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- W4308481544 abstract "The quantum guesswork quantifies the minimum number of queries needed to guess the state of a quantum ensemble if one is allowed to query only one state at a time. Previous approaches to the computation of the guesswork were based on standard semi-definite programming techniques and therefore lead to approximated results. In contrast, we show that computing the quantum guesswork of qubit ensembles with uniform probability distribution corresponds to solving a quadratic assignment problem and we provide an algorithm that, upon the input of any qubit ensemble over a discrete ring, after finitely many steps outputs the exact closed-form expression of its guesswork. While in general the complexity of our guesswork-computing algorithm is factorial in the number of states, our main result consists of showing a more-than-quadratic speedup for symmetric ensembles, a scenario corresponding to the three-dimensional analog of the maximization version of the turbine-balancing problem. To find such symmetries, we provide an algorithm that, upon the input of any point set over a discrete ring, after finitely many steps outputs its exact symmetries. The complexity of our symmetries-finding algorithm is polynomial in the number of points. As examples, we compute the guesswork of regular and quasi-regular sets of qubit states." @default.
- W4308481544 created "2022-11-12" @default.
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- W4308481544 date "2021-12-02" @default.
- W4308481544 modified "2023-09-25" @default.
- W4308481544 title "Computing the quantum guesswork: a quadratic assignment problem" @default.
- W4308481544 doi "https://doi.org/10.26421/qic23.9-10-1" @default.
- W4308481544 hasPublicationYear "2021" @default.
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