Coherent-state linear optical quantum computing gates using simplified diagonal superposition resource states

In this paper we explore the possibility of fundamental tests for coherent-state optical quantum computing gates [ T. C. Ralph et al. Phys. Rev. A 68 042319 (2003)] using sophisticated but not unrealistic quantum states. The major resource required in these gates is a state diagonal to the basis states. We use the recent observation that a squeezed single-photon state [S(r)∣1⟩] approximates well an odd superposition of coherent states (∣α⟩−∣−α⟩) to address the diagonal resource problem. The approximation only holds for relatively small α, and hence these gates cannot be used in a scalable scheme. We explore the effects on fidelities and probabilities in teleportation and a rotated Hadamard gate.

Quantum phase-space simulations of fermions and bosons

We introduce a unified Gaussian quantum operator representation for fermions and bosons. The representation extends existing phase-space methods to Fermi systems as well as the important case of Fermi-Bose mixtures. It enables simulations of the dynamics and thermal equilibrium states of many-body quantum systems from first principles. As an example, we numerically calculate finite-temperature correlation functions for the Fermi Hubbard model, with no evidence of the Fermi sign problem. (c) 2005 Elsevier B.V. All rights reserved.

Conditional quantum-state engineering using ancillary squeezed-vacuum states

We investigate an optical scheme to conditionally engineer quantum states using a beam splitter, homodyne detection, and a squeezed vacuum as an ancillar state. This scheme is efficient in producing non-Gaussian quantum states such as squeezed single photons and superpositions of coherent states (SCSs). We show that a SCS with well defined parity and high fidelity can be generated from a Fock state of n

Dual-symmetric Lagrangians in quantum electrodynamics: I. Conservation laws and multi-polar coupling

By using a complex field with a symmetric combination of electric and magnetic fields, a first-order covariant Lagrangian for Maxwell's equations is obtained, similar to the Lagrangian for the Dirac equation. This leads to a dual-symmetric quantum electrodynamic theory with an infinite set of local conservation laws. The dual symmetry is shown to correspond to a helical phase, conjugate to the conserved helicity. There is also a scaling symmetry, conjugate to the conserved entanglement. The results include a novel form of the photonic wavefunction, with a well-defined helicity number operator conjugate to the chiral phase, related to the fundamental dual symmetry. Interactions with charged particles can also be included. Transformations from minimal coupling to multi-polar or more general forms of coupling are particularly straightforward using this technique. The dual-symmetric version of quantum electrodynamics derived here has potential applications to nonlinear quantum optics and cavity quantum electrodynamics.

First-principles quantum dynamics in interacting Bose gases: I. The positive P representation

The performance of the positive P phase-space representation for exact many- body quantum dynamics is investigated. Gases of interacting bosons are considered, where the full quantum equations to simulate are of a Gross-Pitaevskii form with added Gaussian noise. This method gives tractable simulations of many-body systems because the number of variables scales linearly with the spatial lattice size. An expression for the useful simulation time is obtained, and checked in numerical simulations. The dynamics of first-, second- and third-order spatial correlations are calculated for a uniform interacting 1D Bose gas subjected to a change in scattering length. Propagation of correlations is seen. A comparison is made with other recent methods. The positive P method is particularly well suited to open systems as no conservation laws are hard-wired into the calculation. It also differs from most other recent approaches in that there is no truncation of any kind.

First-principles quantum simulations of dissociation of molecular condensates: Atom correlations in momentum space

We investigate the quantum many-body dynamics of dissociation of a Bose-Einstein condensate of molecular dimers into pairs of constituent bosonic atoms and analyze the resulting atom-atom correlations. The quantum fields of both the molecules and atoms are simulated from first principles in three dimensions using the positive-P representation method. This allows us to provide an exact treatment of the molecular field depletion and s-wave scattering interactions between the particles, as well as to extend the analysis to nonuniform systems. In the simplest uniform case, we find that the major source of atom-atom decorrelation is atom-atom recombination which produces molecules outside the initially occupied condensate mode. The unwanted molecules are formed from dissociated atom pairs with nonopposite momenta. The net effect of this process-which becomes increasingly significant for dissociation durations corresponding to more than about 40% conversion-is to reduce the atom-atom correlations. In addition, for nonuniform systems we find that mode mixing due to inhomogeneity can result in further degradation of the correlation signal. We characterize the correlation strength via the degree of squeezing of particle number-difference fluctuations in a certain momentum-space volume and show that the correlation strength can be increased if the signals are binned into larger counting volumes.

Modelling photo-detectors in quantum optics

Photo-detection plays a fundamental role in experimental quantum optics and is of particular importance in the emerging field of linear optics quantum computing. Present theoretical treatment of photo-detectors is highly idealized and fails to consider many important physical effects. We present a physically motivated model for photo-detectors which accommodates for the effects of finite resolution, bandwidth and efficiency, as well as dark counts and dead-time. We apply our model to two simple well-known applications, which illustrates the significance of these characteristics.

Quantum gate based on Stark tunable nanocrystal interactions with ultrahigh-Q/V field modes in fused silica microcavities

We investigate the use of nanocrystal quantum dots as a quantum bus element for preparing various quantum resources for use in photonic quantum technologies. Using the Stark-tuning property of nanocrystal quantum dots as well as the biexciton transition, we demonstrate a photonic controlled-NOT (CNOT) interaction between two logical photonic qubits comprising two cavity field modes each. We find the CNOT interaction to be a robust generator of photonic Bell states, even with relatively large biexciton losses. These results are discussed in light of the current state of the art of both microcavity fabrication and recent advances in nanocrystal quantum dot technology. Overall, we find that such a scheme should be feasible in the near future with appropriate refinements to both nanocrystal fabrication technology and microcavity design. Such a gate could serve as an active element in photonic-based quantum technologies.

Toy model for a relational formulation of quantum theory

In the absence of an external frame of reference-i.e., in background independent theories such as general relativity-physical degrees of freedom must describe relations between systems. Using a simple model, we investigate how such a relational quantum theory naturally arises by promoting reference systems to the status of dynamical entities. Our goal is twofold. First, we demonstrate using elementary quantum theory how any quantum mechanical experiment admits a purely relational description at a fundamental. Second, we describe how the original non-relational theory approximately emerges from the fully relational theory when reference systems become semi-classical. Our technique is motivated by a Bayesian approach to quantum mechanics, and relies on the noiseless subsystem method of quantum information science used to protect quantum states against undesired noise. The relational theory naturally predicts a fundamental decoherence mechanism, so an arrow of time emerges from a time-symmetric theory. Moreover, our model circumvents the problem of the collapse of the wave packet as the probability interpretation is only ever applied to diagonal density operators. Finally, the physical states of the relational theory can be described in terms of spin networks introduced by Penrose as a combinatorial description of geometry, and widely studied in the loop formulation of quantum gravity. Thus, our simple bottom-up approach (starting from the semiclassical limit to derive the fully relational quantum theory) may offer interesting insights on the low energy limit of quantum gravity.

Quantum optical systems for the implementation of quantum information processing

We review the field of quantum optical information from elementary considerations to quantum computation schemes. We illustrate our discussion with descriptions of experimental demonstrations of key communication and processing tasks from the last decade and also look forward to the key results likely in the next decade. We examine both discrete (single photon) type processing as well as those which employ continuous variable manipulations. The mathematical formalism is kept to the minimum needed to understand the key theoretical and experimental results.

Synapses, quantum theory and panpsychism

The introduction situates the ‘hard problem’ in its historical context and argues that the problem has two sides: the output side (the Kant-Eccles problem of the freedom of the Will) and the input side (the problem of qualia). The output side ultimately reduces to whether quantum mechanics can affect the operation of synapses. A discussion of the detailed molecular biology of synaptic transmission as presently understood suggests that such affects are unlikely. Instead an evolutionary argument is presented which suggests that our conviction of free agency is an evolutionarily induced illusion and hence that the Kant-Eccles problem is itself illusory. This conclusion is supported by well-known neurophysiology. The input side, the problem of qualia, of subjectivity, is not so easily outflanked. After a brief review of the neurophysiological correlates of consciousness (NCC) and of the Penrose-Hameroff microtubular neuroquantology it is again concluded that the molecular neurobiology makes quantum wave-mechanics an unlikely explanation. Instead recourse is made to an evolutionarily- and neurobiologically-informed panpsychism. The notion of an ‘emergent’ property is carefully distinguished from that of the more usual ‘system’ property used by most dual-aspect theorists (and the majority of neuroscientists) and used to support Llinas’ concept of an ‘oneiric’ consciousness continuously modified by sensory input. I conclude that a panpsychist theory, such as this, coupled with the non-classical understanding of matter flowing from quantum physics (both epistemological and scientific) may be the default and only solution to the problem posed by the presence of mind in a world of things.

On the theory of self-similar parabolic optical pulses

Self-similar optical pulses (or “similaritons”) of parabolic intensity profile can be found as asymptotic solutions of the nonlinear Schr¨odinger equation in a gain medium such as a fiber amplifier or laser resonator. These solutions represent a wide-ranging significance example of dissipative nonlinear structures in optics. Here, we address some issues related to the formation and evolution of parabolic pulses in a fiber gain medium by means of semi-analytic approaches. In particular, the effect of the third-order dispersion on the structure of the asymptotic solution is examined. Our analysis is based on the resolution of ordinary differential equations, which enable us to describe the main properties of the pulse propagation and structural characteristics observable through direct numerical simulations of the basic partial differential equation model with sufficient accuracy.

An alternating boundary integral based method for a Cauchy problem for the Laplace equation in semi-infinite regions

We consider a Cauchy problem for the Laplace equation in a two-dimensional semi-infinite region with a bounded inclusion, i.e. the region is the intersection between a half-plane and the exterior of a bounded closed curve contained in the half-plane. The Cauchy data are given on the unbounded part of the boundary of the region and the aim is to construct the solution on the boundary of the inclusion. In 1989, Kozlov and Maz'ya [10] proposed an alternating iterative method for solving Cauchy problems for general strongly elliptic and formally self-adjoint systems in bounded domains. We extend their approach to our setting and in each iteration step mixed boundary value problems for the Laplace equation in the semi-infinite region are solved. Well-posedness of these mixed problems are investigated and convergence of the alternating procedure is examined. For the numerical implementation an efficient boundary integral equation method is proposed, based on the indirect variant of the boundary integral equation approach. The mixed problems are reduced to integral equations over the (bounded) boundary of the inclusion. Numerical examples are included showing the feasibility of the proposed method.

On an indirect integral equation approach for stationary heat transfer in semi-infinite layered domains in R3 with cavities

Regions containing internal boundaries such as composite materials arise in many applications.We consider a situation of a layered domain in IR3 containing a nite number of bounded cavities. The model is stationary heat transfer given by the Laplace equation with piecewise constant conductivity. The heat ux (a Neumann condition) is imposed on the bottom of the layered region and various boundary conditions are imposed on the cavities. The usual transmission (interface) conditions are satised at the interface layer, that is continuity of the solution and its normal derivative. To eciently calculate the stationary temperature eld in the semi-innite region, we employ a Green's matrix technique and reduce the problem to boundary integral equations (weakly singular) over the bounded surfaces of the cavities. For the numerical solution of these integral equations, we use Wienert's approach [20]. Assuming that each cavity is homeomorphic with the unit sphere, a fully discrete projection method with super-algebraic convergence order is proposed. A proof of an error estimate for the approximation is given as well. Numerical examples are presented that further highlights the eciency and accuracy of the proposed method.

On the theory of self-similar parabolic optical pulses

Self-similar optical pulses (or “similaritons”) of parabolic intensity profile can be found as asymptotic solutions of the nonlinear Schr¨odinger equation in a gain medium such as a fiber amplifier or laser resonator. These solutions represent a wide-ranging significance example of dissipative nonlinear structures in optics. Here, we address some issues related to the formation and evolution of parabolic pulses in a fiber gain medium by means of semi-analytic approaches. In particular, the effect of the third-order dispersion on the structure of the asymptotic solution is examined. Our analysis is based on the resolution of ordinary differential equations, which enable us to describe the main properties of the pulse propagation and structural characteristics observable through direct numerical simulations of the basic partial differential equation model with sufficient accuracy.