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Quantum information leverages properties of quantum behaviors in order to perform useful tasks such as secure communication and randomness certification. Nevertheless, not much is known about the intricate geometric features of the set quantum behaviors. In this paper we study the structure of the set of quantum correlators using semidefinite programming. Our main results are (i) a generalization of the analytic description by Tsirelson-Landau-Masanes, (ii) necessary and sufficient conditions for extremality and exposedness, and (iii) an operational interpretation of extremality in the case of two dichotomic measurements, in terms of self-testing. We illustrate the usefulness of our theoretical findings with many examples and extensive computational work.
We apply semidefinite programming for designing 1 to 2 symmetric qubit quantum cloners. These are optimized for the average fidelity of their joint output state with respect to a product of multiple originals. We design 1 to 2 quantum bit cloners usi
Quantum error correction (QEC) is an essential element of physical quantum information processing systems. Most QEC efforts focus on extending classical error correction schemes to the quantum regime. The input to a noisy system is embedded in a code
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