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Stephen D. Bartlett

Publications and source records attributed to Stephen D. Bartlett.

138 records · Page 8Linked to original sources
arXiv2002

Classical Dynamics as Constrained Quantum Dynamics

We show that the classical mechanics of an algebraic model are implied by its quantizations. An algebraic model is defined, and the corresponding classical and quantum realizations are given in terms of a spectrum generating algebra. Classical equations of motion are then obtained by constraining the quantal dynamics of an algebraic model to an appropriate coherent state manifold. For the cases where the coherent state manifold is not symplectic, it is shown that there exist natural projections onto classical phase spaces. These results are illustrated with the extended example of an asymmetric top.

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arXiv2002

From Qubits to Continuous-Variable Quantum Computation

By encoding a qudit in a harmonic oscillator and investigating the d --> infinity limit, we give an entirely new realization of continuous-variable quantum computation. The generalized Pauli group is generated by number and phase operators for harmonic oscillators.

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arXiv2002

Vector coherent state representations, induced representations, and geometric quantization: I. Scalar coherent state representations

Coherent state theory is shown to reproduce three categories of representations of the spectrum generating algebra for an algebraic model: (i) classical realizations which are the starting point for geometric quantization; (ii) induced unitary representations corresponding to prequantization; and (iii) irreducible unitary representations obtained in geometric quantization by choice of a polarization. These representations establish an intimate relation between coherent state theory and geometric quantization in the context of induced representations.

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arXiv2002

Vector coherent state representations, induced representations, and geometric quantization: II. Vector coherent state representations

It is shown here and in the preceeding paper (quant-ph/0201129) that vector coherent state theory, the theory of induced representations, and geometric quantization provide alternative but equivalent quantizations of an algebraic model. The relationships are useful because some constructions are simpler and more natural from one perspective than another. More importantly, each approach suggests ways of generalizing its counterparts. In this paper, we focus on the construction of quantum models for algebraic systems with intrinsic degrees of freedom. Semi-classical partial quantizations, for which only the intrinsic degrees of freedom are quantized, arise naturally out of this construction. The quantization of the SU(3) and rigid rotor models are considered as examples.

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arXiv2002

Quantum Encodings in Spin Systems and Harmonic Oscillators

We show that higher-dimensional versions of qubits, or qudits, can be encoded into spin systems and into harmonic oscillators, yielding important advantages for quantum computation. Whereas qubit-based quantum computation is adequate for analyses of quantum vs classical computation, in practice qubits are often realized in higher-dimensional systems by truncating all but two levels, thereby reducing the size of the precious Hilbert space. We develop natural qudit gates for universal quantum computation, and exploit the entire accessible Hilbert space. Mathematically, we give representations of the generalized Pauli group for qudits in coupled spin systems and harmonic oscillators, and include analyses of the qubit and the infinite-dimensional limits.

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arXiv2002

Photon counting schemes and performance of non-deterministic nonlinear gates in linear optics

The performance of nondeterministic nonlinear gates in linear optics relies on the photon counting scheme being employed and the efficiencies of the detectors in such schemes. We assess the performance of the nonlinear sign gate, which is a critical component of linear optical quantum computing, for two standard photon counting methods: the double detector array and the visible light photon counter. Our analysis shows that the double detector array is insufficient to provide the photon counting capability for effective nondeterministic nonlinear transformations, and we determine the gate fidelity for both photon counting methods as a function of detector efficiencies.

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arXiv2002

Quantum Computation with Harmonic Oscillators

By encoding a qudit in a harmonic oscillator and investigating the infinite limit, we give an entirely new realization of continuous-variable quantum computation. The generalized Pauli group is generated by number and phase operators for harmonic oscillators. We describe a physical realization in terms of modes in a microwave cavity, coupled via a standard Kerr nonlinearity.

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arXiv2002

Quantum walks in higher dimensions

We analyze the quantum walk in higher spatial dimensions and compare classical and quantum spreading as a function of time. Tensor products of Hadamard transformations and the discrete Fourier transform arise as natural extensions of the quantum coin toss in the one-dimensional walk simulation, and other illustrative transformations are also investigated. We find that entanglement between the dimensions serves to reduce the rate of spread of the quantum walk. The classical limit is obtained by introducing a random phase variable.

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arXiv2002

Universal continuous-variable quantum computation: Requirement of optical nonlinearity for photon counting

Although universal continuous-variable quantum computation cannot be achieved via linear optics (including squeezing), homodyne detection and feed-forward, inclusion of ideal photon counting measurements overcomes this obstacle. These measurements are sometimes described by arrays of beam splitters to distribute the photons across several modes. We show that such a scheme cannot be used to implement ideal photon counting and that such measurements necessarily involve nonlinear evolution. However, this requirement of nonlinearity can be moved "off-line," thereby permitting universal continuous-variable quantum computation with linear optics.

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arXiv2002

Efficient Classical Simulation of Continuous Variable Quantum Information Processes

We obtain sufficient conditions for the efficient simulation of a continuous variable quantum algorithm or process on a classical computer. The resulting theorem is an extension of the Gottesman-Knill theorem to continuous variable quantum information. For a collection of harmonic oscillators, any quantum process that begins with unentangled Gaussian states, performs only transformations generated by Hamiltonians that are quadratic in the canonical operators, and involves only measurements of canonical operators (including finite losses) and suitable operations conditioned on these measurements can be simulated efficiently on a classical computer.

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arXiv2001

Geometric Phase of Three-level Systems in Interferometry

We present the first scheme for producing and measuring an Abelian geometric phase shift in a three-level system where states are invariant under a non-Abelian group. In contrast to existing experiments and proposals for experiments, based on U(1)-invariant states, our scheme geodesically evolves U(2)-invariant states in a four-dimensional SU(3)/U(2) space and is physically realized via a three-channel optical interferometer.

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