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We develop a strong connection between maximally commuting bases of orthogonal unitary matrices and mutually unbiased bases. A necessary condition of the existence of mutually unbiased bases for any finite dimension is obtained. Then a constructive proof of the existence of mutually unbiased bases for dimensions that are powers of primes is presented. It is(More)
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We introduce a scalable searching protocol for locating and retrieving content in random networks with Power-Law (PL) and heavy-tailed degree distributions. The proposed algorithm is capable of finding any content in the network with probability one in time O(log N), with a total traffic that provably scales sub-linearly with the network size, N. Moreover,(More)
We prove the security of quantum key distribution against the most general attacks which can be performed on the channel, by an eavesdropper who has unlimited computation abilities, and the full power allowed by the rules of classical and quantum physics. A key created that way can then be used to transmit secure messages in a way that their security is(More)
We characterize the complete set of protocols that may be used to securely encrypt n quantum bits using secret and random classical bits. In addition to the application of such quantum encryption protocols to quantum data security, our framework allows for generalizations of many classical cryptographic protocols to quantum data. We show that the encrypted(More)
We introduce a scalable searching algorithm for finding nodes and contents in random networks with Power-Law (PL) and heavy-tailed degree distributions. The network is searched using a prob-abilistic broadcast algorithm, where a query message is relayed on each edge with probability just above the bond percolation threshold of the network. We show that if(More)
A novel universal and fault-tolerant basis (set of gates) for quantum computation is described. Such a set is necessary to perform quantum computation in a realistic noisy environment. The new basis consists of two single-qubit gates (Hadamard and σ z 1 4), and one double-qubit gate (Controlled-NOT). Since the set consisting of Controlled-NOT and Hadamard(More)