The Quantum Key Distribution (QKD) protocol BB84 has been proven secure against several important types of attacks: the collective attacks and the joint attacks. Here we analyze the security of a modified BB84 protocol, for which information is sent only in the z basis while testing is done in both the z and the x bases, against collective attacks. The proof follows the framework of a previous paper (Boyer, Gelles, and Mor, 2009), but it avoids the classical information-theoretical analysis that caused problems with composability. We show that this modified BB84 protocol is as secure against collective attacks as the original BB84 protocol, and that it requires more bits for testing.

In ensemble (or bulk) quantum computation, all computations are performed on an ensemble of computers rather than on a single computer. Measurements of qubits in an individual computer cannot be performed; instead, only expectation values (over the complete ensemble of computers) can be measured. As a result of this limitation on the model of computation, many algorithms cannot be processed directly on such computers, and must be modified, as the common strategy of delaying the measurements usually does not resolve this ensemble-measurement problem. Here we present several new strategies for resolving this problem. Based on these strategies we provide new versions of some of the most important quantum algorithms, versions that are suitable for implementing on ensemble quantum computers, e.g., on liquid NMR quantum computers. These algorithms are Shor's factorization algorithm, Grover's search algorithm (with several marked items), and an algorithm for quantum fault-tolerant computation. The first two algorithms are simply modified using a randomizing and a sorting strategies. For the last algorithm, we develop a classical-quantum hybrid strategy for removing measurements. We use it to present a novel quantum fault-tolerant scheme. More explicitly, we present schemes for fault-tolerant measurement-free implementation of Toffoli and σ(z)(¼) as these operations cannot be implemented "bitwise", and their standard fault-tolerant implementations require measurement.

Simultaneous near‐certain preparation of qubits (quantum bits) in their ground states is a key hurdle in quantum computing proposals as varied as liquid‐state NMR and ion traps. “Closed‐system” cooling mechanisms are of limited applicability due to the need for a continual supply of ancillas for fault tolerance and to the high initial temperatures of some systems. “Open‐system” mechanisms are therefore required. We describe a new, efficient initialization procedure for such open systems. With this procedure, an n‐qubit device that is originally maximally mixed, but is in contact with a heat bath of bias $\varepsilon \gg 2^{-n}$, can be almost perfectly initialized. This performance is optimal due to a newly discovered threshold effect: For bias $\varepsilon \ll 2^{-n}$ no cooling procedure can, even in principle (running indefinitely without any decoherence), significantly initialize even a single qubit.

In ensemble (or bulk) quantum computation, all computations are performed on an ensemble of computers rather than on a single computer. Measurements of qubits in an individual computer cannot be performed; instead, only expectation values (over the complete ensemble of computers) can be measured. As a result of this limitation on the model of computation, many algorithms cannot be processed directly on such computers, and must be modified. We provide modification of the fault tolerant quantum computation protocols to enable processing on ensemble quantum computers.

Article Free Access Share on A proof of the security of quantum key distribution (extended abstract) Authors: Eli Biham Computer Science Department, Technion, Haifa 32000, Israel Computer Science Department, Technion, Haifa 32000, IsraelView Profile , Michel Boyer DIRO, Université de Montréal, Montréal, Canada DIRO, Université de Montréal, Montréal, CanadaView Profile , P. Oscar Boykin Dept. of Electrical Engineering, UCLA, Los Angeles, CA Dept. of Electrical Engineering, UCLA, Los Angeles, CAView Profile , Tal Mor Dept. of Electrical Engineering, UCLA, Los Angeles, CA and Dept. of Electrical Engineering, College of Judea and Samaria, Ariel, Israel Dept. of Electrical Engineering, UCLA, Los Angeles, CA and Dept. of Electrical Engineering, College of Judea and Samaria, Ariel, IsraelView Profile , Vwani Roychowdhury Dept. of Electrical Engineering, College of Judea and Samaria, Ariel, Israel Dept. of Electrical Engineering, College of Judea and Samaria, Ariel, IsraelView Profile Authors Info & Claims STOC '00: Proceedings of the thirty-second annual ACM symposium on Theory of computingMay 2000 Pages 715–724https://doi.org/10.1145/335305.335406Published:01 May 2000Publication History 38citation1,057DownloadsMetricsTotal Citations38Total Downloads1,057Last 12 Months95Last 6 weeks17 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

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 /spl sigma//sub z//sup 1/4 /) and one double-qubit gate (Controlled-NOT). Since the set consisting of Controlled-NOT and Hadamard gates is not universal, the new basis achieves universality by including only one additional elementary (in the sense that it does not include angles that are irrational multiples of /spl pi/) single-qubit gate, and hence, is potentially the simplest universal basis that one can construct. We also provide an alternative proof of universality for the only other known class of universal and fault-tolerant basis proposed by P.W. Shor (1996) and A.Y. Kitaev (1997).