<div>Field-orthogonal temporal mode analysis of optical fields was recently developed to form a new framework of quantum information science. But so far, the exact profiles of the temporal modes are not known, which makes it difficult to achieve mode selection and de-multiplexing. A novel feedback-iteration method which, combined with the stimulated emission method, can give rise to the exact forms of the temporal mode structure of pulse-pumped spontaneous parametric processes both for high gain parametric process, which gives rise to quantum entanglement in continuous variables, and for the low gain case, which produces a two-photon entangled state for discrete variables.</div><div><br></div><div>For the temporal mode analysis in high gain situations, the common treatment of parametric interaction Hamiltonian does not consider the issue of time ordering problem of interaction Hamiltonian and thus leads to the inaccurate conclusion that the mode structure and the temporal mode functions do not change as the gain increases. We use an approach that is usually employed for treating nonlinear interferometers and avoids the time ordering issue. This allows us to derive an evolution equation in differential-integral form. Numerical solutions for high gain situations indicate a gain-dependent mode structure that has its mode distributions changed and mode functions broadened as the gain increases. This will enable us to have a complete picture of the mode structure of parametric processes and produce high quality quantum sources for a variety of applications of quantum technology.</div><div><br></div><div>To verify the feedback-iteration method which measures temporal mode structure directly, we measure the joint spectral density of photon pairs produced with the spontaneous parametric down-conversion process of a pulse-pumped PPKTP crystal. The measurement method is based on a stimulated emission process which significantly improves the measurement time and accuracy compared with old spectrally resolved photon coincidence measurement. With the measured joint spectral density, the amplitude of the temporal modes can be obtained with the mathematical tool of singular value decomposition and compared with those measured directly with the feedback-iteration method.</div><div><br></div><div>Because the parametric amplifier is in essence a linear four-port device, it couples and linearly mixes two inputs before amplifying and sending them to two output ports. We show that for quadrature phase amplitudes, a parametric amplifier can replace beam splitters to play the role of mixer. We apply this idea to a continuous-variable quantum state teleportation scheme in which a parametric amplifier replaces a beam splitter in the Bell measurement. We show that this scheme is loss-tolerant in the Bell measurement process and thus demonstrate the advantage of parametric amplifiers over beam splitter in the applications in quantum measurement.</div>

Semiconductor quantum dots (QDs) are well established as sub-Poissonian sources of entangled photon pairs. To improve the utility of a QD light source, it would be advantageous to extend their emission further into the near infrared, into the low absorption wavelength windows utilised in long-haul optical telecommunication. Initial experiments succeeded in interfering O-band (1260—1360 nm) photons from an InAs/GaAs QD with dissimilar photons from a laser, an important mechanism for quantum teleportation. Interference visibilities as high as 60 ± 6 % were recorded, surpassing the 50 % threshold imposed by classical electrodynamics. Later, polarisation-entanglement of a similar QD was observed, with pairs of telecom-wavelength photons from the radiative cascade of the biexciton state exhibiting fidelities of 92.0 ± 0.2 % to the Bell state. Subsequently, an O-band telecom-wavelength quantum relay was realised. Again using an InAs/GaAs QD device, this represents the first implementation of a sub-Poissonian telecom-wavelength quantum relay, to the best knowledge of the author. The relay proved capable of implementing the famous four-state BB84 protocol, with a mean teleportation fidelity as high as 94.5 ± 2.2 %, which would contribute 0.385 secure bits per teleported qubit. After characterisation by way of quantum process tomography, the performance of the relay was also evaluated to be capable of implementing a six-state QKD protocol. In an effort to further extend the emitted light from a QD into the telecom C-band (1530—1565 nm), alternative material systems were investigated. InAs QDs on a substrate of InP were shown to emit much more readily in the fibre-telecom O- and C-bands than their InAs/GaAs counterparts, largely due to the reduced lattice mismatch between the QD and substrate for InAs/InP (~3 %) compared to InAs/GaAs (~7 %). Additionally, to minimize the fine structure splitting (FSS) of the exciton level, which deteriorates the observed polarisation-entanglement, a new mode of dot growth was investigated. Known as droplet epitaxy (D-E), QDs grown in this mode showed a fourfold reduction in the FSS compared to dots grown in the Stranski-Krastanow mode. This improvement would allow observation of polarisation-entanglement in the telecom C-band. In subsequent work performed by colleagues at the Toshiba Cambridge Research Labs, these D-E QDs were embedded in a p-i-n doped optical cavity, processed with electrical contacts, and found to emit entangled pairs of photons under electrical excitation. The work of this thesis provides considerable technological advances to the field of entangled-light sources, that in the near future may allow for deterministic quantum repeaters operating at megahertz rates, and in the further future could facilitate the distribution of coherent multipartite states across a distributed quantum network.

La téléportation quantique promet d'être centrale à de nombreuses applications du futur tels la cryptographique quantique et l'ordinateur quantique. Comme toute mise en œuvre physique s'accompagne inévitablement d'imperfections expérimentales, on étudie la téléportation dans un contexte où la ressource quantique, c'est-à-dire l'intrication, que l'on consomme est brouillée. Pour ce faire, on introduit en premier lieu le formalisme de l'informatique quantique. En seconde partie, on approche les protocoles de téléportation quantique standard, de téléportation avec relais quantiques et de téléportation multi-ports. Notre analyse de la téléportation standard et de la téléportation multi-ports poursuit trois objectifs principaux. Le premier est de comparer l'emploi d'un canal brouillé pour la téléportation d'un état quantique avec l'utilisation de ce même canal pour l'envoi direct de l'état. On trouve ainsi les conditions pour lesquelles les deux protocoles de transmission sont équivalents. Le second but est d'observer le caractère non-local de l'intrication brouillée en regardant quand et comment Alice peut réduire le bruit chez elle à un bruit exclusivement chez Bob. En troisième, on quantifie par une borne inférieure la qualité d'un canal de téléportation en réduisant l'effet de toute intrication brouillée à celui d'un bruit de Pauli à un seul paramètre. On accomplit cette tâche en effaçant au moment approprié l'information classique superflue et en appliquant la wernerisation. Finalement, on analyse la composition de bruits de Pauli et l'effet du taux d'effacement sur la téléportation avec relais quantiques pour mieux comprendre comment se combinent les effets de l'intrication brouillée dans un réseau de téléportation quantique. La suite logique est d'établir des protocoles plus robustes de téléportation quantique qui prennent en compte l'effet de l'intrication brouillée. / Quantum teleportation will be a centerpiece of practical quantum cryptography and quantum computing in a soon to be future. As no physical implementation is perfect, we study quantum teleportation in the context of impaired quantum resources which we call noisy entanglement. In a first part, we introduce how quantum mechanics is formalized by quantum information theory. In the second part, we study standard quantum teleportation, in both the absence and presence of quantum repeaters, as well as port-based teleportation. Our analysis of standard quantum teleportation and port-based teleportation follows three main directions. The first goal is to compare the use of a noisy channel for teleportation to the one of the same channel for direct transmission. We thus find the conditions under which the two cases are equivalent. Our second objective is to observe the non-local properties of noisy entanglement by finding when and how Alice can blame Bob for her noise. Thirdly, we quantify, in the worst-case scenario, the quality of a teleportation channel by reducing the effect of any noisy entanglement to the one of a one-parameter Pauli channel that can be interpreted as a depolarizing channel in most instances. We achieve this task by erasing unneeded classical information at the appropriate time and by twirling either the entanglement or the teleported state. Finally, we analyze the composition of Pauli noises and the impact of the erasure channel parameter on the protocol of teleportation with quantum repeaters. We thus aim to understand how the effects of noisy entanglement cumulate in a teleportation network. The next logical step is to create robust teleportation schemes that take into account the effects of noisy entanglement.

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