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Towards practical applications of quantum optics

David Drahi

Published Jan 1, 2019• 0 citations
Publisher

Abstract

This DPhil thesis presents two key works towards practical applications of quantum optics. Both works are novel and achieve competitive state-of-the-art results. Today's most widely used method of encoding quantum information in optical qubits is the dual-rail basis, often carried out through the polarisation of a single photon. On the other hand, many stationary carriers of quantum information | such as atoms | couple to light via the single-rail encoding in which the qubit is encoded in the number of photons. As such, interconversion between the two encodings is paramount in order to achieve cohesive quantum networks. In the first part of this thesis, we demonstrate this by generating a hybrid entangled resource between the two encodings and using it to teleport a dual-rail qubit onto its singlerail counterpart. Our key results yield an average fidelity of F = (92:8±2:2)% for the teleportation and F = (89:7 ± 2:1)% for entanglement swapping, thus confirming the applicability of this scheme towards a real-world implementation. This work completes the set of tools necessary for the interconversion between the three primary encodings of a qubit in the optical field: single-rail, dual-rail and continuous-variable. A remarkable aspect of quantum theory is that certain measurement outcomes are entirely unpredictable to all possible observers. Such quantum events can be harnessed to generate numbers whose randomness is asserted based upon the underlying physical processes. In the second part of this thesis, we formally introduce and experimentally demonstrate an ultrafast optical quantum randomness generator that uses a totally untrusted photonic source and whose idea we have patented. While considering completely general quantum attacks, we certify randomness at a rate of 1:1 Gbps with a rigorous security parameter of 10-20. Our security proof is entirely composable, thereby allowing the generated randomness to be utilised for arbitrary applications in cryptography and beyond.

DOI
10.5287/ora-7j1x9yjbk

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This DPhil thesis presents two key works towards practical applications of quantum optics. Both works are novel and achieve competitive state-of-the-art results. Today's most widely used method of encoding quantum information in optical qubits is the dual-rail basis, often carried out through the polarisation of a single photon. On the other hand, many stationary carriers of quantum information | such as atoms | couple to light via the single-rail encoding in which the qubit is encoded in the number of photons. As such, interconversion between the two encodings is paramount in order to achieve cohesive quantum networks. In the first part of this thesis, we demonstrate this by generating a hybrid entangled resource between the two encodings and using it to teleport a dual-rail qubit onto its singlerail counterpart. Our key results yield an average fidelity of F = (92:8±2:2)% for the teleportation and F = (89:7 ± 2:1)% for entanglement swapping, thus confirming the applicability of this scheme towards a real-world implementation. This work completes the set of tools necessary for the interconversion between the three primary encodings of a qubit in the optical field: single-rail, dual-rail and continuous-variable. A remarkable aspect of quantum theory is that certain measurement outcomes are entirely unpredictable to all possible observers. Such quantum events can be harnessed to generate numbers whose randomness is asserted based upon the underlying physical processes. In the second part of this thesis, we formally introduce and experimentally demonstrate an ultrafast optical quantum randomness generator that uses a totally untrusted photonic source and whose idea we have patented. While considering completely general quantum attacks, we certify randomness at a rate of 1:1 Gbps with a rigorous security parameter of 10-20. Our security proof is entirely composable, thereby allowing the generated randomness to be utilised for arbitrary applications in cryptography and beyond.
Today's most widely used method of encoding quantum information in optical qubits is the dual-rail basis, often carried out through the polarisation of a single photon. On the other hand, many stationary carriers of quantum information - such as atoms - couple to light via the single-rail encoding in which the qubit is encoded in the number of photons. As such, interconversion between the two encodings is paramount in order to achieve cohesive quantum networks. In this paper, we demonstrate this by generating an entangled resource between the two encodings and using it to teleport a dual-rail qubit onto its single-rail counterpart. Our results yield an average fidelity of F=(92.8±2.2)%\mathcal{F}= (92.8\pm2.2)\%F=(92.8±2.2)% for the teleportation and F=(89.7±2.1)%\mathcal{F}= (89.7\pm2.1)\%F=(89.7±2.1)% for entanglement swapping, thus confirming the applicability of this scheme for a real-world implementation. This work completes the set of tools necessary for the interconversion between the three primary encodings of the qubit in the optical field: single-rail, dual-rail and continuous-variable.
Today's most widely used method of encoding quantum information in optical qubits is the dual-rail basis, often carried out through the polarisation of a single photon. On the other hand, many stationary carriers of quantum information – such as atoms – couple to light via the single-rail encoding in which the qubit is encoded in the number of photons. As such, interconversion between the two encodings is paramount in order to achieve cohesive quantum networks. In this paper, we demonstrate this by generating an entangled resource between the two encodings and using it to teleport a dual-rail qubit onto its single-rail counterpart. This work completes the set of tools necessary for the interconversion between the three primary encodings of the qubit in the optical field: single-rail, dual-rail and continuous-variable.
The main topic of this thesis is linear optics and the implementation of quantum operations (measurements, quantum channels, and unitary rotations) on optical systems. \nIn the opening chapter the basic notions needed to understand the rest of the thesis will be explained. \nThese notions include defining a quantum state, measurement, quantum channel and the linear optics tool set. \n \nThe work in this thesis takes both fundamental and practical approaches to studying linear optical networks. \nFor instance in the first chapter a proof is provided that shows that any unitary on a single mode Fock state can be realised with linear optics. \nThe proof is constructive, however the approach to realising the unitary is not suitable for experimental implementation \nbecause it requires complicated ancilla states. \nAs in the KLM proposal the procedure works only stochastically however by allowing the size of the ancilla to grow \nthe probability of failure can be made arbitrarly small. \n \nFurthermore we investigate the realisation of arbitrary channels in a specific encoding that we call a ddd-rail encoding. \nThe only ancilla state that we allow is a vacuum ancilliary state and further restrictions were considered (e.g. photon counting). \nA proof is provided that using these resources only random unitaries can be applied deterministically using linear optics. An expression for the optimal probability of success for realising \nmore general channels with these resources is also discussed. \n \nAs a final topic we also investigate the realisation of a quantum non-demolition measurement onto the dual rail qubit space. \nThe investigation is a blend of both fundamental and practical approaches. \nTo begin we employ a modified KLM-like procedure and show that the scheme can be realised perfectly but stochastically. \nThe probability that the proper measurement is made can be made arbitrarly close to one using a suitably large ancilla state. \nIn addition we consider an existing scheme \\cite{gisin10a} which uses practical sources (two single photon sources) to perform the measurement. \nThe scheme does not realise the true measurement but instead has a free parameter in it which is the transmittiviy of a beamsplitter. The measurement will project onto a space that has a vacuum component. By adjusting the transmittivity of this beamsplitter the vacuum component can be made arbitrarly small but only at the expense of the probability of success of the procedure. \nIn this thesis a modification that can be made to eliminate the vacuum component without changing the sources is introduced. The modification is surprisingly simple and only involves the addition of a single beamsplitter. In the proposal for the original amplifier it was used in simulations for DIQKD that included device imperfections. \nTo show the improvement of our modification these DIQKD simulations are reproduced using the modified amplifier and its results are compared to the results of the original amplifier.
A remarkable aspect of quantum theory is that certain measurement outcomes arc entirely unpredictable to all possible observers. Such quantum events can be harnessed to generate numbers whose randomness is asserted based upon the underlying physical processes. We formally introduce, design, and experimentally demonstrate an ultrafast optical quantum random number generator that uses a totally untrusted photonic source. While considering completely general quantum attacks, we certify and generate in real time random numbers at a rate of 8.05 Gb/s with a composable security parameter of 10(-10). Composable security is the most stringent and useful security paradigm because any given protocol remains secure even if arbitrarily combined with other instances of the same, or other, protocols, thereby allowing the generated randomness to be utilized for arbitrary applications in cryptography and beyond. This work achieves the fastest generation of composably secure quantum random numbers ever reported.
Light is an irreplaceable means of communication among various quantum information processing and storage devices. Due to their different physical nature, some of these devices couple more strongly to discrete, and some to continuous degrees of freedom of a quantum optical wave. It is therefore desirable to develop a technological capability to interconvert quantum information encoded in these degrees of freedom. Here we generate and characterize an entangled state between a dual-rail (polarization-encoded) single-photon qubit and a qubit encoded as a superposition of opposite-amplitude coherent states. We furthermore demonstrate the application of this state as a resource for the interfacing of quantum information between these encodings. In particular, we show teleportation of a polarization qubit onto a freely propagating continuous-variable qubit.