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Algorithms and protocols for quantum information technologies

Robert J. Chapman

Published Feb 13, 2018• 0 citations
Publisher

Abstract

Quantum technologies harness the properties of controlled quantum mechanical systems for applications in computation, communication and metrology, and enable us to further our understanding of fundamental physics. Quantum hardware is designed to manipulate complex and fragile many-particle quantum states, which requires exquisite control machinery, advanced software and near-complete isolation from the surrounding environment. With sufficient capabilities, quantum computers with large registers of quantum bits will perform classically intractable calculations such as quantum chemistry simulations. Quantum key distribution will provide completely secure communications across the world and quantum metrology will enable measurement precision beyond today's capabilities. While quantum technologies are far from surpassing classical hardware today, the vision and potential impact has sparked a world-wide research effort, both theoretical and experimental, to develop a quantum computer. The most sophisticated current quantum technologies have control over small numbers of quantum bits and are limited by environmental decoherence processes. While progress in developing quantum hardware is ongoing, designing and demonstrating new algorithms and protocols for quantum information is a thriving research field. Photonics provides an ideal platform for small-scale proof-of-concept quantum experiments, which are the focus of this thesis. In the coming decades, we will see the realisation of quantum hardware capable of applications that outperform any classical computer. In this thesis, I present several protocols and algorithms for quantum information science and technology, which are implemented in quantum photonic experiments. The applications of these works include robust quantum tomography, quantum state relocation, quantum enhanced data recovery and probing fundamental causality in quantum mechanics. The works presented here are based on two photon experiments from a prototypical spontaneous parametric down-conversion source, which provides an excellent test-bed for quantum information experiments. Photons can be used to encode quantum information in a range of different degrees of freedom. This versatility, along with compatibility with existing technology gives photonics a great advantage in the development of quantum hardware.

DOI
10.25439/rmt.27589968

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Over the last few decades, quantum cryptography has been one of the most important quantum technologies developed. It holds the promise of communicating secure information over untrusted channels. In particular, quantum cryptography is immune to the eventual threats posed by large-scale quantum computers, which is not the case for our current classical cryptography infrastructures. In a world where information, communication and privacy are of paramount importance, the development of secure quantum communication infrastructures becomes imperative. So far, most of the quantum cryptographic systems developed to date are based on two-dimensional encoding schemes, analogous to classical bits, known as qubits. Nevertheless, other than for the polarization of light, photonic degrees of freedom, i.e. position, momentum, time and frequency, naturally occur as high-dimensional quantum systems. Moreover, by considering high-dimensional encoding schemes beyond qubits, advantages in terms of information capacity and noise tolerance are predicted in theory. In this thesis, the basic components of a high-dimensional quantum cryptographic system are investigated. We begin by reviewing important developments in quantum cryptography and high-dimensional quantum information. As a starting point, two different quantum information tasks, i.e. optimal quantum cloning and quantum metrology, are experimentally investigated for high-dimensional quantum systems in order to demonstrate the numerous advantages of performing quantum tasks beyond qubits. The photonic degree of freedom used in these experiments, known as transverse spatial modes, is obtained by combining the position and momentum photonics degrees of freedom. Thus, we develop a novel method to measure high-dimensional quantum states encoded in arbitrary spatial modes. Using a similar characterization technique, several high-dimensional quantum communication channels are characterized to perform high-dimensional quantum cryptography. The tools developed in the laboratory are then brought to realistic conditions in order to test the feasibility of high-dimensional quantum cryptography. Two different types of quantum channels are experimentally investigated, namely an intra-city 300 m long free-space link and a short 3 m outdoor underwater link. Finally, we investigate and compare novel high-dimensional protocols to overcome current limitations.
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Quantum mechanics has profoundly reshaped our knowledge of the physical world: a deep comprehension of the quantum nature of matter yielded to the so-called first quantum revolution, enabling transformative technologies ranging from lasers to semiconductor de- vices, being at the heart of the digital revolution characterizing the second half of the XXth century. Furthermore, the capability of manipulating and controlling individual quantum systems enabled a totally different working paradigm, obeying the logic im- posed by quantum physics, paving the way, at the end of the XXth and the beginning of the XXIst century, for the second quantum revolution. Modern quantum technologies, including quantum computation, quantum simulation, quantum metrology and quantum communication rely on peculiar quantum phenomena, such as superposition, entangle- ment and coherence to perform tasks beyond classical capabilities. This thesis proposes quantum metrology as a unifying conceptual and methodological framework to investigate problems lying at the intersection of fundamental quantum physics and quantum information science. More in detail, it addresses theoretical and experimental protocols to certify the presence of quantum correlations (namely, quantum steering), as well as to design secure sensing in quantum networks under realistic assump- tions. Moreover, it also suggest how tunable-strength measurement-based strategies can be used to extract information from complex systems even in seemingly inaccessible sce- narios. Overall, this thesis proposes quantum metrology as a framework through which the purest nature of information can be probed, certified and secured at the most fundamental level.
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