Gaussian Quantum Information

The science of quantum information has arisen over the last two decades centered on the manipulation of individual quanta of information, known as quantum bits or qubits. Quantum computers, quantum cryptography and quantum teleportation are among the most celebrated ideas that have emerged from this new field. It was realized later on that using continuous-variable quantum information carriers, instead of qubits, constitutes an extremely powerful alternative approach to quantum information processing. This review focuses on continuous-variable quantum information processes that rely on any combination of Gaussian states, Gaussian operations, and Gaussian measurements. Interestingly, such a restriction to the Gaussian realm comes with various benefits, since on the theoretical side, simple analytical tools are available and, on the experimental side, optical components effecting Gaussian processes are readily available in the laboratory. Yet, Gaussian quantum information processing opens the way to a wide variety of tasks and applications, including quantum communication, quantum cryptography, quantum computation, quantum teleportation, and quantum state and channel discrimination. This review reports on the state of the art in this field, ranging from the basic theoretical tools and landmark experimental realizations to the most recent successful developments.Comment: 51 pages, 7 figures, submitted to Reviews of Modern Physic

Remote and Local Entanglement of Ions using Photons and Phonons

The scaling of controlled quantum systems to large numbers of degrees of freedom is one of the long term goals of experimental quantum information science. Trapped-ion systems are one of the most promising platforms for building a quantum information processor with enough complexity to enable novel computational power, but face serious challenges in scaling up to the necessary numbers of qubits. In this thesis, I present both technical and operational advancements in the control of trapped-ion systems and their juxtaposition with photonic modes used for quantum networking. After reviewing the basic physics behind ion trapping, I then describe in detail a new method of implementing Raman transitions in atomic systems using optical frequency combs. Several dierent experimental setups along with simple theoretical models are reviewed and the system is shown to be capable of full control of the qubit-oscillator system. Two-ion entangling operations using optical frequency combs are demonstrated along with an extension of the operation designed to suppress certain experimental errors. I then give an overview of how spatially separated ions can be entangled using a photonic interconnect. Experimental results show that pulsed excitation of trapped ions provide an excellent single photon source that can be used as a heralded entangling gate between macroscopically separated systems. This heralded entangling gate is used to show a violation of a Bell inequality while keeping the detection loophole closed and can be used a source private random numbers. Finally, the coherent Coulomb force-based gates are combined with the probabilistic photon-based gates in a proof of concept experiment that shows the feasibility of a distributed ion-photon network

Multiphoton Quantum Optics and Quantum State Engineering

We present a review of theoretical and experimental aspects of multiphoton quantum optics. Multiphoton processes occur and are important for many aspects of matter-radiation interactions that include the efficient ionization of atoms and molecules, and, more generally, atomic transition mechanisms; system-environment couplings and dissipative quantum dynamics; laser physics, optical parametric processes, and interferometry. A single review cannot account for all aspects of such an enormously vast subject. Here we choose to concentrate our attention on parametric processes in nonlinear media, with special emphasis on the engineering of nonclassical states of photons and atoms. We present a detailed analysis of the methods and techniques for the production of genuinely quantum multiphoton processes in nonlinear media, and the corresponding models of multiphoton effective interactions. We review existing proposals for the classification, engineering, and manipulation of nonclassical states, including Fock states, macroscopic superposition states, and multiphoton generalized coherent states. We introduce and discuss the structure of canonical multiphoton quantum optics and the associated one- and two-mode canonical multiphoton squeezed states. This framework provides a consistent multiphoton generalization of two-photon quantum optics and a consistent Hamiltonian description of multiphoton processes associated to higher-order nonlinearities. Finally, we discuss very recent advances that by combining linear and nonlinear optical devices allow to realize multiphoton entangled states of the electromnagnetic field, that are relevant for applications to efficient quantum computation, quantum teleportation, and related problems in quantum communication and information.Comment: 198 pages, 36 eps figure

Multi-photon entanglement and applications in quantum information

Since the awareness of entanglement was raised by Einstein, Podolski, Rosen and Schrödinger in the beginning of the last century, it took almost 55 years until entanglement entered the laboratories as a new resource. Meanwhile, entangled states of various quantum systems have been investigated. Sofar, their biggest variety was observed in photonic qubit systems. Thereby, the setups of today's experiments on multi-photon entanglement can all be structured in the following way: They consist of a photon source, a linear optics network by which the photons are processed and the conditional detection of the photons at the output of the network. In this thesis, two new linear optics networks are introduced and their application for several quantum information tasks is presented. The workhorse of multi-photon quantum information, spontaneous parametric down conversion, is used in different configurations to provide the input states for the networks. The first network is a new design of a controlled phase gate which is particularly interesting for applications in multi-photon experiments as it constitutes an improvement of former realizations with respect to stability and reliability. This is explicitly demonstrated by employing the gate in four-photon experiments. In this context, a teleportation and entanglement swapping protocol is performed in which all four Bell states are distinguished by means of the phase gate. A similar type of measurement applied to the subsystem parts of two copies of a quantum state, allows further the direct estimation of the state's entanglement in terms of its concurrence. Finally, starting from two Bell states, the controlled phase gate is applied for the observation of a four photon cluster state. The analysis of the results focuses on measurement based quantum computation, the main usage of cluster states. The second network, fed with the second order emission of non-collinear type II spontaneous parametric down conversion, constitutes a tunable source of a whole family of states. Up to now the observation of one particular state required one individually tailored setup. With the network introduced here many different states can be obtained within the same arrangement by tuning a single, easily accessible experimental parameter. These states exhibit many useful properties and play a central role in several applications of quantum information. Here, they are used for the solution of a four-player quantum Minority game. It is shown that, by employing four-qubit entanglement, the quantum version of the game clearly outperforms its classical counterpart. Experimental data obtained with both networks are utilized to demonstrate a new method for the experimental discrimination of different multi-partite entangled states. Although theoretical classifications of four-qubit entangled states exist, sofar there was no experimental tool to easily assign an observed state to the one or the other class. The new tool presented here is based on operators which are formed by the correlations between local measurement settings that are typical for the respective quantum state.Fast 55 Jahre vergingen bis die Entdeckung des Phänomens der Verschränkung durch Einstein, Podolski, Rosen und Schrödinger Ende des zwanzigsten Jahrhunderts Einzug in die Labore hielt. Mittlerweile wurde eine Vielfalt von verschränkten Zuständen untersucht; die größte davon in Systemen photonischer Qubits. Alle modernen Experimente zu viel-Photonen Verschränkung lassen sich in drei wesentliche Bestandteile untergliedern: Eine Photonenquelle, ein Netzwerk aus linearen optischen Komponenten welches die Photonen verarbeitet, und eine bedingte Detektion der Photonen am Ausgang des Netzwerks. Die vorliegende Arbeit führt zwei neue Netzwerke ein und präsentiert deren Anwendungen in verschiedenen Problemstellungen der Quanteninformation. Als Photonenquelle dient hierbei der Prozeß der spontanen parametrischen Fluoreszenz in unterschiedlichen Konfigurationen. Das erste Netzwerk ist ein neuartiges Kontroll-Phasengatter das sich gegenüber früheren Realisierungen vor allem durch seine hohe Stabilität auszeichnet. Wie anhand mehrerer Beispiele gezeigt wird, eignet es sich besonders für den Einsatz in mehr-Photonen Experimenten. Mit Hilfe des Gatters werden alle vier Bell Zustände in einem Teleportations- und "entanglement swapping" Experiment unterschieden. Ein ähnlicher experimenteller Aufbau erlaubt ferner die direkte Messung der Verschränkung zweier Kopien eines Zustands in Form der "Concurrence". Ausgehend von zwei Bell Zuständen wird das Gatter darüberhinaus zur Beobachtung eines Vier-Photonen "Cluster Zustands" verwendet. Die Analyse der Ergebnisse konzentriert sich dabei auf die Hauptanwendung von Cluster Zuständen, das meßbasierte Quantenrechnen. Das zweite Netzwerk bildet, zusammen mit der Emission zweiter Ordnung der parametrischen Fluoreszenz als Input, eine einstellbare Quelle verschiedenster Zustände. Während die Beobachtung eines Zustands bisher einen individuell maßgeschneiderten Versuchsaufbau benötigte, können mit dem neuen Netzwerk viele verschiedene Zustände innerhalb desselben Aufbaus beobachtet werden. Dies erfordert lediglich die Veränderung eines einzelnen, leicht zugänglichen experimentellen Parameters. Die so erzeugten Zustände besitzen eine Reihe nützlicher Eigenschaften und spielen eine zentrale Rolle in vielen Anwendungen. Hier werden sie zur Lösung eines vier-Parteien Quanten "Minority" Spiels verwendet. Es wird gezeigt, dass die Quanten Version des Spiels durch den Einsatz von vier-Qubit Verschränkung sein klassisches Pendant an Möglichkeiten deutlich übertrifft. Mit Hilfe experimenteller Daten beider Netzwerke wird eine neue Methode der Unterscheidung vier-Qubit verschränkter Zustände vorgestellt. Obwohl theoretische Klassifizierungen verschränkter Zustände existieren, gab es bisher keine einfache experimentelle Methode einen beobachteten Zustand der einen oder anderen Klasse zuzuordnen. Das hier vorgestellte Konzept ermöglicht eine experimentelle Klassifizierung basierend auf Operatoren die aus zustandsabhängigen Korrelationsmessungen bestimmt werden

Laserless trapped-ion quantum simulations without spontaneous scattering using microtrap arrays

We propose an architecture and methodology for large-scale quantum simulations using hyperfine states of trapped-ions in an arbitrary-layout microtrap array with laserless interactions. An ion is trapped at each site, and the electrode structure provides for the application of single and pairwise evolution operators using only locally created microwave and radio-frequency fields. The avoidance of short-lived atomic levels during evolution effectively eliminates errors due to spontaneous scattering; this may allow scaling of quantum simulators based on trapped ions to much larger systems than currently estimated. Such a configuration may also be particularly appropriate for one-way quantum computing with trapped-ion cluster states.Comment: 12 pages, 5 figures, edited typos, added refs and text for clarification to reflect published versio

Device-independent key distribution between trapped-ion quantum network nodes

Hybrid quantum systems, combining the advantages of matter-based carriers of quantum information with those of light, have potential applications across many domains of quantum science and technology. In this thesis, we present a high-fidelity, high-rate interface between trapped ions and polarisation-encoded photonic qubits, based on the spontaneous emission of 422 nm photons from ⁸⁸Sr⁺, entangled in polarisation with the resulting electronic state of the ion. We show that photons can be efficiently collected perpendicular to the ambient magnetic field without loss of polarisation purity by exploiting the symmetry properties of single-mode optical fibres, and analyse the impact of a number of common experimental imperfections, including in the heralded entanglement swapping step used to probabilistically generate entanglement between remote ion qubits. Our experimental platform consists of two ⁸⁸Sr⁺–⁴³Ca⁺ mixed-species quantum network nodes, linked by 2 × 1.75 m of single-mode optical fibre. We measure an ion–photon entanglement fidelity of 97.7(1) %, generated at an attempt rate of 1 MHz and up to 2.3 % overall collection/detection efficiency. Bell states between remote ⁸⁸Sr⁺ ions are generated at a fidelity of 96.0(1) % and rate of 100 s⁻¹. This is the highest fidelity for optically mediated entanglement between distant qubits reported across all matter qubit platforms, and the highest rate among those with fidelities >70 %. To compensate stray electric fields that would cause a periodic modulation of the ion position, we introduce a versatile method which relies on the synchronous detection of parametrically excited motion through time-stamped detection of photons scattered during laser cooling. Crucially, only a single laser beam is required to resolve fields in multiple directions; we achieve a stray field sensitivity of 0.1 V m⁻¹ / √Hz. Finally, we present the first experimental demonstration of device-independent quantum key distribution, by which two distant parties can share an information-theoretically secure private key even in the presence of an arbitrarily powerful eavesdropper without placing any trust in the quantum behaviour of their devices. This is enabled by a record-high detection-loophole-free CHSH inequality violation of 2.677(6) and low quantum bit error rate of 1.44(2) %, stable across millions of Bell pairs, and an improved security analysis and post-processing pipeline. We implement the complete end-to-end protocol in a realistic setting, allowing Alice and Bob to obtain a 95 884-bit key across 8.5 hours that is secure against the most general quantum attacks. Our results establish trapped ions as a state-of-the-art platform for photonic entanglement distribution at algorithmically relevant speeds and error rates. The link performance nevertheless remains far from fundamental limits; further improvements are discussed from the perspective of large-scale modular quantum computation as well as from that of long-distance quantum networking applications

Quantum Information Exchange Between Photons and Atoms

Ph.DDOCTOR OF PHILOSOPH

Robust laser-free entanglement with trapped ions

Trapped ions with microwave radiation are a promising platform for universal quantum computing. However, a major obstacle in the way of scalability is the coupling of the qubits to their noisy environment. This thesis offers means to improve the fidelity of two-qubit entangling gates. To this end, we investigate noise from classical control hardware and study quantum control methods that increase the gate’s robustness. The noise spectrums of classical control hardware typically exhibit non-Markovian behaviour. Therefore, a transfer function in frequency space is derived for each source, transforming hardware noise to qubit-frame noise. It is found that voltage noise on the electrodes is a significant contribution to decoherence as it displaces the ions within the static magnetic field gradient. We propose and demonstrate a voltage noise cancellation scheme that is compatible with microfabricated surface traps. We then identify a library of quantum control methods that increase the robustness of a bichromatic interaction to both spin and motional decoherence. We also propose a novel σz ⊗ σz entangling gate which makes use of the intrinsic J-coupling interaction of ions in a static magnetic gradient. The resulting interaction is virtually insensitive to motional decoherence, which alleviates stringent experimental requirements. We finally demonstrate a bichromatic interaction that is simultaneously robust to spin and motional decoherence, by means of continuous dynamical decoupling and phase modulation on the sidebands. Recalling that noise in the ion’s position couples into magnetic field noise due to the static magnetic field gradient, we use this noise mechanism as the basis of a promising electric field sensor. We experimentally demonstrate AC electrometry with a sensitivity of S = 7.0(5)mVm−1Hz−1/2. Noise spectroscopy was also demonstrated and was limited by the noise floor, where the minimum sensitivity was 545 nVm−1Hz−1/2.Open Acces

Quantum information dynamics

Presented is a study of quantum entanglement from the perspective of the theory of quantum information dynamics. We consider pairwise entanglement and present an analytical development using joint ladder operators, the sum of two single-particle fermionic ladder operators. This approach allows us to write down analytical representations of quantum algorithms and to explore quantum entanglement as it is manifested in a system of qubits.;We present a topological representation of quantum logic that views entangled qubit spacetime histories (or qubit world lines) as a generalized braid, referred to as a super-braid. The crossing of world lines may be either classical or quantum mechanical in nature, and in the latter case most conveniently expressed with our analytical expressions for entangling quantum gates. at a quantum mechanical crossing, independent world lines can become entangled. We present quantum skein relations that allow complicated superbraids to be recursively reduced to alternate classical histories. If the superbraid is closed, then one can decompose the resulting superlink into an entangled superposition of classical links. Also, one can compute a superlink invariant, for example the Jones polynomial for the square root of a knot.;We present measurement-based quantum computing based on our joint number operators. We take expectation values of the joint number operators to determine kinetic-level variables describing the quantum information dynamics in the qubit system at the mesoscopic scale. We explore the issue of reversibility in quantum maps at this scale using a quantum Boltzmann equation. We then present an example of quantum information processing using a qubit system comprised of nuclear spins. We also discuss quantum propositions cast in terms of joint number operators.;We review the well known dynamical equations governing superfluidity, with a focus on self-consistent dynamics supporting quantum vortices in a Bose-Einstein condensate (BEC). Furthermore, we review the mutual vortex-vortex interaction and the consequent Kelvin wave instability. We derive an effective equation of motion for a Fermi condensate that is the basis of our qubit representation of superfluidity.;We then present our quantum lattice gas representation of a superfluid. We explore aspects of our model with two qubits per point, referred to as a Q2 model, particularly its usefulness for carrying out practical quantum fluid simulations. We find that it is perhaps the simplest yet most comprehensive model of superfluid dynamics. as a prime application of Q2, we explore the power-law regions in the energy spectrum of a condensate in the low-temperature limit. We achieved the largest quantum simulations to date of a BEC and, for the first time, Kolmogorov scaling in superfluids, a flow regime heretofore only obtainably by classical turbulence models.;Finally, we address the subject of turbulence regarding information conservation on the small scales (both mesoscopic and microscopic) underlying the flow dynamics on the large hydrodynamic (macroscopic) scale. We present a hydrodynamic-level momentum equation, in the form of a Navier-Stokes equation, as the basis for the energy spectrum of quantum turbulence at large scales. Quantum turbulence, in particular the representation of fluid eddies in terms of a coherent structure of polarized quantum vortices, offers a unique window into the heretofore intractable subject of energy cascades