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QUANTUM REFERENCE FRAMES It is common in quantum mechanics to assume that clocks and rulers – “reference frames” with respect to which we measure all systems are perfect, and classical – i.e. large. We have been researching how to treat them in the quantum mechanical formalism and see what type of limitations doing this does or does not impose. This has interesting foundational issues in understanding quantum space and time in extreme conditions such as near black holes. A comparison of probability of success for obtaining the However it also is important for building ideal measurement result in three different cases of a small quantum information processing devices! For quantum reference frame. The dashed line corresponds to quantum computers the reference frames take the case of sequential measurements without any correction, the dashed-dotted line is for the case in which the form of lasers, and we want to use as small we correct the measurement result via applying unitary and weak lasers as possible, to miniaturize the interactions after any two measurements and the solid line belongs to the case of correction via applying corrections devices. after specific outcomes are obtained. Currently we are focusing on a program of research initiated by Dr. Rudolph and colleagues concerning how long a quantum reference frame (QRF) lasts if it is used as a resource for performing quantum operations and also how we can make it to last longer. The special case that we are looking at is the effect that the measurement of the angle between a directional quantum reference frame and a spin-1/2 particle has on the ability of QRF to act as a reliable reference for future measurements. We show that each time one of these spin-1/2 particles is measured against the QRF, it causes the reference frame to suffer from a back-action which makes the probability of getting the correct measurement result decrease as the number of measurements increases. We recently have found two different ways of fighting this seemingly inevitable degradation – either through an active corrective mechanism, or by a careful monitoring of the dynamics involved. In the figure below, we can see how these two ways of fighting the degradation of the QRF makes it useful for a larger number of measurements. TIME AND THE SECOND LAW OF THERMODYNAMICS Time is one of our most ancient mysteries, while in stark contrast it is only in the past century that we have become aware of the quantum mechanical properties of Nature. Why do events seem to flow past us only in one direction? Why do we only know the past and not the future? Why do all parts of the universe experience the same Arrow of Time? While these questions may seem better suited to a philosophy department, central to all these deep and significant questions is the notion of “information”, and within the field of Quantum Information Theory we are applying recent discoveries in the theory of quantum entanglement to better understand how Time works, and how entanglement in an actual physical system can be used to bend or even reverse the Arrow of Time! Beyond being of foundational importance, the research also offers practical insights into the fundamental limits in the efficiency of thermodynamic engines, and into how heat flow and energy transfer in quantum systems can be modified and controlled via quantum correlations. We were recently by Scientific American to comment on a provocative proposal by Maccone - our understanding of this issue allowed us to identify the flaw in his proposal [Physical Review Letters,104,148901], and to subsequently undertake a thorough analysis of the time reversals possible due to quantum entanglement http://arxiv.org/abs/1002.0314. CLASSICAL NOTIONS IN A QUANTUM UNIVERSE Quantum Mechanics encompasses not only the strange particle world of atoms, photons and quarks, but also the more familiar classical world of galaxies, stars, trees and humans. How our classical notions fit into the counterintuitive world of Quantum Mechanics is far from being a trivial question and brings with it delicate technical challenges and a greater mastery of how quantum information behaves. We are currently conducting research on how classical correlation patterns fundamentally fit into the underlying quantum world and asking the surprisingly difficult question: How much classical correlation can we create in the simplest setting of two fundamental particles? Our interface with the quantum world is ultimately classical, so beyond its foundational importance, understanding how traditional classical information relates to quantum information is significant for the manipulation of quantum systems and for information processing tasks. We have recently solved this problem for a variety of special cases, and are now focussed on obtaining a fully general solution. RELATIVISTIC QUANTUM INFORMATION THEORY When we combine Relativity with Quantum Mechanics we are inexorably lead to the notion of a quantum field. Currently quantum field theories in the setting of curved spacetimes are pushing the frontier of our understanding of the laws of Nature. In recent times we have come to realise the important role that certain information theoretic notions play at this frontier. The most famous being the socalled Black Hole Information Paradox, which asks whether information is truly destroyed in the most extreme conditions of a black hole. Relativistic Quantum Information Theory seeks to investigate at a fundamental level, how does information behave in the presence of gravity and at velocities close to the speed of light. Two such questions of interest for us are: How does vacuum entanglement relate to the causal structure of a spacetime? How are global spacetime properties encoded in the local state of a quantum field that we access with a particle detector? For many years the question has been open of whether the relativistic version of quantum information theory is different with respect to fundamental information processing power from nonrelativistic quantum information theory. By considering these foundational questions we have recently managed to show that certain important cryptographic protocols – such as “secure gambling on the quantum internet” are possible only in relativistic quantum information theory, a result which may lead to many new practical uses for quantum communication theory. ROBUST COMPUTERS MADE OF LIGHT A quantum paradigm for information promises more reliable communications and enhanced algorithms for many important problems, such as quantum chemistry leading to better drug design, simulation of light harvesting complexes leading to better solar cells or design of new exotic materials capable of withstanding extremes such as heat, pressure or electrical current. One of our areas of research in the IMS group is trying to bring the quantum computer closer. Our focus is on optical and solid state (semiconductor) systems. Recently [Phys. Rev. Lett.103, 113602 (2009)] we proposed a device at the interface of these two technologies – a “quantum dot machine gun” for entangled photons. This idea captured some media attention and is currently being pursued by three different experimental groups. Even having such a device we still need a robust way of computing with it. To this end we have been investigating how it could be used in a so-called “fault tolerant one-way quantum computer”, a model in which one starts with a three-dimensional lattice of correlated quantum bits and then measures them out following an order dictated by the quantum algorithm, in such a way that the overall shape of the resulting lattice will enact a series of quantum logical gates. We have proposed a way of building of this lattice using arrays of quantum dots – tiny pyramidal structures that are able of firing correlated photons - linear optical gates and very efficient detectors. All these components offer very good controllability and scalability. Simulations have been carried out which suggest that our proposal would be quite robust against errors in the Schematic setting of our proposal: An array of quantum dots (purple) fire strings of photons which at a later stage are quantum dots, the optical gates and in the combined in the optical gates to create correlations between parallel beams (yellow vertical lines). This constitutes the detectors. substrate ON-CHIP PHOTONIC NETWORKS With recent advances in fabrication techniques, scientists have been able to make devices that manipulate light at smaller and smaller scales. This has opened up the possibility of information processing with light at the nanoscale. Here, the new field of nanophotonics promises high bandwidth, high speed and ultra-small scalable components. Within the Controlled Quantum Dynamics group we are actively pursuing research in into quantum-controlled devices based on the potential offered by nanophotonics. One of the main topics we are investigating is the use of measurement-based quantum control, a new paradigm for controlling quantum systems. Here, the networking of fundamental on-chip components is employed in systems such as photonic crystals, atom chips and photonic waveguides (see Fig. 1). By On-chip network of photonic waveguides performing complex mathematical simulations we are generating entangled resource states for developing devices for deployment in applications measurement-based quantum control. such as quantum communication and quantum computing. These applications offer far superior performance compared to their non-quantum counterparts. In addition to this applied research, we are also investigating scenarios in which novel physical effects such as quantum phase transitions, chaotic dynamics and the creation of multipartite entangled states arise. The goal is to probe the foundations of quantum physics and find new ways to harness quantum effects for efficient and scalable on-chip quantum information processing. NONLINEAR QUANTUM OPTICS WITH NANOSTRUCTURED MEDIA An active area of our research is the generation of large nonlinear effects at the quantum level – a field in which Imperial researchers have been leading the world for many years. A major problem for quantum information processing is that photons interact very weakly with each other. If large nonlinear effects become possible in the single-photon regime, it will allow the efficient production of entangled states, the generation of nonclassical states such as Schrödinger cat states, and the processing of quantum information encoded into continuous and discrete variables. To tackle this problem we consider surface plasmon polaritons (see Efficient single-photon excitation figure), an exotic form of light (photons) coupled to matter of on-chip surface plasmon (electrons), where it has recently been recognised that they polaritons using attenuatedprovide the potential for achieving large nonlinear effects with reflection geometries. deep sub-wavelength field confinement in nanostructured media. We are working on developing efficient nonlinear plasmonic waveguides and investigating coupled nonlinear plasmonic systems. The proposal of experimentally realisable schemes for plasmonic quantum control and information processing is one of our major goals. Mathematical modelling and careful application of quantum optics theory is essential in our research on this topic. PEEKING INSIDE THE QUANTUM BOX: INDIRECT SYSTEM THEORY FOR MANY-BODY HAMILTONIANS. Estimating the nature and strength of interactions has been one of the main goals in quantum theory for almost a century. But it is only now that we are capable, in principle, of experimentally identifying the specific individual interactions – so called “Hamiltonians” of large systems of particles. However; in general the complexity of such Hamiltonian estimation is vast, as each particle needs to be initialised and its dynamics monitored. In collaboration with RIKEN, Japan, we have discovered efficient methods for estimating certain types of interactions often encountered in experiments. These can be identified indirectly- by only monitoring the quantum dynamics of the surface of the system, the inner dynamics is revealed. This is analogous to tomography as used in, e.g., seismology and ultrasonography. Our results provide further evidence for a “holographic principle” of many-body Hamiltonians, which was previously conjectured by our group based on the scaling of entanglement in these systems. TOPOLOGICAL ORDER, QUANTUM ERROR CORRECTION AND FAULT TOLERANT QUANTUM COMPUTING The ability to store and process quantum states is key to the nascent field of quantum information technology. However, quantum information is delicate. It can be corrupted by imperfect control of the 'knobs' accessible to the experimentalist, or by unwanted coupling to other systems. One of the most important discoveries in quantum information in the last 15 years was the discovery of methods to protect quantum information from noise, and also to process the resulting protected states. Two main approaches have been developed - one based on the use of quantum generalizations of error correcting codes, the other based on a newly discovered property of matter known as 'topological order': topologically ordered systems can protect quantum information without active error correction.Within the CQD program we are currently studying an approach to protecting and coherently processing quantum information which combines both of A topological fault tolerant quantum computing these approaches. Two recent breakthroughs in the group scheme that can tolerate significant loss errors. have concerned the effect of a particular type of error where the information carrying entity (which could be an atom, photon, or solid state device) is completely lost. We have shown that certain error correcting codes can tolerate loss of up to half of their quantum bits, while still retaining the ability to correct for other types of noise [Phys. Rev. Lett. 102, 200501 (2009)]. Secondly, we have shown that Error threshold tradeoff curve for topological fault tolerant quantum computing scheme, determined by Monte-Carlo simulations. Horizontal axis: loss error a quantum computing scheme probability per qubit. Vertical axis: computational error probability. The large using such topological codes is "correctable" region indicates that the practical realisation of quantum computing also robust to loss errors at may be much easier than hitherto expected. rates of up to 25 percent. These schemes, exhibiting very high thresholds that are comparable with state of the art experiments, indicate that the practical realisation of quantum computing may be much easier than hitherto expected. DISTRIBUTED MEASUREMENT BASED QUANTUM COMPUTING A significant problem in building a quantum computer is the seemingly contradictory requirements of having well isolated physical systems (qubits) that can be independently addressed, while at the same time having the qubits interact strongly with each other in order to build up quantum entanglement - the key resource that enables the power of a quantum computer. One of the most significant contributions of CQD group members was to propose a scheme for distributed quantum computation that overcomes this contradiction: we showed that distant qubits can be entangled via single photon interference effects and photodetection, in such a way that a large scale quantum computer can be constructed. This work has had significant impact on the field, with both extensive further theoretical work (within the group and elsewhere) as well as experimental demonstrations of the core components of the scheme. Within the group, we have recently examined the effect of noise in quantum dot based implementations, and also shown that the idea can be made to work using the rather more mature technology of gas vapour cells.