Theory and applications of quantum process calculus

Formal methods is an area in theoretical computer science that provides the theories and tools for describing and verifying the correctness of computing systems. Usually, such systems comprise of concurrent and communicating components. The success of this field led to the development of quantum formal methods by transferring the ideas of formal methods to quantum systems. In particular, formal methods provides a systematic methodology for verification of systems. Quantum process calculus is a specialised field in quantum formal methods that helps to describe and analyse the behaviour of systems that combine quantum and classical elements. We focus on the theory and applications of quantum process calculus in particular to use Communicating Quantum Processes (CQP), a quantum process calculus, to model and analyse quantum information processing (QIP) systems. Previous work on CQP defined labelled transition relations for CQP in order to describe external interactions and also established the theory of behavioural equivalence in CQP based on probabilistic branching bisimilarity. This theory formalizes the idea of observational indistinguishability in order to prove or verify the correctness of a system, and an important property of the equivalence is the congruence property. We use the theory to analyse two versions of a quantum error correcting code system. We use the equational theory of CQP from the previous work and define an additional three new axioms in order to analyse quantum protocols comprising quantum secret-sharing, quantum error correction, remote-CNOT and superdense coding. We have expanded the framework of modelling in CQP from providing an abstract view of the quantum system to describe a realistic QIP system such as linear optical quantum computing (LOQC) and its associated experimental processes. By extending the theory of behavioural equivalence of CQP, we have formally verified two models of an LOQC CNOT gate using CQP. The two models use different measurement semantics in order to work at different levels of abstraction. This flexibility of the process calculus approach allows descriptions from detailed hardware implementations up to more abstract specifications. The orbital angular momentum (OAM) property of light allows us to perform experiments in studying higher dimensional quantum systems and their applications to quantum technologies. In relation to this work, we have extended CQP to model higher dimensional quantum protocols

Application of Quantum Process Calculus to Higher Dimensional Quantum Protocols

We describe the use of quantum process calculus to describe and analyze quantum communication protocols, following the successful field of formal methods from classical computer science. We have extended the quantum process calculus to describe d-dimensional quantum systems, which has not been done before. We summarise the necessary theory in the generalisation of quantum gates and Bell states and use the theory to apply the quantum process calculus CQP to quantum protocols, namely qudit teleportation and superdense coding.Comment: In Proceedings QPL 2012, arXiv:1407.842

Verification of Linear Optical Quantum Computing using Quantum Process Calculus

We explain the use of quantum process calculus to describe and analyse linear optical quantum computing (LOQC). The main idea is to define two processes, one modelling a linear optical system and the other expressing a specification, and prove that they are behaviourally equivalent. We extend the theory of behavioural equivalence in the process calculus Communicating Quantum Processes (CQP) to include multiple particles (namely photons) as information carriers, described by Fock states or number states. We summarise the theory in this paper, including the crucial result that equivalence is a congruence, meaning that it is preserved by embedding in any context. In previous work, we have used quantum process calculus to model LOQC but without verifying models against specifications. In this paper, for the first time, we are able to carry out verification. We illustrate this approach by describing and verifying two models of an LOQC CNOT gate.Comment: In Proceedings EXPRESS/SOS 2014, arXiv:1408.127

Measurement-device-independent quantum digital signatures

Digital signatures play an important role in software distribution, modern communication and financial transactions, where it is important to detect forgery and tampering. Signatures are a cryptographic technique for validating the authenticity and integrity of messages, software, or digital documents. The security of currently used classical schemes relies on computational assumptions. Quantum digital signatures (QDS), on the other hand, provide information-theoretic security based on the laws of quantum physics. Recent work on QDS shows that such schemes do not require trusted quantum channels and are unconditionally secure against general coherent attacks. However, in practical QDS, just as in quantum key distribution (QKD), the detectors can be subjected to side-channel attacks, which can make the actual implementations insecure. Motivated by the idea of measurement-device-independent quantum key distribution (MDI-QKD), we present a measurement-device-independent QDS (MDI-QDS) scheme, which is secure against all detector side-channel attacks. Based on the rapid development of practical MDI-QKD, our MDI-QDS protocol could also be experimentally implemented, since it requires a similar experimental setup.Comment: 12 pages, 2 figures and supplementary material is include

Imperfect 1-Out-of-2 Quantum Oblivious Transfer: Bounds, a Protocol, and its Experimental Implementation

Oblivious transfer is an important primitive in modern cryptography. Applications include secure multiparty computation, oblivious sampling, e-voting, and signatures. Information-theoretically secure perfect 1-out-of 2 oblivious transfer is impossible to achieve. Imperfect variants, where both participants' ability to cheat is still limited, are possible using quantum means while remaining classically impossible. Precisely what security parameters are attainable remains unknown. We introduce a theoretical framework for studying semi-random quantum oblivious transfer, which is shown equivalent to regular oblivious transfer in terms of cheating probabilities. We then use it to derive bounds on cheating. We also present a protocol with lower cheating probabilities than previous schemes, together with its optical realisation.Comment: 20 pages, 1 figur

Experimental measurement-device-independent quantum digital signatures over a metropolitan network

Quantum digital signatures (QDS) provide a means for signing electronic communications with informationtheoretic security. However, all previous demonstrations of quantum digital signatures assume trusted measurement devices. This renders them vulnerable against detector side-channel attacks, just like quantum key distribution. Here, we exploit a measurement-device-independent (MDI) quantum network, over a 200-square-kilometer metropolitan area, to perform a field test of a three-party measurement-device-independent quantum digital signature (MDI-QDS) scheme that is secure against any detector side-channel attack. In so doing, we are able to successfully sign a binary message with a security level of about 1E-7. Remarkably, our work demonstrates the feasibility of MDI-QDS for practical applications.Comment: 5 pages, 1 figure, 2 tables, supplemental materials included as ancillary fil

Unconditionally secure digital signatures implemented in an eight-user quantum network

The ability to know and verifiably demonstrate the origins of messages can often be as important as encrypting the message itself. Here we present an experimental demonstration of an unconditionally secure digital signature (USS) protocol implemented for the first time, to the best of our knowledge, on a fully connected quantum network without trusted nodes. We choose a USS protocol which is secure against forging, repudiation and messages are transferrable. We show the feasibility of unconditionally secure signatures using only bi-partite entangled states distributed throughout the network and experimentally evaluate the performance of the protocol in real world scenarios with varying message lengths