QIPIRC

Entanglement is a key resource in quantum information tasks and much effort is being expended in its theoretical and experimental exploration. As a consequence, the quantitative exploration of entanglement as a resource is a central concern of quantum information science.  Basic questions such as the characterization, the manipulation, and the quantification of entangled states are addressed in this endeavour. Their answers establish the theory of entanglement and are of interest to theorists and experimentalists alike.

Over the last years the theory of entanglement has grown enormously and many fundamental properties are now well established. Unfortunately, the forest of publications is becoming increasingly dense and frightening for novice and expert alike.  QIP IRC partners Martin Plenio and Shashank Virmani from the Institute for Mathematical Sciences at Imperial College http://www.imperial.ac.uk/quantuminformation have recently finished a comprehensive tutorial overview on the subject, presenting the basics and offering many useful explicit formulae.

The article, soon to be published in Quantum Information and Computation, is also available at http://xxx.arxiv.org/abs/quant-ph/0504163

The annual report describes a selection of the activities in QIP IRC. It is hoped that it will convey some of the challenges that have been addressed and some of the results that have been achieved. The annual report serves to inform the QIP IRC Board and EPSRC about progress. The scientific summaries are edited from annual reports from investigators, which will be available on this website shortly. Investigators are asked to check that the list of publications is accurate and complete, and to send corrections to qipirc@materials.ox.ac.uk.

The Annual Report can be downloaded from the Forms and Documents section of the website.

This document, produced within the QIP IRC in Autumn 2005, brings out some common scientific themes which have emerged from the first year or so of the QIP IRC's work. It is not intended to be any kind of full progress report, a quality review of the projects, or a list of scientific highlights; rather, it is a subset of the results recently reported by the IRC (either in quarterly scientific progress reports to the management team, or in publications and preprints) that, while interesting in themselves, relate to more than one of the IRC projects or seem to have the potential to lead to further work in several different areas.

It was discussed at the QIP IRC Conference in September 2005; two of the areas highlighted for their developing connections were chosen for discussion symposia at that meeting. For each topic we mention one or two names as contact points for those who are interested in the work; this is not intended to be any kind of formal assignment of scientific credit, for which the author lists of the papers referenced provide a better indication.

The present document was written by Andrew Fisher and the selection corresponds to his own subjective choices. It has benefited from the input of others in the IRC, but the responsibility for the selection and any remaining errors is entirely his – comments are welcome (andrew.fisher@ucl.ac.uk), If it is found to be useful we will update it regularly and also produce versions for other audiences.

The document can be downloaded from the Forms and Documents section of this website.

Dr Simon Benjamin and Dr Arzhang Ardavan discuss the “bang-bang” technique to isolate quantum information in the April 2006 edition of Excellence in Science, the online newsletter from the Royal Society.

QIP IRC members Dr Simon Benjamin and Dr Pieter Kok discuss quantum computing with graph states with Quentin Cooper on The Material World, BBC Radio 4. For more information and to listen to the programme (originally broadcast on 6th April 2006) go to http://www.bbc.co.uk/radio4/science/thematerialworld_20060406.shtml

There are many practical limitations to the implementation of quantum computing. One problem is dissipation, i.e. the loss of information due to unwanted interactions with the environment. Another limitation is the sensitivity to parameter fluctuations. For example, if the amplitude of an applied laser field fluctuates by a few percent, this should not result in a failure of the computation. One solution to these problems is to use measurements: They can be used to project a quantum system into any desired state and are commonly used for state preparation in quantum optics experiments.

However, measurements can also play a much more subtle role in quantum computing. They can provide the main ingredient for the implementation of entangling two-qubit gate operations. Together with single-qubit operations, entangling two-qubit gates are universal for quantum computing. To avoid the destruction of qubits, it is not allowed to measure the qubits directly. Measurements should be performed only on ancillas which have interacted and therefore share entanglement with the qubits [1]. In order to implement a quantum gate on the qubits, we measure the ancillas in a basis that is mutually unbiased with respect to the computational basis. This ensures that an observer does not learn anything about the state of the qubits and the information might remain stored inside the computer. The most famous example of such a measurement-based quantum computer is the linear optics scheme for photonic qubits by Knill, Laflamme and Milburn [2].

However, ancillas and qubits do not have to be of the same physical nature. For example, if the qubits are atoms in a cavity, the ancillas can be the quantised cavity field mode [3], a common vibrational mode [4], or newly generated photons [5,6]. Vice versa, one can use collective atomic states as ancillas for photonic qubits [7,8]. Quantum computing with hybrid systems should help to overcome some of the most pressing problems in existing non-hybrid proposals, including the difficulty of scaling conventional stationary qubit architectures and the lack of practical means for storing single photons in linear optics setups.

In a recent collaboration between Imperial College London and HP in Bristol, we analysed an architecture for robust and scalable quantum computation using both stationary qubits and flying qubits [9]. Our scheme combines elements of two previous proposals for distributed quantum computing, namely the efficient photon-loss tolerant build up of cluster states by Barrett and Kok [5] with the idea of Repeat-Until-Success (RUS) quantum computing by Lim, Beige and Kwek [6].

The considered setup consists of a network of single stationary qubits (like trapped atoms, molecules, ions, quantum dots or nitrogen-vacancy colour centres) inside optical cavities, which act as a source for the generation of single photons on demand. Read-out measurements and single qubit rotations can be performed on the stationary qubits using laser pulses and standard quantum optics techniques as employed in ion trap experiments.

The main building block for the realization of an eventually deterministic two-qubit gate is shown in the Figure. It requires the simultaneous generation of a photon in each source involved in the operation. Afterwards, the photons pass through a linear optics setup, and a two-photon measurement is performed in the output ports. This measurement results either in the completion of the two-qubit gate, or it will induce two correctable single-qubit gates on the qubits. In the latter event the gate can be repeated, as no quantum information is lost. Hence the name Repeat-Until-Success quantum computing [6].

When we use photon detectors with finite efficiencies and when the photon generation is not ideal, a failure of the two-qubit gate does not always leave the qubits undisturbed. Consequently, the Repeat-Until-Success procedure fails occasionally. However, the setup in the Figure can still be used for the efficient implementation of two-qubit gates with a very high fidelity. As shown recently by Barrett and Kok [5], it is possible to use entangling operations with arbitrarily high photon losses to efficiently generate graph states for one-way quantum computing [10]: A so-called "double-heralding" scheme employs two rounds of photo-detection which eliminate unwanted separable contributions to the density matrix. Combining the loss-tolerant mechanism behind double-heralding with the Repeat-Until-Success protocol leads to a quantum computer architecture that is robust against inevitable losses, and succeeds with reasonably high probability but, most importantly, does not require direct qubit-qubit interactions.

[1] G.G. Lapaire, P. Kok, J.P. Dowling, and J.E. Sipe, Phys. Rev. A 68, 042314 (2003).

[2] E. Knill, R. Laflamme, and G.J. Milburn, Nature 409, 46 (2001).

[3] A. Beige, D. Braun, B. Tregenna, and P. L. Knight, Phys. Rev. Lett. 85, 1762 (2000).

[4] A. Beige, Phys. Rev. A 69, 012303 (2004).

[5] S.D. Barrett and P. Kok, Phys. Rev. A 71, 060310(R) (2005).

[6] Y.L. Lim, A. Beige, and L.C. Kwek, Phys. Rev. Lett. 95, 030505 (2005).

[7] J.D. Franson, B.C. Jacobs, and T.B. Pittman, Phys. Rev. A 70, 062302 (2004).

[8] S.D. Barrett, P. Kok, K. Nemoto, R.G. Beausoleil, W.J. Munro, and T.P. Spiller, Phys. Rev. A 71, 060303(R) (2005).

[9] Y.L. Lim, S.D. Barrett, A. Beige, P. Kok, and L.C. Kwek, Phys. Rev. A (in press); quant-ph/0508218.

[10] R. Raussendorf and H.J. Briegel, Phys. Rev. Lett. 86, 5188 (2001).

(Almut Beige and Pieter Kok, November 2005)