A Universal Two--Bit Gate for Quantum Computation

We prove the existence of a class of two--input, two--output gates any one of which is universal for quantum computation. This is done by explicitly constructing the three--bit gate introduced by Deutsch [Proc.~R.~Soc.~London.~A {\bf 425}, 73 (1989)] as a network consisting of replicas of a single two--bit gate.Comment: 3 pages, RevTeX, two figures in a uuencoded fil

Quantum Algorithms: Entanglement Enhanced Information Processing

We discuss the fundamental role of entanglement as the essential nonclassical feature providing the computational speed-up in the known quantum algorithms. We review the construction of the Fourier transform on an Abelian group and the principles underlying the fast Fourier transform algorithm. We describe the implementation of the FFT algorithm for the group of integers modulo 2^n in the quantum context, showing how the group-theoretic formalism leads to the standard quantum network and identifying the property of entanglement that gives rise to the exponential speedup (compared to the classical FFT). Finally we outline the use of the Fourier transform in extracting periodicities, which underlies its utility in the known quantum algorithms.Comment: 17 pages latex, no figures. To appear in Phil. Trans. Roy. Soc. (Lond.) 1998, Proceedings of Royal Society Discussion Meeting ``Quantum Computation: Theory and Experiment'', held in November 199

Direct estimation of functionals of density operators by local operations and classical communication

We present a method of direct estimation of important properties of a shared bipartite quantum state, within the "distant laboratories" paradigm, using only local operations and classical communication. We apply this procedure to spectrum estimation of shared states, and locally implementable structural physical approximations to incompletely positive maps. This procedure can also be applied to the estimation of channel capacity and measures of entanglement

Quantum networks for elementary arithmetic operations

Quantum computers require quantum arithmetic. We provide an explicit construction of quantum networks effecting basic arithmetic operations: from addition to modular exponentiation. Quantum modular exponentiation seems to be the most difficult (time and space consuming) part of Shor's quantum factorising algorithm. We show that the auxiliary memory required to perform this operation in a reversible way grows linearly with the size of the number to be factorised

Analysis and interpretation of high transverse entanglement in optical parametric down conversion

Quantum entanglement associated with transverse wave vectors of down conversion photons is investigated based on the Schmidt decomposition method. We show that transverse entanglement involves two variables: orbital angular momentum and transverse frequency. We show that in the monochromatic limit high values of entanglement are closely controlled by a single parameter resulting from the competition between (transverse) momentum conservation and longitudinal phase matching. We examine the features of the Schmidt eigenmodes, and indicate how entanglement can be enhanced by suitable mode selection methods.Comment: 4 pages, 4 figure

Optimal purification of single qubits

We introduce a new decomposition of the multiqubit states of the form $\rho^{\otimes N}$ and employ it to construct the optimal single qubit purification procedure. The same decomposition allows us to study optimal quantum cloning and state estimation of mixed states.Comment: 4 pages, 1 figur

Robust Multi-Partite Multi-Level Quantum Protocols

We present a tripartite three-level state that allows a secret sharing protocol among the three parties, or a quantum key distribution protocol between any two parties. The state used in this scheme contains entanglement even after one system is traced out. We show how to utilize this residual entanglement for quantum key distribution purposes, and propose a realization of the scheme using entanglement of orbital angular momentum states of photons.Comment: 9 pages, 2 figure

Quantum Cryptography with Coherent States

The safety of a quantum key distribution system relies on the fact that any eavesdropping attempt on the quantum channel creates errors in the transmission. For a given error rate, the amount of information that may have leaked to the eavesdropper depends on both the particular system and the eavesdropping strategy. In this work, we discuss quantum cryptographic protocols based on the transmission of weak coherent states and present a new system, based on a symbiosis of two existing ones, and for which the information available to the eavesdropper is significantly reduced. This system is therefore safer than the two previous ones. We also suggest a possible experimental implementation.Comment: 20 pp. Revtex, Figures available from the authors upon request, To be published in PRA (March 95

Quantum cryptography based on qutrit Bell inequalities

We present a cryptographic protocol based upon entangled qutrit pairs. We analyze the scheme under a symmetric incoherent attack and plot the region for which the protocol is secure and compare this with the region of violations of certain Bell inequalities

Mimicking Time Evolution within a Quantum Ground State: Ground-State Quantum Computation, Cloning, and Teleportation

Ground-state quantum computers mimic quantum mechanical time evolution within the amplitudes of a time-independent quantum state. We explore the principles that constrain this mimicking. A no-cloning argument is found to impose strong restrictions. It is shown, however, that there is flexibility that can be exploited using quantum teleportation methods to improve ground-state quantum computer design.Comment: 10 pages, 7 figure