The work in this thesis can be divided into three parts. The first two parts deal with optical quantum communication protocols and the third part deals with quantum cryptography. The first part of the thesis is a step towards reformulating quantum protocols in terms of coherent states. Quantum communication protocols are typically formulated in terms of abstract qudit states and operations. This leaves the question of an experimental realization open. Direct translation of these protocols, say into single photons with some d-dimensional degree of freedom, are typically challenging to realize. Multi-mode coherent states, on the other hand, can be easily generated experimentally. Reformulation of protocols in terms of these states has been a successful strategy for implementation of quantum protocols. Quantum key distribution and the quantum fingerprinting protocol have both followed this route. In Chapter 3, we characterize the Gram matrices of multi-mode coherent states in an attempt to understand the class of communication protocols, which can be implemented using these states. We also derive the closure of the Gram matrices, which can be implemented in this way, so that we also characterize those matrices, which can be approximated arbitrarily well using multi-mode coherent states. \n \nIn the second part of the thesis, Chapter 4, we describe our collaboration with an experimental group to implement the quantum fingerprinting protocol and examine the tradeoffs between the resources required to implement such protocols. It is seen that it is difficult to implement the quantum fingerprinting protocol experimentally for large input sizes. This leads us to study the tradeoff between the two resources expended during optically implemented simultaneous message passing communication protocols: the duration of the protocol and the energy required to run it. We derive general bounds on the growth of these quantities which are valid for all optical protocols. We also develop tighter bounds for the growth of these resources for protocols implementing quantum fingerprinting with coherent states. \n \nFinally in Chapter 5, we venture into quantum cryptography. We introduce a new setting for two-party cryptography with temporarily trusted third parties. In this setting, in addition to Alice and Bob, there are third parties, which Alice and Bob both trust to be honest during the course of the protocol. However, once the protocol concludes, there is no guarantee over the behaviour of these third parties. It is possible that they collaborate and act adversarially against the honest parties. We implement a variant of bit commitment in this setting, which we call erasable bit commitment. In this primitive, Alice has the choice of either opening or erasing her commitment after the commit phase. The ability to ask for an erasure allows Alice to ask the trusted nodes to erase her commitment in case the trust period is about to expire. However, this ability also makes erasable bit commitment weaker than the standard version of bit commitment. In addition to satisfying the security requirements of bit commitment, our protocol also does not reveal any information about the commitment to the third parties. Lastly, our protocol for this primitive requires a constant number of trusted third parties and can tolerate a small number of dishonest trusted nodes as well as implementation errors.
The work in this thesis can be divided into three parts. The first two parts deal with optical quantum communication protocols and the third part deals with quantum cryptography. The first part of the thesis is a step towards reformulating quantum protocols in terms of coherent states. Quantum communication protocols are typically formulated in terms of abstract qudit states and operations. This leaves the question of an experimental realization open. Direct translation of these protocols, say into single photons with some d-dimensional degree of freedom, are typically challenging to realize. Multi-mode coherent states, on the other hand, can be easily generated experimentally. Reformulation of protocols in terms of these states has been a successful strategy for implementation of quantum protocols. Quantum key distribution and the quantum fingerprinting protocol have both followed this route. In Chapter 3, we characterize the Gram matrices of multi-mode coherent states in an attempt to understand the class of communication protocols, which can be implemented using these states. We also derive the closure of the Gram matrices, which can be implemented in this way, so that we also characterize those matrices, which can be approximated arbitrarily well using multi-mode coherent states. \n \nIn the second part of the thesis, Chapter 4, we describe our collaboration with an experimental group to implement the quantum fingerprinting protocol and examine the tradeoffs between the resources required to implement such protocols. It is seen that it is difficult to implement the quantum fingerprinting protocol experimentally for large input sizes. This leads us to study the tradeoff between the two resources expended during optically implemented simultaneous message passing communication protocols: the duration of the protocol and the energy required to run it. We derive general bounds on the growth of these quantities which are valid for all optical protocols. We also develop tighter bounds for the growth of these resources for protocols implementing quantum fingerprinting with coherent states. \n \nFinally in Chapter 5, we venture into quantum cryptography. We introduce a new setting for two-party cryptography with temporarily trusted third parties. In this setting, in addition to Alice and Bob, there are third parties, which Alice and Bob both trust to be honest during the course of the protocol. However, once the protocol concludes, there is no guarantee over the behaviour of these third parties. It is possible that they collaborate and act adversarially against the honest parties. We implement a variant of bit commitment in this setting, which we call erasable bit commitment. In this primitive, Alice has the choice of either opening or erasing her commitment after the commit phase. The ability to ask for an erasure allows Alice to ask the trusted nodes to erase her commitment in case the trust period is about to expire. However, this ability also makes erasable bit commitment weaker than the standard version of bit commitment. In addition to satisfying the security requirements of bit commitment, our protocol also does not reveal any information about the commitment to the third parties. Lastly, our protocol for this primitive requires a constant number of trusted third parties and can tolerate a small number of dishonest trusted nodes as well as implementation errors.
In this thesis, I study quantum resources for quantum communication and cryptography. The first part deals with bit commitment, a cryptographic primitive in which a party commits a secret bit to another party. After shortly presenting the security issues faced by quantum bit commitment, I demonstrate the first realization of a secure relativistic bit commitment sustained for 24 hours. The second part deals with the development of efficient methods to generate, distribute and characterize photonic entangled states. I address the problem of certifying entanglement in the presence of measurement imperfections, and demonstrate a practical implementation of a measurement-device-independent entanglement witness. I then address the challenge of long-distance distribution of entanglement. I demonstrate a heralded photon amplifier and entanglement swapping protocols adapted for the distribution of single photon entanglement, and further discuss the advantages and limitations of using single photon entanglement as a resource for quantum communication.
Current communication networks are based on classical physics and classical information-processing. However, for nearly a century, we have known that at its most fundamental level, the universe is governed by the laws of quantum mechanics. With quantum communication, new possibilities arise in our capabilities to transmit and process information which, in many cases, lead to advantages compared to what is classically possible. The entire scope of tasks for which quantum communication can offer improvements has not yet been fully explored, but several quantum protocols are known that can either perform tasks which are impossible with classical resources or can outperform classical protocols. These quantum protocols are well understood from a theoretical point of view, but many of them have never been demonstrated in practice. Thus, in the context of quantum communication, there is a significant gap between theory and experiment that must be removed in order to harness the advantages provided by quantum mechanics in a practical setting. \n \nIn this thesis, we develop a series of tools for developing and testing practical quantum communication protocols. Our main technique is a theoretical reformulation of existing quantum communication protocols that converts them into a form in which they can be demonstrated with existing experimental techniques. More precisely, they can be implemented using only coherent states of light and linear optics circuits while still retaining the crucial properties of the original abstract protocols. We use this result to construct practical protocols for the Hidden Matching problem and quantum fingerprinting. \n \n \nIn the case of quantum fingerprinting, we make a thorough analysis of the role played by experimental errors and show that our practical protocol can still be implemented in the presence of these imperfections. In fact, we report a proof of concept experimental demonstration of a quantum fingerprinting system that is capable of transmitting less information than the best known classical protocol for this problem. Our implementation is based on a modified version of a commercial quantum key distribution system using off-the-shelf optical components over telecom wavelengths, and is practical for messages as large as 100 Mbits, even in the presence of experimental imperfections. \n \nSimilarly, in the context of cryptography, we propose a multiparty quantum signature protocol that can be implemented from any point-to-point quantum key distribution network, proving its security against forging, repudiation and non-transferability. Crucially, since quantum key distribution is already a practical technology, so is this protocol. However, unlike other tasks in quantum communication, there has not been significant theoretical work on establishing a security model for quantum signature schemes. Consequently, we also constructed a security framework for these schemes and proved several properties that these protocols must satisfy in order to achieve their security goals. \n \nFinally, in addition to proposing new practical protocols, we provide a reliable data analysis technique to verify an important property of many quantum communication protocols: the presence of entanglement. Our technique is based on entanglement witnesses and it does not require the specification of a prior distribution nor the assumption of independent measurements. The technique is suitable to be used with nonlinear entanglement witnesses, which we show can be constructed from any linear witness and evaluated from the same experimental data. We also develop numerical tools necessary to employ this approach in practice, rendering the procedure ready to be applied to current experiments. We demonstrate this by analyzing the data of a photonic experiment generating two-photon states whose entanglement is verified with the use of an accessible nonlinear witness.
Entangled photons are at the heart of experimental quantum physics. They were used for the first fundamental tests of quantum theory, and became a basic building block for many novel quantum protocols, such as quantum cryptography, dense coding or teleportation. Therefore, the efficient generation of entangled photons, as well as their distribution and accurate analysis are of paramount importance, particularly with regard to the practicability of many applications of quantum communication. This thesis deals largely with the problem of efficient generation of photonic entanglement with the principal aim of developing a bright source of polarization-entangled photon pairs, which meets the requirements for reliable and economic operation of quantum communication prototypes and demonstrators. Our approach uses a correlated photon-pair emission in nonlinear process of spontaneous parametric down-conversion pumped by light coming from a compact and cheap blue laser diode. Two alternative source configurations are examined within the thesis. The first makes use of a well established concept of degenerate non-collinear emission from a single type-II nonlinear crystal and the second relies on a novel method where the emissions from two adjacent type-I phase-matched nonlinear crystals operated in collinear non-degenerate regime are coherently overlapped. The latter approach showed to be more effective, yielding a total detected rate of almost 10^6 pairs/s at >98 % quantum interference visibility of polarization correlations. This performance, together with the almost free of alignment operation of the system, suggest that it is an especially promising candidate for many future practical applications, including quantum cryptography, detector calibration or use in undergraduate lab courses. The second issue addressed within the thesis is the simplification and practical implementation of quantum-assisted solutions to multiparty communication tasks. While the recent rapid progress in the development of bright entangled photon-pair sources has been followed with ample experimental reports on two-party quantum communication tasks, the practical implementations of tasks for more than two parties have been held back, so far. This is mainly due to the requirement of multiparty entangled states, which are very difficult to be produced with current methods and moreover suffer from a high noise. We show that entanglement is not the only non-classical resource endowing the quantum multiparty information processing its power. Instead, only the sequential communication and transformation of a single qubit can be sufficient to accomplish certain tasks. This we prove for two distinct communication tasks, secret sharing and communication complexity. Whereas the goal of the first is to split a cryptographic key among several parties in a way that its reconstruction requires their collaboration, the latter aims at reducing the amount of communication during distributed computational tasks. Importantly, our qubit-assisted solutions to the problems are feasible with state-of-the-art technology. This we clearly demonstrate in the laboratory implementation for 6 and 5 parties, respectively, which is to the best of our knowledge the highest number of actively performing parties in a quantum protocol ever implemented. Thus, by successfully solving and implementing a cryptographic task as well as a task originating in computer science, we clearly illustrate the potential to introduce multiparty communication problems into real life.
We introduce a new setting for two-party cryptography by introducing the notion of temporarily trusted third parties. These third parties act honest-but-curious during the execution of the protocol. Once the protocol concludes and the trust period expires, these third parties may collaborate with an adversarial party. We implement a variant of the cryptographic primitive of bit commitment in this setting, which we call erasable bit commitment. In this primitive, the sender has the choice of either opening or erasing her commitment after the commit phase. For example, she can ask for an erase before the trust period expires in case the conditions for opening the commitment have not been met. The erasure prevents a future coalition of the trusted party and the receiver from extracting any information about the commitment. However, this option also weakens the cryptographic primitive relative to standard bit commitment. Furthermore, the committed information is not revealed to the trusted node at any stage during the protocol. Our protocol requires a constant number of third parties and can tolerate a small number of corrupt third parties as well as implementation errors.
Quantum cryptography including quantum key distribution and quantum secret sharing, a fundamental branch in quantum information processing, is the process whereby two or more parties agree on a key for subsequent cryptographic use. The goal of quantum cryptography is to establish a secure key in an insecure communication environment, leading to the difficulty of the protocols' design and analysis. In this thesis we focus on the design and analysis of secure and efficient protocols of two or more parties in quantum settings.