Optical Quantum Computation

We review the field of Optical Quantum Computation, considering the various implementations that have been proposed and the experimental progress that has been made toward realizing them. We examine both linear and nonlinear approaches and both particle and field encodings. In particular we discuss the prospects for large scale optical quantum computing in terms of the most promising physical architectures and the technical requirements for realizing them

Quantum teleportation and entanglement swapping with linear optics logic gates

We report on the usage of a linear optics phase gate for distinguishing all four Bell states simultaneously in a quantum teleportation and entanglement swapping protocol. This is demonstrated by full state tomography of the one and two qubit output states of the two protocols, yielding average state fidelities of about 0.83 and 0.77, respectively. In addition, the performance of the teleportation channel is characterised by quantum process tomography. The non classical properties of the entanglement swapping output states are further confirmed by the violation of a CHSH-type Bell inequality of 2.14 on average.Comment: 11 pages, 3 figure

Nonadiabatic Holonomic Quantum Computation and Its Optimal Control

Geometric phase has the intrinsic property of being resistant to some types of local noises as it only depends on global properties of the evolution path. Meanwhile, the non-Abelian geometric phase is in the matrix form, and thus can naturally be used to implement high performance quantum gates, i.e., the so-called holonomic quantum computation. This article reviews recent advances in nonadiabatic holonomic quantum computation, and focuses on various optimal control approaches that can improve the gate performance, in terms of the gate fidelity and robustness. Besides, we also pay special attention to its possible physical realizations and some concrete examples of experimental realizations. Finally, with all these efforts, within state-of-the-art technology, the performance of the implemented holonomic quantum gates can outperform the conventional dynamical ones, under certain conditions

Two-photon self-Kerr nonlinearities for quantum computing and quantum optics

The self-Kerr interaction is an optical nonlinearity that produces a phase shift proportional to the square of the number of photons in the field. At present, many proposals use nonlinearities to generate photon-photon interactions. For propagating fields these interactions result in undesirable features such as spectral correlation between the photons. Here, we engineer a discrete network composed of cross-Kerr interaction regions to simulate a self-Kerr medium. The medium has effective long-range interactions implemented in a physically local way. We compute the one- and two-photon S matrices for fields propagating in this medium. From these scattering matrices we show that our proposal leads to a high fidelity photon-photon gate. In the limit where the number of nodes in the network tends to infinity, the medium approximates a perfect self-Kerr interaction in the one- and two-photon regime.Comment: V2: published version; with new section with a qualitative description and new appendix comparing to probabilistic gates. V1: also see arXiv:1604.04278 and arXiv:1604.0391

Quantum Optical Systems for the Implementation of Quantum Information Processing

We review the field of Quantum Optical Information from elementary considerations through to quantum computation schemes. We illustrate our discussion with descriptions of experimental demonstrations of key communication and processing tasks from the last decade and also look forward to the key results likely in the next decade. We examine both discrete (single photon) type processing as well as those which employ continuous variable manipulations. The mathematical formalism is kept to the minimum needed to understand the key theoretical and experimental results

Decoherence Effects on All-optical Quantum Information Processing

학위논문 (박사)-- 서울대학교 대학원 : 물리천문학부, 2012. 8. 정현석.It has been thought for long that information is something useful but does not have physical reality, irrelevant to physical laws. Landauers principle concerning the entropy increase accompanying the erasure of a bit implies that this belief is not true. The recent developments in quantum information processing (QIP) have brought the advantages inaccessible for classical means, such as unconditionally secure communication, exponential speed-ups in factoring integers and database search. Optical QIP, using light for information carrier, has been a popular choice among many candidates due to the significant developments in photon manipulation. In addition, it is easy to combine communication and computation using light. Linear optics using only passive optical elements (e.g. beam splitter) which conserve energy of the states is of interest, as naturally occurring non-linearity is very small. Decoherence caused by the openness of the system of interest is nowadays considered as a major factor of the occurrence of classicality out of quantum physics. Decoherence destroys coherence inevitable for quantum aspect of information, and is a big obstacle for QIP. In this thesis, the focus will be put on the effect of decoherence on the optical QIP, particularly on the quantum teleportation proposed by Bennett \textit{et al.}, which is one of the core ingredient of linear optical QIP. Quantum teleportation can be a very efficient way to implement quantum gate operations, and thus the degradation on it will affect the efficiency of total quantum circuit. I will introduce the two works related to this topic. First, we study entangled coherent states versus entangled photon pairs for practical quantum-information processing. We compare effects of decoherence and detection inefficiency on entangled coherent states (ECSs) and entangled photon pairs (EPPs), both of which are known to be particularly useful for quantum information processing. When decoherence effects caused by photon losses are heavy, the ECSs outperform the EPPs as quantum channels for teleportation both in fidelities and in success probabilities. On the other hand, when inefficient detectors are used, the teleportation scheme using the ECSs suffers undetected errors that result in the degradation of fidelity, while this is not the case for the teleportation scheme using the EPPs. Our study reveals the merits and demerits of the two types of entangled states in realizing practical QIP under realistic conditions. Secondly, we study quantum teleportation between two different types of optical qubits, one of which is ``particle-like'' and the other ``field-like,'' via hybrid entangled states under the effects of decoherence. We find that teleportation from particle-like to field-like qubits can be achieved with a higher fidelity than that in the opposite direction. However, teleportation from field-like to particle-like qubits is found to be more efficient in terms of the success probabilities. Our study shows that the direction of teleportation should be considered an important factor in developing optical hybrid architectures for quantum information processing.Abstract vii 1 Introduction 1 2 Entanglement 4 2.1 Applications with entanglement . . . . . . . . . . . . . . . . . . . 4 2.2 Nonlocal character of entanglement . . . . . . . . . . . . . . . . . 7 2.3 Quantication of entanglement . . . . . . . . . . . . . . . . . . . 10 2.4 Quantum steering . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3 Decoherence 14 3.1 Conceptual importance . . . . . . . . . . . . . . . . . . . . . . . . 14 3.1.1 Decoherence . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.1.2 Measurements, the preferred basis problem and environment-induced superselection . . . . . . . . . . . . . 15 3.1.3 Environmental-induced decoherence . . . . . . . . . . . . . 17 3.2 Mathematical description of decoherence . . . . . . . . . . . . . . 18 3.2.1 Born and Markov Approximations . . . . . . . . . . . . . . 18 x 3.2.2 Master equation of optical dissipative process . . . . . . . 19 3.2.3 Non-markovian dynamics . . . . . . . . . . . . . . . . . . . 21 3.3 Decay rate of optical decoherence . . . . . . . . . . . . . . . . . . 22 4 Optical Quantum Information Processing 24 4.1 Linear optical quantum computation . . . . . . . . . . . . . . . . 24 4.2 Coherent state quantum computation . . . . . . . . . . . . . . . . 29 5 Entangled Coherent States versus Entangled Photon Pairs for Practical Quantum Information Processing 33 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 5.2 Decoherence of ECSs and EPPs . . . . . . . . . . . . . . . . . . . 36 5.2.1 Solutions of master equation . . . . . . . . . . . . . . . . . 37 5.2.2 Degrees of entanglement . . . . . . . . . . . . . . . . . . . 39 5.3 Teleportation with ECS and EPP . . . . . . . . . . . . . . . . . . 41 5.3.1 Eects of channel decoherence . . . . . . . . . . . . . . . . 43 5.3.2 Eects of detection ineciency . . . . . . . . . . . . . . . 51 5.3.3 Photon losses both in channels and at detectors . . . . . . 55 5.4 Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 6 Quantum Teleportation between Particle-like and Field-like Qubits under Decoherence 59 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 6.2 Time evolution of teleportation channels . . . . . . . . . . . . . . 62 6.3 Entanglement of hybrid channels . . . . . . . . . . . . . . . . . . 64 xi 6.4 Teleportation between polarization and coherent-state qubits . . . 66 6.4.1 Teleportation delities . . . . . . . . . . . . . . . . . . . . 67 6.4.2 Success probabilities . . . . . . . . . . . . . . . . . . . . . 75 6.5 Teleportation between polarization and single-rail Fock state qubits 78 6.6 Single-qubit rotation of coherent state qubit by hybrid strategy . 82 6.7 Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 7 Conclusion 88 Bibliography 91Docto