programmable quantum processors. This approach opens new perspectives in quantum information processing when both the data and the programs are represented by states of quantum registers. In particular, quantum programs that specify control over data can be treated using methods of quantum information theory.

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