arXiv subjects

M. A. Nielsen

Publications and source records attributed to M. A. Nielsen.

27 records · Page 2Linked to original sources

arXiv1997

Computable functions, quantum measurements, and quantum dynamics

We construct quantum mechanical observables and unitary operators which, if implemented in physical systems as measurements and dynamical evolutions, would contradict the Church-Turing thesis which lies at the foundation of computer science. We conclude that either the Church-Turing thesis needs revision, or that only restricted classes of observables may be realized, in principle, as measurements, and that only restricted classes of unitary operators may be realized, in principle, as dynamics.

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arXiv1997

Approximate quantum error correction can lead to better codes

We present relaxed criteria for quantum error correction which are useful when the specific dominant noise process is known. These criteria have no classical analogue. As an example, we provide a four-bit code which corrects for a single amplitude damping error. This code violates the usual Hamming bound calculated for a Pauli description of the error process, and does not fit into the GF(4) classification.

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arXiv1997

Programmable quantum gate arrays

We show how to construct quantum gate arrays that can be programmed to perform different unitary operations on a data register, depending on the input to some program register. It is shown that a universal quantum gate array - a gate array which can be programmed to perform any unitary operation - exists only if one allows the gate array to operate in a probabilistic fashion. The universal quantum gate array we construct requires an exponentially smaller number of gates than a classical universal gate array.

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arXiv1997

Information transmission through a noisy quantum channel

Noisy quantum channels may be used in many information carrying applications. We show that different applications may result in different channel capacities. Upper bounds on several of these capacities are proved. These bounds are based on the coherent information, which plays a role in quantum information theory analogous to that played by the mutual information in classical information theory. Many new properties of the coherent information and entanglement fidelity are proved. Two non-classical features of the coherent information are demonstrated: the failure of subadditivity, and the failure of the pipelining inequality. Both properties arise as a consequence of quantum entanglement, and give quantum information new features not found in classical information theory. The problem of a noisy quantum channel with a classical observer measuring the environment is introduced, and bounds on the corresponding channel capacity proved. These bounds are always greater than for the unobserved channel. We conclude with a summary of open problems.

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arXiv1996

Prescription for experimental determination of the dynamics of a quantum black box

We give an explicit prescription for experimentally determining the evolution operators which completely describe the dynamics of a quantum mechanical black box -- an arbitrary open quantum system. We show necessary and sufficient conditions for this to be possible, and illustrate the general theory by considering specifically one and two quantum bit systems. These procedures may be useful in the comparative evaluation of experimental quantum measurement, communication, and computation systems.

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arXiv1996

Reversible quantum operations and their application to teleportation

Quantum operations provide a general description of the state changes allowed by quantum mechanics. Simple necessary and sufficient conditions for an ideal quantum operation to be reversible by a unitary operation are derived in this paper. These results generalize recent work on reversible measurements by Mabuchi and Zoller [Phys. Rev. Lett. {\bf 76}, 3108 (1996)]. Quantum teleportation can be understood as a special case of the problem of reversing quantum operations. We characterize completely teleportation schemes of the type proposed by Bennett {\it et al.} [Phys. Rev. Lett. {\bf 70}, 1895 (1993)].

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arXiv1996

The entanglement fidelity and quantum error correction

Two new expressions for the entanglement fidelity recently introduced by Schumacher (LANL e-print quant-ph/9604023, to appear in Phys. Rev. A) are derived. These expressions show that it is the entanglement fidelity which must be maximized when performing error correction on qubits for quantum computers, not the fidelity, which is the most-often used generalization of the probability for storing a qubit correctly.

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arXiv1996

Quantum data processing and error correction

This paper investigates properties of noisy quantum information channels. We define a new quantity called {\em 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 sufficient condition for the existence of perfect quantum error correction.

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arXiv1995

Chaos in the Quantum Measurement Record

We investigate measures of chaos in the measurement record of a quantum system which is being observed. Such measures are attractive because they can be directly connected to experiment. Two measures of chaos in the measurement record are defined and investigated numerically for the case of a quantum kicked top. A smooth transition between chaotic and regular behavior is found.

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