In this thesis, we will discuss the possibility of wave manipulation by graded materials and/or systems. In contrast to the traditional inhomogeneous media, i.e. periodically modulated system and randomly disordered system, graded system demonstrates a unique way to control wave, resulting in a new type of localization-delocalization transition, which can confine the primary excitations (e.g., photons, phonons, and surface plasmons) and redistribute them spatially. This is not only of fundamental significance, but will also pave new avenue for various applications, for example, in surface elastic waves, nanooptics, and plasmonics. It also has implications with practical problems in industry such as oil probing and earthquake study. / Manipulating waves (e.g., elastic or electromagnetic) inside nanostructures has attracted ever increasing interest over the past decades due to the rapid advancement of nanofabrication techniques. Particularly, interactions of light with structures modulated at the wavelength or subwavelength scale offer an opportunity to achieve novel properties and designated functionalities in nanophotonics. Notable examples include photonic crystals, various metamaterials, and plasmonic devices. / Moreover, we consider to combine the novel properties of gradons and surface plasmons (SPs), in an attempt to explore new mechanisms to manipulate SP. Firstly, we study an incrementally-spaced nanoparticle chain waveguide, in which coupled plasmon waves show a localization-delocalization transition, in analogy to the elastic gradons. Secondly, we propose waveguides using periodic plasmonic chains immersed in a graded host which can sustain "light", "heavy", and "light-heavy" plasmonic gradons. Existence of tunable passband is demonstrated in these systems. / Thus, in view of the success, we discuss many potential applications in plasmonics, such as junctions, transistors, and even on-chip integrated plasmonic-dielectric devices. In this regard, we further study the most commonly used coplanar photonic elements, i.e., ring resonators and their integrated devices. To explore the interactions between various gradons and typical excitations would be very interesting and rewarding. Our findings have important ramifications for understanding excitations with transition spectra in many condensed matter systems, ranging from ultrasonic waves, seismic waves to light waves, microwaves, as well as quantum waves. / We started with one-dimensional graded networks of coupled harmonic oscillators. By examining the vibrational mode characteristics, we have identified a new kind of vibrational excitations, which are named "gradons". The features of elastic gradon are elab orated. Gradon localization is also different from well-known mechanisms of localization transition, such as defect(s) and Anderson-type localization. Gradons in higher dimensional graded elastic networks show more intriguing behaviors; we proved the existence of "soft", "hard", and "soft-hard" gradons in two dimensional cases. / Xiao Junjun = 新型调波功能材料 : 梯度子及其在纳米光学中的应用 / 肖君军. / "May 2006." / Adviser: Kin Wah Yu. / Source: Dissertation Abstracts International, Volume: 68-03, Section: B, page: 1694. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (p. 108-118). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307. / Xiao Junjun = Xin xing diao bo gong neng cai liao : ti du zi ji qi zai na mi guang xue zhong de ying yong / Xiao Junjun.

Ng Kin Man. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (leaves 186-189). / Ng Kin Man. / Contents --- p.i / List of Figures --- p.ii / Abstract --- p.iv / Acknowledgement --- p.v / Chapter Chapter 1. --- Introduction --- p.1 / Chapter 1.1 --- Introduction --- p.1 / Chapter 1.2 --- Objective and Methodology --- p.3 / Chapter Chapter 2. --- Theory of the Jaynes-Cummings model --- p.6 / Chapter 2.1 --- Formulation of the Problem --- p.6 / Chapter 2.1.1 --- Quantization of the Electromagnetic Field --- p.7 / Chapter 2.1.2 --- Quantization of the Matter Field --- p.11 / Chapter 2.1.3 --- The Interaction between the Radiation and the Matter --- p.12 / Chapter 2.1.4 --- Formulation of the one-photon JCM --- p.14 / Chapter 2.2 --- Eenergy eigenstates and Eigenvalue Spectrum --- p.16 / Chapter 2.3 --- Dynamics of the one-photon JCM --- p.18 / Chapter 2.3.1 --- The time evolution of the system --- p.19 / Chapter 2.3.2 --- Atomic Observables --- p.20 / Chapter 2.3.3 --- Field Observables --- p.23 / Chapter 2.4 --- Asymptotic solution of the JCM --- p.27 / Chapter 2.5 --- Discussion of the role of the RWA in the JCM --- p.29 / Chapter 2.6 --- Conclusion --- p.30 / Chapter Chapter 3. --- Numerical Results for the one-photon JCM --- p.40 / Chapter 3.1 --- Eigenstates and Eigenvalue Spectrum --- p.40 / Chapter 3.2 --- Dynamics of the System --- p.44 / Chapter 3.2.1 --- Atomic Observables --- p.44 / Chapter 3.2.2 --- Field Observables --- p.45 / Chapter 3.3 --- Conclusion --- p.47 / Chapter Chapter 4. --- Generalization of the JCM --- p.60 / Chapter 4.1 --- Multiphoton JCM --- p.60 / Chapter 4.2 --- Intensity-dependent JCM --- p.62 / Chapter 4.3 --- Two-mode two-photon JCM --- p.64 / Chapter 4.4 --- Conclusion --- p.66 / Chapter Chapter 5. --- Multiphoton Jaynes-Cummings model --- p.67 / Chapter 5.1 --- Energy Eigenstates and Eigenvalue Spectrum --- p.67 / Chapter 5.1.1 --- Energy Eigenstates and Eigenvalue Spectrum of the two- photon JCM --- p.71 / Chapter 5.1.2 --- Eigenstates and Eigenvalue Spectrum for the k-photon JCM with k>2 --- p.73 / Chapter 5.2 --- Dynamics of the two-photon JCM --- p.75 / Chapter 5.2.1 --- Atomic Observables --- p.75 / Chapter 5.2.2 --- Field Observables --- p.77 / Chapter 5.3 --- Conclusion --- p.84 / Chapter Chapter 6. --- Intensity-dependent Jaynes-Cummings model --- p.107 / Chapter 6.1 --- Eigenstates and Eigenvalue Spectrum --- p.107 / Chapter 6.1.1 --- Energy Eigenstates and Eigenvalue Spectrum of the one- photon intensity-dependent JCM --- p.110 / Chapter 6.1.2 --- "Energy Eigenstates and Eigenvalue Spectrum for the k-photon intensity-dependent, JCM with k > 1" --- p.113 / Chapter 6.2 --- Dynamics of the one-photon intensity-dependent JCM --- p.115 / Chapter 6.2.1 --- Atomic Observables --- p.115 / Chapter 6.2.2 --- Field Observables --- p.116 / Chapter 6.3 --- Conclusion --- p.123 / Chapter Chapter 7. --- Two-mode Two-photon Jaynes- Cummings model --- p.148 / Chapter 7.1 --- Eigenstates and Eigenvalue Spectrum --- p.148 / Chapter 7.2 --- Dynamics of the System --- p.156 / Chapter 7.2.1 --- Atomic Observables --- p.156 / Chapter 7.2.2 --- Field Observables --- p.160 / Chapter 7.3 --- Conclusion --- p.161 / Chapter Chapter 8. --- Conclusion --- p.183 / Bibliography --- p.186

Poon, Sin Yau = 光子在噪聲環境中的解糾纏 / 潘善柔. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 101-110). / Abstracts in English and Chinese. / Poon, Sin Yau = Guang zi zai zao sheng huan jing zhong de jie jiu chan / Pan Shanrou. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Review on entanglement theory --- p.4 / Chapter 2.1 --- Pure state entanglement --- p.4 / Chapter 2.2 --- Mixed state entanglement --- p.7 / Chapter 2.3 --- Positive partial transposition (PPT) criterion --- p.9 / Chapter 2.4 --- Negativity of pTA --- p.9 / Chapter 2.4.1 --- Basic properties --- p.10 / Chapter 2.4.2 --- Comparison with concurrence --- p.11 / Chapter 2.5 --- Entanglement witness --- p.12 / Chapter 2.6 --- Inseparability criterion based on uncertainty relations --- p.13 / Chapter 2.7 --- Limitations of the PPT criterion --- p.14 / Chapter 2.8 --- Other manifestations of entanglement --- p.16 / Chapter 2.8.1 --- Non-classicality by negative P-representation --- p.16 / Chapter 2.8.2 --- Non-locality by violation of Bell´ةs inequality --- p.17 / Chapter 3 --- Quantum decoherence: General considerations for open systems --- p.22 / Chapter 3.1 --- A master equation approach --- p.22 / Chapter 3.1.1 --- Master equation in Markovian channels --- p.25 / Chapter 3.2 --- Negativity as a monotone in Markovian systems --- p.26 / Chapter 3.3 --- Finite time disentanglement --- p.29 / Chapter 3.4 --- Non-classicality of harmonic oscillating systems in finite temperature baths --- p.32 / Chapter 4 --- Disentanglement dynamics of two-mode Gaussian states --- p.36 / Chapter 4.1 --- Two-mode Gaussian states: General descriptions --- p.36 / Chapter 4.1.1 --- Covariance matrices and symplectic eigenvalues --- p.37 / Chapter 4.1.2 --- Squeezed states as a source of entanglement --- p.39 / Chapter 4.2 --- Eigenvalues and eigenvectors of pTA --- p.41 / Chapter 4.3 --- Physical interpretation of negativity --- p.43 / Chapter 4.4 --- Disentanglement of two-mode squeezed states in damping and amplifying environment --- p.47 / Chapter 4.4.1 --- Block structures of pTA in Fock space --- p.47 / Chapter 4.4.2 --- Analytic solution of p in position space --- p.49 / Chapter 4.4.3 --- Evolution of eigenvalues and eigenvectors of pTA --- p.51 / Chapter 4.4.4 --- Robust structure of entanglement witness --- p.56 / Chapter 4.5 --- Beam splitter as a model for thermal damping of initial Gaussian states --- p.59 / Chapter 4.6 --- Evolution of entanglement of a damped parametric oscillator --- p.63 / Chapter 4.6.1 --- Eigenvalues and Eigenvectors of pTA --- p.64 / Chapter 4.6.2 --- Negativity and sub-negativity --- p.66 / Chapter 4.7 --- Dissipation in baths with both amplitude and phase damping --- p.68 / Chapter 4.8 --- Loss of nonlocality: An optimized Bell's inequality approach --- p.69 / Chapter 5 --- Disentanglement via polarization mode dispersion --- p.73 / Chapter 5.1 --- Review on polarization mode dispersion --- p.73 / Chapter 5.2 --- A model for stochastic polarization mode dispersion --- p.75 / Chapter 5.3 --- General description of two-photon states --- p.78 / Chapter 5.4 --- Disentanglement of two-photon states in separate fibers --- p.81 / Chapter 5.4.1 --- Polarization negativity and frequency negativity --- p.83 / Chapter 5.4.2 --- Polarization disentanglement --- p.84 / Chapter 5.4.3 --- Frequency disentanglement --- p.85 / Chapter 5.5 --- Disentanglement of two-photon states in a common fiber --- p.86 / Chapter 5.5.1 --- Polarization disentanglement of the singlet state --- p.90 / Chapter 5.5.2 --- Frequency entanglement of the singlet state --- p.91 / Chapter 5.6 --- Non-Markovian channels --- p.92 / Chapter 6 --- Conclusion --- p.99 / Bibliography --- p.101 / Chapter A --- CHSH Inequality for bipartite two level systems --- p.111 / Chapter B --- Transformation from general two-mode Gaussian to double Gaussian product --- p.113 / Chapter C --- Time evolution of general real symmetric two-mode Gaussian density operator --- p.116 / Chapter D --- Time evolution of a damped parametric oscillator --- p.119 / Chapter E --- Optimal Bell values for a damped TMSV in pseudo-spin formalism --- p.123 / Chapter F --- Derivation of master equation for two-photon states --- p.125 / Chapter G --- Solution of master equation for two-photon states --- p.127 / Chapter G.1 --- Evolution of two-photon states in separate fibers --- p.127 / Chapter G.2 --- Evolution of two-photon state in a common fiber --- p.129

acase@tulane.edu / In this dissertation we test our ability to implement linear entangling operations between small numbers of photons for application in quantum communication and computation. We begin by presenting a fast and highly parallelizable numerical algorithm for simulating linear optical circuits on classical hardware. Then, we apply this algorithm to three independent topics in quantum information: First, in Chapter 2, we determine the information capacity of an optical quantum channel and show that a linear encoding is generally sufficient to achieve this capacity. In Chapter 3 we introduce a computational encoding basis wherein qubits are stored in single-photon blocks and then test our ability to apply entangling operations between blocks. Finally, in Chapter 4, we use our algorithm to make progress in the long-standing problem of designing a near-perfect optical Bell state analyzer. We find a clear trend in state distinguishability as we incorporate unentangled pairs of ancilla photons. We also prove that if a measurement outcome in which all photons are bunched into only two output modes is possible, then perfect state discrimination is impossible. We then present a set of conditions that prevent this outcome. / 1 / Jake A Smith

No description available.

Quantum cryptography, or quantum key distribution (QKD), provides a means of unconditionally secure communication. The security is in principle based on the fundamental laws of physics. Security proofs show that if quantum cryptography is appropriately implemented, even the most powerful eavesdropper cannot decrypt the message from a cipher. The implementations of quantum crypto-systems in real life may not fully comply with the assumptions made in the security proofs. Such discrepancy between the experiment and the theory can be fatal to the security of a QKD system. In this thesis we address a number of these discrepancies. A perfect single-photon source is often assumed in many security proofs. However, a weak coherent source is widely used in a real-life QKD implementation. Decoy state protocols have been proposed as a novel approach to dramatically improve the performance of a weak coherent source based QKD implementation without jeopardizing its security. Here, we present the first experimental demonstrations of decoy state protocols. Our experimental scheme was later adopted by most decoy state QKD implementations. In the security proof of decoy state protocols as well as many other QKD protocols, it is widely assumed that a sender generates a phase-randomized coherent state. This assumption has been enforced in few implementations. We close this gap in two steps: First, we implement and verify the phase randomization experimentally; second, we prove the security of a QKD implementation without the coherent state assumption. In many security proofs of QKD, it is assumed that all the detectors on the receiver's side have identical detection efficiencies. We show experimentally that this assumption may be violated in a commercial QKD implementation due to an eavesdropper's malicious manipulation. Moreover, we show that the eavesdropper can learn part of the final key shared by the legitimate users as a consequence of this violation of the assumptions.

Quantum cryptography, or quantum key distribution (QKD), provides a means of unconditionally secure communication. The security is in principle based on the fundamental laws of physics. Security proofs show that if quantum cryptography is appropriately implemented, even the most powerful eavesdropper cannot decrypt the message from a cipher. The implementations of quantum crypto-systems in real life may not fully comply with the assumptions made in the security proofs. Such discrepancy between the experiment and the theory can be fatal to the security of a QKD system. In this thesis we address a number of these discrepancies. A perfect single-photon source is often assumed in many security proofs. However, a weak coherent source is widely used in a real-life QKD implementation. Decoy state protocols have been proposed as a novel approach to dramatically improve the performance of a weak coherent source based QKD implementation without jeopardizing its security. Here, we present the first experimental demonstrations of decoy state protocols. Our experimental scheme was later adopted by most decoy state QKD implementations. In the security proof of decoy state protocols as well as many other QKD protocols, it is widely assumed that a sender generates a phase-randomized coherent state. This assumption has been enforced in few implementations. We close this gap in two steps: First, we implement and verify the phase randomization experimentally; second, we prove the security of a QKD implementation without the coherent state assumption. In many security proofs of QKD, it is assumed that all the detectors on the receiver's side have identical detection efficiencies. We show experimentally that this assumption may be violated in a commercial QKD implementation due to an eavesdropper's malicious manipulation. Moreover, we show that the eavesdropper can learn part of the final key shared by the legitimate users as a consequence of this violation of the assumptions.

This thesis describes the deployment of a free-space quantum key distribution system across the University of Waterloo campus. The quantum key distribution system has the ability to provide unconditionally secure communication between two parties: Alice and Bob. The system exploits the quantum mechanical property of entanglement in order to generate a key. Security is then guaranteed by the No-Cloning theorem and the laws of quantum mechanics which prevent a quantum system from being measured without disturbing it. Polarization-entangled photon pairs are created using the non-linear optical process of type-II spontaneous parametric down-conversion. A free-space link of approximately $\mathrm{580~m}$ is used to distribute one-half of the pairs to Alice at a distant location, while the other half of the pairs are locally detected by Bob. The details of the detection apparatus necessary to measure the polarization of the photons and the software used to process the measurement data according to the BBM92 protocol are described. An experimental violation of the CHSH inequality (a derivative of the original Bell inequality) is demonstrated to show that polarization-entangled photon pairs are in fact being distributed to the two parties. Finally, the full BBM92 protocol is performed using the entangled photon pairs to generate a secure key and transmit an encrypted message between Alice and Bob. Currently, the system can only be operated at night because background light saturates the detectors during the day; however, future work will focus on making daylight operation feasible.

This thesis describes a linear-optical device for performing generalized quantum measurements on quantum bits (qubits) encoded in photon polarization, the implementation of said device, and its use in two diff erent but related experiments. The device works by coupling the polarization degree of freedom of a single photon to a `mode' or `path' degree of freedom, and performing a projective measurement in this enlarged state space in order to implement a tunable four-outcome positive operator-valued measure (POVM) on the initial quantum bit. In both experiments, this POVM is performed on one photon from a two-photon entangled state created through spontaneous parametric down-conversion. In the fi rst experiment, this entangled state is viewed as a two-qubit photonic cluster state, and the POVM as a means of increasing the computational power of a given resource state in the cluster-state model of quantum computing. This model traditionally achieves deterministic outputs to quantum computations via successive projective measurements, along with classical feedforward to choose measurement bases, on qubits in a highly entangled resource called a cluster state; we show that `virtual qubits' can be appended to a given cluster by replacing some projective measurements with POVMs. Our experimental demonstration fully realizes an arbitrary three-qubit cluster computation by implementing the POVM, as well as fast active feed-forward, on our two-qubit photonic cluster state. Over 206 diff erent computations, the average output delity is 0.9832 +/- 0.0002; furthermore the error contribution from our POVM device and feedforward is only of order 10^-3, less than some recent thresholds for fault-tolerant cluster computing. In the second experiment, the POVM device is used to implement a deterministic protocol for remote state preparation (RSP) of arbitrary photon polarization qubits. RSP is the act of preparing a quantum state at a remote location without actually transmitting the state itself. We are able to remotely prepare 178 diff erent pure and mixed qubit states with an average delity of 0.995. Furthermore, we study the the fidelity achievable by RSP protocols permitting only classical communication, without shared entanglement, and compare the resulting benchmarks for average fidelity against our experimental results. Our experimentally-achieved average fi delities surpass the classical thresholds whenever classical communication alone does not trivially allow for perfect RSP.

This thesis describes the deployment of a free-space quantum key distribution system across the University of Waterloo campus. The quantum key distribution system has the ability to provide unconditionally secure communication between two parties: Alice and Bob. The system exploits the quantum mechanical property of entanglement in order to generate a key. Security is then guaranteed by the No-Cloning theorem and the laws of quantum mechanics which prevent a quantum system from being measured without disturbing it. Polarization-entangled photon pairs are created using the non-linear optical process of type-II spontaneous parametric down-conversion. A free-space link of approximately $\mathrm{580~m}$ is used to distribute one-half of the pairs to Alice at a distant location, while the other half of the pairs are locally detected by Bob. The details of the detection apparatus necessary to measure the polarization of the photons and the software used to process the measurement data according to the BBM92 protocol are described. An experimental violation of the CHSH inequality (a derivative of the original Bell inequality) is demonstrated to show that polarization-entangled photon pairs are in fact being distributed to the two parties. Finally, the full BBM92 protocol is performed using the entangled photon pairs to generate a secure key and transmit an encrypted message between Alice and Bob. Currently, the system can only be operated at night because background light saturates the detectors during the day; however, future work will focus on making daylight operation feasible.