Program Manager
Prof Howard Wiseman - Griffith University

Measurement and Control Researchers
Students
Mr Neil Oxtoby (PhD)
Mr Daniel Atkins (PhD)
Mr Joshua Combes (PhD)
Mr Steve Jones (PhD)

Staff
Prof David Pegg
Dr John Vaccaro
Dr He-Bi Sun
Dr Kurt Jacobs

Collaborating Centre Researchers
A/Prof Timothy Ralph - University of Queensland
Prof Gerard Milburn - University of Queensland
Prof Andrew White - University of Queensland
Dr Jeremy O’Brien - University of Queensland
Dr Geoff Pryde - University of Queensland
Mr Austin Lund - University of Queensland
Dr Elanor Huntington - UNSW@ADFA

OTHER COLLABORATORS
Dr Damian Pope - Griffith University
A/Prof Andrew Doherty - University of Queensland
Dr Dominic Berry - University of Queensland
Mr Mark Dowling - University of Queensland
Dr Stephen Bartlett - University of Sydney
Dr Jingbo Wang - University of Western Australia
Mr Chris Hines - University of Western Australia
Dr Tom Stace - University of Cambridge
Dr Fabio Anselmi - University of Hertfordshire
Prof Stephen Barnett - University of Strathclyde
Dr John Jeffers - University of Strathclyde
A/Prof Kosuke Shizume - Tsukuba University
Mr Benjamin Greenbaum - Columbia University
Prof Bala Sundaram - U.Mass. Boston
Dr Robert Spekkens - Perimeter Institute
Mr Asa Hopkins - California Institute of Technology
Dr Salman Habib - Los Alamos National Laboratory
Dr Tanmoy Bhattacharya - Los Alamos National Laboratory
Dr Daniel Steck - Los Alamos National Laboratory
Dr Jay Gambetta - Yale University
Dr Jin Wang - University of Nebraska

Program Description
The aim of this program is to understand the measurement and control of devices operating on a quantum scale and to apply this understanding to quantum information processing. The program has four sub-programs: Quantum Measurement Theory for Read-Out Devices; Quantum Feedback Control; Quantum Information – Measurement Interface; Quantum Computing – Measurement Interface.

1. Quantum Measurement Theory for Read-Out Devices
The aim of this sub-program is to develop methods for determining the state of a qubit (or register) conditioned on the results of monitoring the qubit using a realistic read-out device. The main outcome for this year has been a detailed analysis of the quantum effi ciency of a single-electron transistor (SET) in the regime of strong coupling. We (Oxtoby, Wiseman and Sun) have shown that, unlike the weakly-coupled SET, the strongly-coupled SET need not be highly ineffi cient, and can be described by a mathematically valid master equation. This means that it is sensible to calculate the quantum state of a qubit conditioned on the output of such a detector, and also conditioned on the output of a more realistic read-out device such as the SET embedded in an external circuit.

Figure 1 Comparison between the average conditional variance V(t) in the logical state of the qubit (blue) and the qubit coherence function g(t) (red) showing the qubit’s measurement-induced decoherence during the measurement. Plots (a) and (c) show results for the single-electron transistor (SET) with weak response (a) and strong response (c). Plots (b) and (d) show the corresponding results for the quantum point contact (QPC), which is a quantum-limited detector.

The second main result in 2005 has been to fi nd a numerically feasible (approximate) method for treating dispersion in one-way quantum channels [Stace and Wiseman, to be published in Phys. Rev. A]. This applies in many solid-state systems such as the propagation of edge-state quasi-electrons in the Hall effect, and also propagation of radiation in a transmission line. We show that the technique works for bosonic systems and for fermionic systems with a low fl ux, and can be extended to treat fermionic systems with large fl ux. It has obvious application for modelling measurement, which involves propagation of the signal (fermionic or bosonic) in a channel with dispersion, and also for statetransfer protocols.

Figure 2 Schematic of a triply cascaded system, for modelling propagation with dispersion between source (s) and target (t). The output of subsystem s propagates without dispersion to subsystem f, where it is refl ected, and the refl ected fi eld propagates without dispersion to subsystem t. The parameters for the fi ctitious device fare chosen to mimic the dispersion in the real channel.

2. Quantum Feed Back Control
The aim of this sub-program is to investigate feedback control of quantum systems useful for quantum information processing, such as error correction or state preparation. The main outcome for this year has been in rapid preparation of qudit states by continuous measurement plus feedback [Combes and Jacobs, to be published in Phys. Rev. Lett.]. Previous work [Jacobs, Phys. Rev. A 67, 030301(R) (2003)] showed that by using Hamiltonian feedback in conjunction with continuous weak measurement, a qubit could be purified (asymptotically) in half the time required using measurement alone. Now for a qudit (a d dimensional quantum system) we have shown a lower bound on the reduction factor scaling as 1/d for large d. We have also obtained exact numerical results for finited.

Figure 3 A plot of the lower bound on the speed-up factor provided by the feedback algorithm as a function of the target impurity, when the initial state is completely mixed. The Solid line gives the result for system dimension d=2, the dashed line for d=3 and the dotdashed line for d=4.

Figure 4 Plot of concurrence (a measure of entanglement) versus purity for the stationary two-qubit state under a wide range of parameters. The stars represent the case of unmodulated driving only with one adjustable parameter, the driving strength. The dots represent the case of a feedback-modulated driving laser with a second adjustable parameter, the degree of modulation of the driving by the feedback. The continuous diagonal curve shows the states with the maximum possible concurrence for a given degree of purity.

3. Quantum Information - Measurement Interface
The aim of this sub-program is to study questions at the interface of quantum information and quantum measurement. This year we have continued working on the influence on entanglement of constraints on what local measurements can be performed. We consider the following scenario [Jones, Wiseman, and Pope, Phys. Rev. A 72, 022330 (2005)]. A company C manufactures pure entangled pairs of particles, each pair intended for a distinct pair of distant customers. Unfortunately, the probability that any given customer pair receives its intended particles is S < 1, and the customers cannot detect whether an error has occurred. Remarkably, we show that no matter how small S is, it is still possible for C to distribute entanglement by starting with non-maximally entangled pairs. We determine the maximum entanglement distributable for a given S, and also determine the ability of the parties to perform nonlocal tasks with the qubits they receive.

Figure 5 Diagram of entanglement distributed versus success probability S for states of the form. Curve (a) shows the maximum entanglement distributable, and curve (b) is an analytical approximation. Curves (c) and (d) are for the specifi c cases and respectively, showing how less entangled states are more robust.

4. Quantum Computing - Measurement Interface
The aim of this sub-program is to study questions at the interface of quantum
measurement and quantum computing. The main outcome for this year has been in collaboration with the LOQC theory program at UQ [Ralph, Lund, and Wiseman, J. Opt. B 7, S245-S249 (2005)]. Previous approaches to LOQC have relied upon photon counting to induce an effective non-linear optical phase shift. The most obvious way to encode a qubit optically is as a superposition of the vacuum and a single photon in one mode – so-called ‘single-rail’ logic. Previously [Lund and Ralph, Phys Rev A 66, 032307 (2002)] this approach was thought to be prohibitively expensive (in resources) compared to ‘dual-rail’ logic where a qubit is stored by a photon across two modes. We show that by using real-time feedback control to realize a quantum-limited phase measurement on a single mode, the resource requirements for single-rail LOQC are not substantially different from those of dual-rail LOQC. The key to this approach is that, with adaptive phase measurements an arbitrary single-rail qubit state can be prepared deterministically.

Figure 6 A schematic representation of the application of an arbitrary single qubit unitary to a single rail qubit. The single rail qubit is teleported onto a dual rail qubit, the unitary is applied, then an adaptive phase measurement is used to convert back to a single rail qubit. BSM means Bell state measurement and APM means adaptive phase measurement. All operations are deterministic except the Bell state measurement, which succeeds 50% of the time.