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1 What the book is about This book provides a thorough introduction to quantum information theory and quantum computation in general, especially covering the theoretical and computational , rather than experimental, aspects of these fields. The particular strengths of the volume are: the completeness of both basic and more advanced aspects of quantum… (More)

- M. A. Nielsen
- 1999

Suppose Alice and Bob jointly possess a pure state, jc͘. Using local operations on their respective systems and classical communication it may be possible for Alice and Bob to transform jc͘ into another joint state jf͘. This Letter gives necessary and sufficient conditions for this process of entanglement transformation to be possible. These conditions… (More)

- Christopher M. Dawson, Michael A. Nielsen
- Quantum Information & Computation
- 2006

This pedagogical review presents the proof of the Solovay-Kitaev theorem in the form of an efficient classical algorithm for compiling an arbitrary single-qubit gate into a sequence of gates from a fixed and finite set. The algorithm can be used, for example, to compile Shor's algorithm, which uses rotations of π/2 k , into an efficient fault-tolerant form… (More)

- Howard Barnum, Emanuel Knill, Michael A. Nielsen
- IEEE Trans. Information Theory
- 2000

— We show the equivalence of two different notions of quantum channel capacity: that which uses the en-tanglement fidelity as its criterion for success in transmission , and that which uses the minimum fidelity of pure states in a subspace of the input Hilbert space as its criterion. As a corollary, any source with entropy less than the capacity may be… (More)

This article is a short introduction to and review of the cluster-state model of quantum computation, in which coherent quantum information processing is accomplished via a sequence of single-qubit measurements applied to a fixed quantum state known as a cluster state. We also discuss a few novel properties of the model, including a proof that the cluster… (More)

This paper investigates properties of noisy quantum information channels. We deene a new quantity called coherent information which measures the amount of quantum information conveyed in the noisy channel. This quantity can never be increased by quantum information processing, and it yields a simple necessary and suucient condition for the existence of… (More)

This Letter presents a simple formula for the average fidelity between a unitary quantum gate and a general quantum operation on a qudit, generalizing the formula for qubits found by Bowdrey et al. [Phys. Lett. A 294 (2002) 258]. This formula may be useful for experimental determination of average gate fidelity. We also give a simplified proof of a formula… (More)

- Michael A. Nielsen
- Quantum Information & Computation
- 2006

- Michael A Nielsen, Mark R Dowling, Mile Gu, Andrew C Doherty
- Science
- 2006

Quantum computers hold great promise for solving interesting computational problems, but it remains a challenge to find efficient quantum circuits that can perform these complicated tasks. Here we show that finding optimal quantum circuits is essentially equivalent to finding the shortest path between two points in a certain curved geometry. By recasting… (More)

- Michael A. Nielsen, Dénes Petz
- Quantum Information & Computation
- 2005