Proofs of the security of quantum key distribution are propositions about models written in the mathematical language of quantum mechanics, and the issue is the linking of such models to actual devices in an experiment on security. To explore this issue, we adapt Wittgenstein's method of language games to view quantum language in its application to experimental activity involving transmitting and receiving devices. We sketch concepts with which to think about models in relation to experiments, without assuming the experiments accord with any model included is a concept of one quantum-mechanical model enveloping another. For any model that agrees with given experimental results and implies the security of a key, there is an enveloping model that agrees with the same results while denying that security. As a result there is a gap between equations and the behavior recorded from devices in an experiment, a gap bridged only by resort to something beyond the reach of logic and measured data, well named by the word guesswork. While this recognition of guesswork encourages eavesdropping, a related recognition of guesswork in the design of feedback loops can help a transmitter and receiver to reduce their vulnerability to eavesdropping.
Proofs of the security of quantum key distribution are propositions about models written in the mathematical language of quantum mechanics, and the issue is the linking of such models to actual devices in an experiment on security. To explore this issue, we adapt Wittgenstein's method of language games to view quantum language in its application to experimental activity involving transmitting and receiving devices. We sketch concepts with which to think about models in relation to experiments, without assuming the experiments accord with any model included is a concept of one quantum-mechanical model enveloping another. For any model that agrees with given experimental results and implies the security of a key, there is an enveloping model that agrees with the same results while denying that security. As a result there is a gap between equations and the behavior recorded from devices in an experiment, a gap bridged only by resort to something beyond the reach of logic and measured data, well named by the word guesswork. While this recognition of guesswork encourages eavesdropping, a related recognition of guesswork in the design of feedback loops can help a transmitter and receiver to reduce their vulnerability to eavesdropping.
Traditional methods of cryptographic key distribution rest on judgments about an attacker.With the advent of quantum key distribution (QKD) came proofs of security for the mathematical models that define the protocols BB84 and B92; however, applying such proofs to actual transmitting and receiving devices has been questioned.Proofs of QKD security are propositions about models written in the mathematical language of quantum mechanics, and the issue is the linking of such models to actual devices in an experiment on security.To explore this issue, we adapt Wittgenstein's method of language games to view quantum language in its application to experimental activity involving transmitting and receiving devices.We sketch concepts with which to think about models in relation to experiments, without assuming the experiments accord with any model; included is a concept of one quantummechanical model enveloping another.For any model that agrees with given experimental results and implies the security of a key, there is an enveloping model that agrees with the same results while denying that security.As a result there is a gap between equations and the behavior recorded from devices in an experiment, a gap bridged only by resort to something beyond the reach of logic and measured data, well named by the word guesswork.While this recognition of guesswork encourages eavesdropping, a related recognition of guesswork in the design of feedback loops can help a transmitter and receiver to reduce their vulnerability to eavesdropping.
To clarify what is involved in linking models to instruments, we adapt quantum mechanics to define models that display explicitly the points at which they can be linked to statistics of results of the use of instruments. Extending an earlier proof that linking models to instruments takes guesswork, we show: Any model of cryptographic instruments can be *enveloped*, nonuniquely, by another model that expresses conditions of instruments that must be met if the first model is to fit a set of measured outcomes. As a result, model A of key distribution can be enveloped in various ways to reveal alternative models that Eve can try to implement, in conflict with model A and its promise of security. A different enveloping model can help Alice and Bob by expressing necessities of synchronization that they manipulate to improve their detection of eavesdropping. Finally we show that models based on pre-quantum physics are also open to envelopment.
The main goal of this research project is to analyse the security of practical implementations of discrete-variable QKD systems. While it is true that in theory QKD can offer unconditional security based on the laws of physics, in practice, however, at the moment it does not, because typical security proofs of QKD include assumptions that are not actually met by current implementations, as they usually ignore many experimental device imperfections. This means that these proofs cannot be applied to practical realisations because real devices behave differently from the theoretical models that are assumed in the proofs. This project aims to fill in this big gap between the theory and the practice of QKD by developing efficient security proof methods for the finite sample-size setting scenario that can include typical devices’ flaws to be applied to QKD experiments, particularly to decoy-state-based QKD platforms.
One of the most fascinating recent developments in research has been how different disciplines have become more and more interconnected. So much so that fields as disparate as information theory and fundamental physics have combined to produce ideas for the next generation of computing and secure information technologies, both of which have far reaching consequences. For more than fifty years Moore's law, which describes the trend of the transistor's size shrinking by half every two years, has proven to be uncannily accurate. However, the computing industry is now approaching a fundamental barrier as the size of a transistor approaches that of an individual atom and the laws of physics and quantum mechanics take over. Rather then look at this as the end, quantum information science has emerged to ask the question of what additional power and functionality might be realized by harnessing some of these quantum effects. This thesis presents work on the sub-field of quantum cryptography which seeks to use quantum means in order to assure the security of ones communications. The beauty of quantum cryptographic methods are that they can be proven secure, now and indefinitely into the future, relying solely on the validity of the laws of physics for their proofs of security. This is something which is impossible for nearly all current classical cryptographic methods to claim. \n \nThe thesis begins by examining the first implementation of an entangled quantum key distribution system over two free-space optical links. This system represents the first test-bed of its kind in the world and while its practical importance in terrestrial applications is limited to a smaller university or corporate campus, the system mimics the setup for an entangled satellite system aiding in the study of distributing entangled photons from an orbiting satellite to two earthbound receivers. Having completed the construction of a second free-space link and the automation of the alignment system, I securely distribute keys to Alice and Bob in two distant locations separated by 1,575 m with no direct line-of-sight between them. I examine all of the assumptions necessary for my claims of security, something which is particularly important for moving these systems out of the lab and into commercial industry. I then go on to describe the free-space channel over which the photons are sent and the implementation of each of the major system components. I close with a discussion of the experiment which saw raw detected entangled photon rates of 565 s^{-1} and a quantum bit error rate (QBER) of 4.92% resulting in a final secure key rate of 85 bits/s. Over the six hour night time experiment I was able to generate 1,612,239 bits of secure key. \n \nWith a successful QKD experiment completed, this thesis then turns to the problem of improving the technology to make it more practical by increasing the key rate of the system and thus the speed at which it can securely encrypt information. It does so in three different ways, involving each of the major disciplines comprising the system: measurement hardware, source technology, and software post-processing. First, I experimentally investigate a theoretical proposal for biasing the measurement bases in the QKD system showing a 79% improvement in the secret key generated from the same raw key rates. Next, I construct a second generation entangled photon source with rates two orders of magnitude higher than the previous source using the idea of a Sagnac interferometer. More importantly, the new source has a QBER as low as 0.93% which is not only important for the security of the QKD system but will be required for the implementation of a new cryptographic primitive later. Lastly, I study the free-space link transmission statistics and the use of a signal-to-noise ratio (SNR) filter to improve the key rate by 25.2% from the same amount of raw key. The link statistics have particular relevance for a current project with the Canadian Space Agency to exchange a quantum key with an orbiting satellite - a project which I have participated in two feasibility studies for. \n \nWanting to study the usefulness of more recent ideas in quantum cryptography this thesis then looks at the first experimental implementation of a new cryptographic primitive called oblivious transfer (OT) in the noisy storage model. This primitive has obvious important applications as it can be used to implement a secure identification scheme provably secure in a quantum scenario. Such a scheme could one day be used, for example, to authenticate a user over short distances, such as at ATM machines, which have proven to be particularly vulnerable to hacking and fraud. Over a four hour experiment, Alice and Bob measure 405,642,088 entangled photon pairs with an average QBER of 0.93% allowing them to create a secure OT key of 8,939,150 bits. As a first implementer, I examine many of the pressing issues currently preventing the scheme from being more widely adopted such as the need to relax the dependance of the OT rate on the loss of the system and the need to extend the security proof to cover a wider range of quantum communication channels and memories. It is important to note that OT is fundamentally different than QKD for security as the information is never physically exchanged over the communication line but rather the joint equality function f(x) = f(y) is evaluated. Thus, security in QKD does not imply security for OT. \n \nFinally, this thesis concludes with the construction and initial alignment of a second generation free-space quantum receiver, useful for increasing the QKD key rates, but designed for a fundamental test of quantum theory namely a Svetlichny inequality violation. Svetlichny's inequality is a generalization of Bell's inequality to three particles where any two of the three particles maybe be non-locally correlated. Even so, a violation of Svetlichny's inequality shows that certain quantum mechanical states are incompatible with this restricted class of non-local yet realistic theories. Svetlichny's inequality is particularly important because while there has been an overwhelming number of Bell experiments performed testing two-body correlations, experiments on many-body systems have been few and far between. Experiments of this type are particularly valuable to explore since we live in a many-body world. The new receiver incorporates an active polarization analyzer capable of switching between measurement bases on a microsecond time-scale through the use of a Pockels cell while maintaining measurements of a high fidelity. Some of the initial alignment and analysis results are detailed including the final measured contrasts of 1:25.2 and 1:22.6 in the rectilinear and diagonal bases respectively.
In contrast to classical public-key cryptosystems, where the security of encoded messages relies on on computational assumptions, Quantum Key Distribution (QKD) enables two distant parties to establish a shared secret key that, when combined with a one-time pad, provides information-theoretically secure encryption, provided that the QKD protocol is supported by a rigorous security proof. In the last decades, security proofs robust against a wide range of eavesdropping strategies have established the theoretical soundness of several QKD protocols. However, most proofs are based on idealized models of the physical systems involved in such protocols and often include assumptions that are not satisfied in practical implementations. This mismatch creates a gap between theoretical security guarantees and actual experimental realizations, making QKD protocols vulnerable to attacks. To ensure the security of real-world QKD systems, it is therefore essential to account for imperfections in security analyses. In this article, we present an overview of recent analytical and numerical developments in QKD security proofs, which provide a versatile approach for incorporating imperfections and re-establishing the security of quantum communication protocols under realistic conditions.
Despite enormous theoretical and experimental progress in quantum cryptography, the security of most current implementations of quantum key distribution is still not rigorously established. One significant problem is that the security of the final key strongly depends on the number, M, of signals exchanged between the legitimate parties. Yet, existing security proofs are often only valid asymptotically, for unrealistically large values of M. Another challenge is that most security proofs are very sensitive to small differences between the physical devices used by the protocol and the theoretical model used to describe them. Here we show that these gaps between theory and experiment can be simultaneously overcome by using a recently developed proof technique based on the uncertainty relation for smooth entropies. Although they offer significant promise, practical implementations of quantum key distribution are often not as rigorous as theory predicts. This study demonstrates how two instances of such discrepancies can be resolved by taking advantage of an enotropic formulation of the uncertainty principle.