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.

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.

This PhD thesis contains a general introduction and three main chapters. Chapter 2 investigates Bell inequalities that generalize the CHSH and Braunstein-Caves inequalities. Chapter 3 shows a derivation of an upper bound on the success probability of a class of quantum teleportation protocols, denoted as port-based teleportation, from the no-cloning theorem and the no-signalling principle. Chapter 4 introduces the principle of quantum information causality. Chapter 2 considers the predictions of quantum theory and local hidden variable theories (LHVT) for the correlations obtained by measuring a pair of qubits by projections defined by randomly chosen axes separated by a given angle θ. The predictions of LHVT correspond to binary colourings of the Bloch sphere with antipodal points oppositely coloured. We show a Bell inequality for all θ, which generalizes the CHSH and the Braunstein-Caves inequalities in the sense that the measurement choices are not restricted to be in a finite set, but are constrained only by the angle θ. We motivate and explore the hypothesis that for a continuous range of θ > 0, the maximum correlation (anticorrelation) is obtained by assigning to one qubit the colouring with one hemisphere black and the other white, and assigning the same (reverse) colouring to the other qubit. We describe numerical tests that are consistent with this hypothesis and bound the range of θ. Chapter 3 shows a derivation of an upper bound on the success probability of port-based teleportation from the no-cloning theorem and the no-signalling principle. Chapter 4 introduces the principle of quantum information causality, a quantum version of the information causality principle. The quantum information causality principle states the maximum amount of quantum information that a transmitted quantum system can communicate as a function of its dimension, independently of any quantum physical resources previously shared by the communicating parties. These principles reduce to the no-signalling principle if no systems are transmitted. We present a new quantum information task, the quantum information causality game, whose success probability is upper bounded by the new principle, and show that an optimal strategy to perform it combines the quantum teleportation and superdense coding protocols with a task that has classical inputs.

We investigate the coupling of a single trapped ion to a miniature optical cavity operating in the ultraviolet. Our cavity provides a source of single photons at a high rate into a single spatial mode. Using our apparatus, we have demonstrated the highest atom-cavity coupling rate achieved with a single ion by an order of magnitude. When the ion is continuously excited, we observe phase-sensitive correlations between emission into free-space and into the cavity mode, which can be explained by a cavity induced back-action effect on a driven dipole. We demonstrate coherent manipulation of a hyperfine qubit and ultra-short optical π rotations, which are essential tools for creation and detection of spin-photon entanglement. To this end, we have developed optical fibre-based Fabry-Perot cavities in the ultraviolet spectral range. These cavities operate near the primary dipole transition of Yb at 370 nm, and allow us to couple a pure atomic two-level system offered by a single trapped ion to the cavity mode. A new Paul trap apparatus in an ultra-high vacuum chamber has been built which allows for the integration of these cavities at very small ion-mirror separations. In order for independent operation of the trap, a compact system of diode lasers has been built which are stabilised to low-drift optical reference cavities. Coherent control of the hyperfine qubit in Yb 171 is achieved through application of microwave radiation, and ultra-short optical π rotations are performed with resonant light pulses derived from a frequency-doubled mode-locked titanium-sapphire laser. The experiment is controlled through a system of hardware and software which has been developed in a modular fashion and will allow for efficient control on the nanosecond time-scale when several such systems are interconnected. The success of our system opens the door to future experiments with trapped ions which will reach the strong coupling regime with a single ion. Furthermore, when operated in the fast-cavity regime, systems based on our approach will enable high-efficiency collection of photons from the ion into the single mode of an optical fibre. These systems will allow for the generation of distributed entanglement and will prove ideal as nodes in a larger quantum network of trapped ions.

No description available.

Quantum computers offer the possibility of solving some problems more efficiently than their classical counterparts. The current forerunner in the experimental demonstration of quantum algorithms is Nuclear Magnetic Resonance (NMR). Known for its implementations at liquid state, NMR quantum computing consists of computing on nuclear spins. In the liquid crystal state, dipolar couplings are available, offering an increased clock frequency and a faster recycling of algorithms. Here investigated is the cost at which this comes, namely, a more complicated internal Hamiltonian, making the system harder to characterize and harder to control. In this thesis I present new methods for characterizing the Hamiltonian of dipolar coupled spin systems, and I report experimental results of characterizing an oriented 6-spin system. I then present methods and results concerning the quantum optimal control of this same spin system. Finally, I present experiments and simulations regarding the certification of computational quantum gates implemented in that same dipolar coupled spin system.

The computational problem of distinguishing two quantum channels is central to quantum computing. It is a generalization of the well-known satisfiability problem from classical to quantum computation. This problem is shown to be surprisingly hard: it is complete for the class QIP of problems that have quantum interactive proof systems, which implies that it is hard for the class PSPACE of problems solvable by a classical computation in polynomial space. Several restrictions of distinguishability are also shown to be hard. It is no easier when restricted to quantum computations of logarithmic depth, to mixed-unitary channels, to degradable channels, or to antidegradable channels. These hardness results are demonstrated by finding reductions between these classes of quantum channels. These techniques have applications outside the distinguishability problem, as the construction for mixed-unitary channels is used to prove that the additivity problem for the classical capacity of quantum channels can be equivalently restricted to the mixed unitary channels.

The computational problem of distinguishing two quantum channels is central to quantum computing. It is a generalization of the well-known satisfiability problem from classical to quantum computation. This problem is shown to be surprisingly hard: it is complete for the class QIP of problems that have quantum interactive proof systems, which implies that it is hard for the class PSPACE of problems solvable by a classical computation in polynomial space. Several restrictions of distinguishability are also shown to be hard. It is no easier when restricted to quantum computations of logarithmic depth, to mixed-unitary channels, to degradable channels, or to antidegradable channels. These hardness results are demonstrated by finding reductions between these classes of quantum channels. These techniques have applications outside the distinguishability problem, as the construction for mixed-unitary channels is used to prove that the additivity problem for the classical capacity of quantum channels can be equivalently restricted to the mixed unitary channels.

In this thesis, we answer several questions about the behaviour of prover-verifier interactions under parallel repetition when quantum information is allowed, and the verifier acts independently in them. We first consider the case in which a value is associated with each of the possible outcomes of an interaction. We prove that it is not possible for the prover to improve on the optimum average value per repetition by repeating the protocol multiple times in parallel. We look then at games in which the outcomes are classified into two types, winning outcomes and losing outcomes. We ask what is the optimal probability for the prover of winning at least k times out of n parallel repetitions, given that the optimal probability of winning when only one repetition is considered is p. A reasonable conjecture for the answer would be the answer when it is optimal for the prover to act independently. This is known to be the correct answer when k=n. We will show how this cannot be extended to the general case, presenting an example of an interaction with k=1,n=2 in which p is approximately 0.85, but it is possible to always win at least once. We will then give some upper bounds on the optimal probability for the prover of winning k times out of n parallel repetitions. These bounds are expressed as a function of p. Finally, we connect our results to the study of error reduction for quantum interactive proofs using parallel repetition.

In practice, quantum systems are not completely isolated from their environment and the resulting system-environment interaction can lead to information leakage from the system. As a result, if a quantum system is to be used for storing or manipulating information, one would like to characterize these environmental noise effects. Such a characterization affords one the ability to design robust methods for preserving the information contained in the system. Unfortunately, completely characterizing the noise in a realistic amount of time is impossible for even moderately large systems. In this thesis we discuss methods and diagnostics for partially characterizing quantum noise processes that are especially useful in quantum information and computation. We present a randomized benchmarking protocol that provides a scalable method for determining important properties of the noise affecting the set of gates used on a quantum information processor. We also prove various properties of the quantum gate fidelity, which is a useful state-dependent measure of the distance between two quantum operations, and an important diagnostic of the noise affecting a quantum process. Some non-intuitive generic features of quantum operations acting on large-dimensional quantum systems are also presented.