Main article: Quantum cryptography Integer factorization , which underpins the security of public key cryptographic systems, is believed to be computationally infeasible with an ordinary computer for large integers if they are the product of few prime numbers e. This ability would allow a quantum computer to break many of the cryptographic systems in use today, in the sense that there would be a polynomial time in the number of digits of the integer algorithm for solving the problem. These are used to protect secure Web pages, encrypted email, and many other types of data. Breaking these would have significant ramifications for electronic privacy and security. However, other cryptographic algorithms do not appear to be broken by those algorithms. Quantum cryptography could potentially fulfill some of the functions of public key cryptography.

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Stan n-kubitowego rejestru kwantowego jest zatem opisywany jako wektor znormalizowany w 2n-wymiarowej, zespolonej przestrzeni Hilberta. Kwantowa Maszyna Turinga.

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