G. J. Milburn

Linear optical quantum computing with photonic qubits

Linear optics with photon counting is a prominent candidate for practical quantum computing. The protocol by Knill, Laflamme, and Milburn [Nature 409, 46 (2001)] explicitly demonstrates that efficient scalable quantum computing with single photons, linear optical elements, and projective measurements is possible. Subsequently, several improvements on this protocol have started to bridge the gap between theoretical scalability and practical implementation. We review the original theory and its improvements, and we give a few examples of experimental two-qubit gates. We discuss the use of realistic components, the errors they induce in the computation, and how these errors can be corrected.

Universal state inversion and concurrence in arbitrary dimensions

Wootters [Phys. Rev. Lett. 80, 2245 (1998)] has given an explicit formula for the entanglement of formation of two qubits in terms of what he calls the concurrence of the joint density operator. Wootterss concurrence is defined with the help of the superoperator that flips the spin of a qubit. We generalize the spin-flip superoperator to a universal inverter, which acts on quantum systems of arbitrary dimension, and we introduce the corresponding generalized concurrence for joint pure states of D-1 X D-2 bipartite quantum systems. We call this generalized concurrence the I concurrence to emphasize its relation to the universal inverter. The universal inverter, which is a positive, but not completely positive superoperator, is closely related to the completely positive universal-NOT superoperator, the quantum analogue of a classical NOT gate. We present a physical realization of the universal-NOT Superoperator.

Charge-based quantum computing using single donors in semiconductors

Solid-state quantum computer architectures with qubits encoded using single atoms are now feasible given recent advances in the atomic doping of semiconductors. Here we present a charge qubit consisting of two dopant atoms in a semiconductor crystal, one of which is singly ionized. Surface electrodes control the qubit and a radio-frequency single-electron transistor provides fast readout. The calculated single gate times, of order 50 ps or less, are much shorter than the expected decoherence time. We propose universal one- and two-qubit gate operations for this system and discuss prospects for fabrication and scale up.

Quantum Technology: The Second Quantum Revolution

We are currently in the midst of a second quantum revolution The first quantum revolution gave us new rules that govern physical reality. The second quantum revolution will take these rules and use them to develop new technologies. In this review we discuss the principles upon which quantum technology is based and the tools required to develop it. We discuss a number of examples of research programs that could deliver quantum technologies in coming decades including: quantum information technology, quantum electromechanical systems, coherent quantum electronics, quantum optics and coherent matter technology.

Generalized uncertainty relations: Theory, examples, and Lorentz invariance

The quantum-mechanical framework in which observables are associated with Hermitian operators is too narrow to discuss measurements of such important physical quantities as elapsed time or harmonic-oscillator phase. We introduce a broader framework that allows us to derive quantum-mechanical limits on the precision to which a parameter - e.g., elapsed time - may be determined via arbitrary data analysis of arbitrary measurements on N identically prepared quantum systems. The limits are expressed as generalized Mandelstam-Tamm uncertainty relations, which involve the operator that generates displacements of the parameter - e.g., the Hamiltonian operator in the case of elapsed time. This approach avoids entirely the problem of associating a Hermitian operator with the parameter. We illustrate the general formalism, first, with nonrelativistic uncertainty relations for spatial displacement and momentum, harmonic-oscillator phase and number of quanta, and time and energy and, second, with Lorentz-invariant uncertainty relations involving the displacement and Lorentz-rotation parameters of the Poincare group.

Production of squeezed states in a degenerate parametric amplifier

Abstract An analysis of the degenerate parametric amplifier including the quantisation of pump and signal modes is presented. It is shown that the fluctuations in one quadrature of the signal mode may be reduced at most by a factor of two. This is in contradistinction to analyses where the pump field is treated classically which overestimate the reduction in fluctuations possible.

Teleportation with a uniformly accelerated partner

In this work, we give a description of the process of teleportation between Alice in an inertial frame, and Rob who is in uniform acceleration with respect to Alice. The fidelity of the teleportation is reduced due to Davies-Unruh radiation in Robs frame. In so far as teleportation is a measure of entanglement, our results suggest that quantum entanglement is degraded in noninertial frames.

All-optical versus electro-optical quantum-limited feedback.

All-optical feedback can be effected by putting the output of a source cavity through a Faraday isolator and into a second cavity which is coupled to the source cavity by a nonlinear crystal. If the driven cavity is heavily damped, then it can be adiabatically eliminated and a master equation or quantum Langevin equation derived for the first cavity alone. This is done for an input bath in an arbitrary state, and for an arbitrary nonlinear coupling. If the intercavity coupling involves only the intensity (or one quadrature) of the driven cavity, then the effect on the source cavity is identical to that which can be obtained from electro-optical feedback using direct (or homodyne) detection. If the coupling involves both quadratures, this equivalence no longer holds and a coupling linear in the source amplitude can produce a nonclassical state in the source cavity. The analogous electro-optic scheme using heterodyne detection introduces extra noise which prevents the production of nonclassical light. Unlike the electro-optical case, the all-optical feedback loop has an output beam (reflected from the second cavity). We show that this may be squeezed, even if the source cavity remains in a classical state.

Dynamical tunnelling of ultracold atoms

The divergence of quantum and classical descriptions of particle motion is clearly apparent in quantum tunnelling between two regions of classically stable motion. An archetype of such non-classical motion is tunnelling through an energy barrier. In the 1980s, a new process, ‘dynamical’ tunnelling, was predicted, involving no potential energy barrier; however, a constant of the motion (other than energy) still forbids classically the quantum-allowed motion. This process should occur, for example, in periodically driven, nonlinear hamiltonian systems with one degree of freedom. Such systems may be chaotic, consisting of regions in phase space of stable, regular motion embedded in a sea of chaos. Previous studies predicted dynamical tunnelling between these stable regions. Here we observe dynamical tunnelling of ultracold atoms from a Bose–Einstein condensate in an amplitude-modulated optical standing wave. Atoms coherently tunnel back and forth between their initial state of oscillatory motion (corresponding to an island of regular motion) and the state oscillating 180° out of phase with the initial state.

Ion Trap Quantum Computing with Warm Ions

We describe two schemes to manipulate the electronic qubit states of trapped ions independent of the collective vibrational state of the ions. The first scheme uses an adiabatic method, and thus is intrinsically slow. The second scheme takes the opposite approach and uses fast pulses to produce an effective direct coupling between the electronic qubits. This last scheme enables the simulation of a number of nonlinear quantum systems including systems that exhibit phase transitions, and other semiclassical bifurcations. Quantum tunnelling and entangled states occur in such systems.