Control and coupling of individual quantum systems remains an important research area in experimental quantum information. Single quantum systems in the solid state offer many attractive properties in terms of isolation and control: strong interaction due to close proximity, and scalability using mature fabrication techniques. Similar to atoms, many solid state quantum systems can couple to photons, offering potential for long-range interaction. Two such candidate systems are the nitrogen vacancy center in diamond, and the nanowire semiconductor quantum dot. These systems can act like isolated atoms in a solid state system, and can serve as sources of indistinguishable photons. This report discusses low temperature excitation of these systems, a regime in which the spectral properties are desirable for applications in quantum information, such as long-distance entanglement.

Control and coupling of individual quantum systems remains an important research area in experimental quantum information. Single quantum systems in the solid state offer many attractive properties in terms of isolation and control: strong interaction due to close proximity, and scalability using mature fabrication techniques. Similar to atoms, many solid state quantum systems can couple to photons, offering potential for long-range interaction. Two such candidate systems are the nitrogen vacancy center in diamond, and the nanowire semiconductor quantum dot. These systems can act like isolated atoms in a solid state system, and can serve as sources of indistinguishable photons. This report discusses low temperature excitation of these systems, a regime in which the spectral properties are desirable for applications in quantum information, such as long-distance entanglement.

Open quantum systems refer to systems that are affected by interaction with the environment. The effects of these unwanted interactions, called \emph{quantum noise}, are studied using dynamical maps. We study the geometry of these maps in this work. We review the canonical representations of dynamical maps such as reduced dynamics, $\mathcal{A}$ and $\mathcal{B}$ forms and operator sum representation. We develop a framework for simplifying the action of dynamical maps in terms of their action on the coherence vector associated with the density matrix. We use the framework to describe the geometry of depolarization, dephasing and dissipation in the domain of complete positivity. We give a geometric picture of how two-, three- and four-level systems are affected by these common forms of quantum noises. We show useful similarities between two- and four-level depolarizing maps and give a generalization for $n$-qubits. We also derive important results that restrict dephasing and dissipation. / text

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This thesis deals with the implementation of quantum channels using linear optics. We begin with overviews of some important concepts in both quantum information and quantum optics. First, we discuss the quantum bit and describe the evolution of the states via quantum channels. We then discuss both quantum state and process tomography, methods for how to determine which states and operations we are experimentally implementing in the lab. Second, we discuss topics in quantum optics such the generation of single photons, polarization entanglement, and the construction of an entangling gate. The first experiment is the implementation of a quantum damping channel, which intentionally can add a specific type and amount of decohering noise to a photonic qubit. Specifically, we realized a class of quantum channels which contains both the amplitude-damping channel and the bit-flip channel, and did so with a single, static, optical setup. Many quantum channels, and some gates, can only be implemented probabilistically when using linear optics and postselection. Our main result is that the optical setup achieves the optimal success probability for each channel. Using a novel ancilla-assisted tomography, we characterize each case of the channel, and find process fideilities of $0.98 \pm 0.01$ for the amplitude-damping channel and $0.976 \pm 0.009$ for the bit-flip. The second experiment is an implementation of a protocol for quantum computing on encrypted data. The protocol provides the means for a client with very limited quantum power to use a server's quantum computer while maintaining privacy over the data. We perform a quantum process tomography for each gate in a universal set, showing that only when the proper decryption key is used on the output states, which is hidden from the server, then the action of the quantum gate is recovered. Otherwise, the gate acts as the completely depolarizing channel.

Cryptography plays an integral role in secure communication and is usually the strongest link in the chain of security. Yet security problems abound in electronic communication: spyware, phishing, denial of service, and side-channel attacks are still major concerns. The main goal in this thesis is to consider how cryptographic techniques can be extended to offer greater defence against these non-traditional security threats. In the first part of this thesis, we consider problems in classical cryptography. We introduce multi-factor password-authenticated key exchange which allows secure authentication and key agreement based on multiple short secrets, such as a long-term password and a one-time response; it can provide an enhanced level of assurance in higher security scenarios because a multi-factor protocol is designed to remain secure even if all but one of the factors has been compromised due to attacks such as phishing or spyware. Next, we consider the integration of denial of service countermeasures with key exchange protocols: by introducing a formal model for denial of service resilience that complements the extended Canetti-Krawczyk model for secure key agreement, we cover a wide range of existing denial of service attacks and prevent them by carefully using client puzzles. Additionally, we look at how side-channel attacks affect certain types of formulae used in elliptic curve cryptography, and demonstrate that information leaked during field operations such as addition, subtraction, and multiplication can be exploited by an attacker. In the second part of this thesis, we examine cryptography in the quantum setting. We argue that quantum key distribution will have an important role to play in future information security infrastructures and will operate best when integrated with the powerful public key infrastructures that are used today. Finally, we present a new look at quantum money and describe a quantum coin scheme where the coins are not easily counterfeited, are locally verifiable, and can be transferred to another party.

The main results of this thesis fall in to two areas, firstly quantum reference frames as a resource for quantum computations and secondly quantum algorithms. The results relating to quantum references consider their scaling with a requirements to perform measurements, operations and computations with a certain fidelity. For the case of a directional frame, the central question considered is of how many operations or measurements can be performed with it before its fidelity falls below some threshold. This is found to scale as the square of the size of the reference frame under for a range of physically interesting cases. To prove that result a new general form for any rotationally invariant map. This could have many applications is comparing and classifying rotationally invariant behaviour of quantum systems. Phase references are also considered for the case of performing quantum computations under an energy conservation law. The restriction that the expected energy be conserved for large quantum computations is shown to be manageable in many different potential architectures. In the case of completing computations is an energy conserving subspace, the requirements for ancillas are sublinear in the number of qubits, and even in a circuit model implementation, the errors due to phase reference imperfections are shown to not limit the apparent algorithmic improvements of quantum computing over classical computing. A quantum walk for the novel concept of two entangled walkers is proposed and analyzed. A modest improvement is found in the scaling of the expected separation of the walkers over the separable case. It illustrates the potential for making use of particle statistic behaviour in algorithms. Lastly, the relation between discrete and continuous time models of quantum computing is explored through the analysis of a new algorithm for simulating the Hamiltonian behaviour of a black box unitary operation. The scaling of the number of calls to the unitary required to obtain a simulation correct to within a parameter ϵ is found, as is a case where the efficiency of the algorithm is superior to directly applying the unitary repeatedly. Applications of the algorithm are considered.

Cryptography plays an integral role in secure communication and is usually the strongest link in the chain of security. Yet security problems abound in electronic communication: spyware, phishing, denial of service, and side-channel attacks are still major concerns. The main goal in this thesis is to consider how cryptographic techniques can be extended to offer greater defence against these non-traditional security threats. In the first part of this thesis, we consider problems in classical cryptography. We introduce multi-factor password-authenticated key exchange which allows secure authentication and key agreement based on multiple short secrets, such as a long-term password and a one-time response; it can provide an enhanced level of assurance in higher security scenarios because a multi-factor protocol is designed to remain secure even if all but one of the factors has been compromised due to attacks such as phishing or spyware. Next, we consider the integration of denial of service countermeasures with key exchange protocols: by introducing a formal model for denial of service resilience that complements the extended Canetti-Krawczyk model for secure key agreement, we cover a wide range of existing denial of service attacks and prevent them by carefully using client puzzles. Additionally, we look at how side-channel attacks affect certain types of formulae used in elliptic curve cryptography, and demonstrate that information leaked during field operations such as addition, subtraction, and multiplication can be exploited by an attacker. In the second part of this thesis, we examine cryptography in the quantum setting. We argue that quantum key distribution will have an important role to play in future information security infrastructures and will operate best when integrated with the powerful public key infrastructures that are used today. Finally, we present a new look at quantum money and describe a quantum coin scheme where the coins are not easily counterfeited, are locally verifiable, and can be transferred to another party.

The main results of this thesis fall in to two areas, firstly quantum reference frames as a resource for quantum computations and secondly quantum algorithms. The results relating to quantum references consider their scaling with a requirements to perform measurements, operations and computations with a certain fidelity. For the case of a directional frame, the central question considered is of how many operations or measurements can be performed with it before its fidelity falls below some threshold. This is found to scale as the square of the size of the reference frame under for a range of physically interesting cases. To prove that result a new general form for any rotationally invariant map. This could have many applications is comparing and classifying rotationally invariant behaviour of quantum systems. Phase references are also considered for the case of performing quantum computations under an energy conservation law. The restriction that the expected energy be conserved for large quantum computations is shown to be manageable in many different potential architectures. In the case of completing computations is an energy conserving subspace, the requirements for ancillas are sublinear in the number of qubits, and even in a circuit model implementation, the errors due to phase reference imperfections are shown to not limit the apparent algorithmic improvements of quantum computing over classical computing. A quantum walk for the novel concept of two entangled walkers is proposed and analyzed. A modest improvement is found in the scaling of the expected separation of the walkers over the separable case. It illustrates the potential for making use of particle statistic behaviour in algorithms. Lastly, the relation between discrete and continuous time models of quantum computing is explored through the analysis of a new algorithm for simulating the Hamiltonian behaviour of a black box unitary operation. The scaling of the number of calls to the unitary required to obtain a simulation correct to within a parameter ϵ is found, as is a case where the efficiency of the algorithm is superior to directly applying the unitary repeatedly. Applications of the algorithm are considered.

This thesis describes the back action of microwave-photon detection via a Josephson photomultiplier (JPM), a superconducting qubit coupled strongly to a high-quality mi- crowave cavity, and the applications of these devices. The back action operator depends qualitatively on the duration of the measurement interval, resembling the regular photon annihilation operator at short interaction times and approaching a variant of the photon subtraction operator at long times. The optimal operating conditions of the JPM differ from those considered optimal for processing and storing of quantum information, in that a short T2 of the JPM suppresses the cavity dephasing incurred during measurement. Un- derstanding this back action opens the possibility to perform multiple JPM measurements on the same state, hence performing efficient state tomography. In addition, this the- sis describes the creation of non-classical states of microwave radiation via single photon detection using JPMs. When operated in the low T2 regime, the back action of a JPM resembles the photon subtraction operator. Using the non-linearity of this back action, it is possible to create non-classical states of microwave radiation, including squeezed vacuum and odd Schro ̈dinger cat states, starting from a coherent state.