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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)

— 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 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 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 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)

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)

We introduce a model of computation based on read only memory (ROM), which allows us to compare the space-efficiency of reversible, error-free classical computation with reversible, error-free quantum computation. We show that a ROM-based quantum computer with one writable qubit is universal, whilst two writable bits are required for a universal classical… (More)