Quantum key distribution in the classical authenticated key exchange framework

Key establishment is a crucial primitive for building secure channels in a multi-party setting. Without quantum mechanics, key establishment can only be done under the assumption that some computational problem is hard. Since digital communication can be easily eavesdropped and recorded, it is important to consider the secrecy of information anticipating future algorithmic and computational discoveries which could break the secrecy of past keys, violating the secrecy of the confidential channel. Quantum key distribution (QKD) can be used generate secret keys that are secure against any future algorithmic or computational improvements. QKD protocols still require authentication of classical communication, although existing security proofs of QKD typically assume idealized authentication. It is generally considered folklore that QKD when used with computationally secure authentication is still secure against an unbounded adversary, provided the adversary did not break the authentication during the run of the protocol. We describe a security model for quantum key distribution extending classical authenticated key exchange (AKE) security models. Using our model, we characterize the long-term security of the BB84 QKD protocol with computationally secure authentication against an eventually unbounded adversary. By basing our model on traditional AKE models, we can more readily compare the relative merits of various forms of QKD and existing classical AKE protocols. This comparison illustrates in which types of adversarial environments different quantum and classical key agreement protocols can be secure.

Quantum models of cognition and decision

Much of our understanding of human thinking is based on probabilistic models. This innovative book by Jerome R. Busemeyer and Peter D. Bruza argues that, actually, the underlying mathematical structures from quantum theory provide a much better account of human thinking than traditional models. They introduce the foundations for modelling probabilistic-dynamic systems using two aspects of quantum theory. The first, "contextuality", is a way to understand interference effects found with inferences and decisions under conditions of uncertainty. The second, "entanglement", allows cognitive phenomena to be modelled in non-reductionist ways. Employing these principles drawn from quantum theory allows us to view human cognition and decision in a totally new light...

A quantum probability perspective on borderline vagueness

The term “vagueness” describes a property of natural concepts, which normally have fuzzy boundaries, admit borderline cases, and are susceptible to Zeno’s sorites paradox. We will discuss the psychology of vagueness, especially experiments investigating the judgment of borderline cases and contradictions. In the theoretical part, we will propose a probabilistic model that describes the quantitative characteristics of the experimental finding and extends Alxatib’s and Pelletier’s (2011) theoretical analysis. The model is based on a Hopfield network for predicting truth values. Powerful as this classical perspective is, we show that it falls short of providing an adequate coverage of the relevant empirical results. In the final part, we will argue that a substan- tial modification of the analysis put forward by Alxatib and Pelletier and its probabilistic pendant is needed. The proposed modification replaces the standard notion of probabilities by quantum probabilities. The crucial phenomenon of borderline contradictions can be explained then as a quantum interference phenomenon.

Quantum one-time programs

A one-time program is a hypothetical device by which a user may evaluate a circuit on exactly one input of his choice, before the device self-destructs. One-time programs cannot be achieved by software alone, as any software can be copied and re-run. However, it is known that every circuit can be compiled into a one-time program using a very basic hypothetical hardware device called a one-time memory. At first glance it may seem that quantum information, which cannot be copied, might also allow for one-time programs. But it is not hard to see that this intuition is false: one-time programs for classical or quantum circuits based solely on quantum information do not exist, even with computational assumptions. This observation raises the question, "what assumptions are required to achieve one-time programs for quantum circuits?" Our main result is that any quantum circuit can be compiled into a one-time program assuming only the same basic one-time memory devices used for classical circuits. Moreover, these quantum one-time programs achieve statistical universal composability (UC-security) against any malicious user. Our construction employs methods for computation on authenticated quantum data, and we present a new quantum authentication scheme called the trap scheme for this purpose. As a corollary, we establish UC-security of a recent protocol for delegated quantum computation.

Simulations of the spontaneous emission of a quantum dot near a gap plasmon waveguide

In this paper we modeled a quantum dot at near proximity to a gap plasmon waveguide to study the quantum dot-plasmon interactions. Assuming that the waveguide is single mode, this paper is concerned about the dependence of spontaneous emission rate of the quantum dot on waveguide dimensions such as width and height. We compare coupling efficiency of a gap waveguide with symmetric configuration and asymmetric configuration illustrating that symmetric waveguide has a better coupling efficiency to the quantum dot. We also demonstrate that optimally placed quantum dot near a symmetric waveguide with 50 nm x 50 nm cross section can capture 80% of the spontaneous emission into a guided plasmon mode.

Quantum direct secret sharing with efficient eavesdropping-check and authentication based on distributed fountain codes

We propose to use a simple and effective way to achieve secure quantum direct secret sharing. The proposed scheme uses the properties of fountain codes to allow a realization of the physical conditions necessary for the implementation of no-cloning principle for eavesdropping-check and authentication. In our scheme, to achieve a variety of security purposes, nonorthogonal state particles are inserted in the transmitted sequence carrying the secret shares to disorder it. However, the positions of the inserted nonorthogonal state particles are not announced directly, but are obtained by sending degrees and positions of a sequence that are pre-shared between Alice and each Bob. Moreover, they can confirm that whether there exists an eavesdropper without exchanging classical messages. Most importantly, without knowing the positions of the inserted nonorthogonal state particles and the sequence constituted by the first particles from every EPR pair, the proposed scheme is shown to be secure.

Using the quantum probability ranking principle to rank interdependent documents

A known limitation of the Probability Ranking Principle (PRP) is that it does not cater for dependence between documents. Recently, the Quantum Probability Ranking Principle (QPRP) has been proposed, which implicitly captures dependencies between documents through “quantum interference”. This paper explores whether this new ranking principle leads to improved performance for subtopic retrieval, where novelty and diversity is required. In a thorough empirical investigation, models based on the PRP, as well as other recently proposed ranking strategies for subtopic retrieval (i.e. Maximal Marginal Relevance (MMR) and Portfolio Theory(PT)), are compared against the QPRP. On the given task, it is shown that the QPRP outperforms these other ranking strategies. And unlike MMR and PT, one of the main advantages of the QPRP is that no parameter estimation/tuning is required; making the QPRP both simple and effective. This research demonstrates that the application of quantum theory to problems within information retrieval can lead to significant improvements.

A formalization of logical imaging for information retrieval using quantum theory

In this paper we introduce a formalization of Logical Imaging applied to IR in terms of Quantum Theory through the use of an analogy between states of a quantum system and terms in text documents. Our formalization relies upon the Schrodinger Picture, creating an analogy between the dynamics of a physical system and the kinematics of probabilities generated by Logical Imaging. By using Quantum Theory, it is possible to model more precisely contextual information in a seamless and principled fashion within the Logical Imaging process. While further work is needed to empirically validate this, the foundations for doing so are provided.

Social tagging, guppy effect and the role of interference : a quantum-inspired model for tags combination

Social tagging systems are shown to evidence a well known cognitive heuristic, the guppy effect, which arises from the combination of different concepts. We present some empirical evidence of this effect, drawn from a popular social tagging Web service. The guppy effect is then described using a quantum inspired formalism that has been already successfully applied to model conjunction fallacy and probability judgement errors. Key to the formalism is the concept of interference, which is able to capture and quantify the strength of the guppy effect.

Developing the quantum probability ranking principle

In this work, we summarise the development of a ranking principle based on quantum probability theory, called the Quantum Probability Ranking Principle (QPRP), and we also provide an overview of the initial experiments performed employing the QPRP. The main difference between the QPRP and the classic Probability Ranking Principle, is that the QPRP implicitly captures the dependencies between documents by means of quantum interference". Subsequently, the optimal ranking of documents is not based solely on documents' probability of relevance but also on the interference with the previously ranked documents. Our research shows that the application of quantum theory to problems within information retrieval can lead to consistently better retrieval effectiveness, while still being simple, elegant and tractable.

On the use of complex numbers in quantum models for information retrieval

Quantum-inspired models have recently attracted increasing attention in Information Retrieval. An intriguing characteristic of the mathematical framework of quantum theory is the presence of complex numbers. However, it is unclear what such numbers could or would actually represent or mean in Information Retrieval. The goal of this paper is to discuss the role of complex numbers within the context of Information Retrieval. First, we introduce how complex numbers are used in quantum probability theory. Then, we examine van Rijsbergen’s proposal of evoking complex valued representations of informations objects. We empirically show that such a representation is unlikely to be effective in practice (confuting its usefulness in Information Retrieval). We then explore alternative proposals which may be more successful at realising the power of complex numbers.

Document ranking with quantum probabilities

In this thesis we investigate the use of quantum probability theory for ranking documents. Quantum probability theory is used to estimate the probability of relevance of a document given a user's query. We posit that quantum probability theory can lead to a better estimation of the probability of a document being relevant to a user's query than the common approach, i. e. the Probability Ranking Principle (PRP), which is based upon Kolmogorovian probability theory. Following our hypothesis, we formulate an analogy between the document retrieval scenario and a physical scenario, that of the double slit experiment. Through the analogy, we propose a novel ranking approach, the quantum probability ranking principle (qPRP). Key to our proposal is the presence of quantum interference. Mathematically, this is the statistical deviation between empirical observations and expected values predicted by the Kolmogorovian rule of additivity of probabilities of disjoint events in configurations such that of the double slit experiment. We propose an interpretation of quantum interference in the document ranking scenario, and examine how quantum interference can be effectively estimated for document retrieval. To validate our proposal and to gain more insights about approaches for document ranking, we (1) analyse PRP, qPRP and other ranking approaches, exposing the assumptions underlying their ranking criteria and formulating the conditions for the optimality of the two ranking principles, (2) empirically compare three ranking principles (i. e. PRP, interactive PRP, and qPRP) and two state-of-the-art ranking strategies in two retrieval scenarios, those of ad-hoc retrieval and diversity retrieval, (3) analytically contrast the ranking criteria of the examined approaches, exposing similarities and differences, (4) study the ranking behaviours of approaches alternative to PRP in terms of the kinematics they impose on relevant documents, i. e. by considering the extent and direction of the movements of relevant documents across the ranking recorded when comparing PRP against its alternatives. Our findings show that the effectiveness of the examined ranking approaches strongly depends upon the evaluation context. In the traditional evaluation context of ad-hoc retrieval, PRP is empirically shown to be better or comparable to alternative ranking approaches. However, when we turn to examine evaluation contexts that account for interdependent document relevance (i. e. when the relevance of a document is assessed also with respect to other retrieved documents, as it is the case in the diversity retrieval scenario) then the use of quantum probability theory and thus of qPRP is shown to improve retrieval and ranking effectiveness over the traditional PRP and alternative ranking strategies, such as Maximal Marginal Relevance, Portfolio theory, and Interactive PRP. This work represents a significant step forward regarding the use of quantum theory in information retrieval. It demonstrates in fact that the application of quantum theory to problems within information retrieval can lead to improvements both in modelling power and retrieval effectiveness, allowing the constructions of models that capture the complexity of information retrieval situations. Furthermore, the thesis opens up a number of lines for future research. These include: (1) investigating estimations and approximations of quantum interference in qPRP; (2) exploiting complex numbers for the representation of documents and queries, and; (3) applying the concepts underlying qPRP to tasks other than document ranking.

Response to “Comment on ‘Indications of energetic consequences of decoherence at short times for scattering from open quantum systems’” [AIP Advances 1, 049101 (2011)]

The Comment by Mayers and Reiter criticizes our work on two counts. Firstly, it is claimed that the quantum decoherence effects that we report in consequence of our experimental analysis of neutron Compton scattering from H in gaseous H2 are not, as we maintain, outside the framework of conventional neutron scatteringtheory. Secondly, it is claimed that we did not really observe such effects, owing to a faulty analysis of the experimental data, which are claimed to be in agreement with conventional theory. We focus in this response on the critical issue of the reliability of our experimental results and analysis. Using the same standard Vesuvio instrument programs used by Mayers et al., we show that, if the experimental results for H in gaseous H2 are in agreement with conventional theory, then those for D in gaseous D2 obtained in the same way cannot be, and vice-versa. We expose a flaw in the calibration methodology used by Mayers et al. that leads to the present disagreement over the behaviour of H, namely the ad hoc adjustment of the measured H peak positions in TOF during the calibration of Vesuvio so that agreement is obtained with the expectation of conventional theory. We briefly address the question of the necessity to apply the theory of open quantum systems.

Indications of energetic consequences of decoherence at short times for scattering from open quantum systems

Decoherence of quantum entangled particles is observed in most systems, and is usually caused by system-environment interactions. Disentangling two subsystems A and B of a quantum systemAB is tantamount to erasure of quantum phase relations between A and B. It is widely believed that this erasure is an innocuous process, which e.g. does not affect the energies of A and B. Surprisingly, recent theoretical investigations by different groups showed that disentangling two systems, i.e. their decoherence, can cause an increase of their energies. Applying this result to the context of neutronCompton scattering from H2 molecules, we provide for the first time experimental evidence which supports this prediction. The results reveal that the neutron-proton collision leading to the cleavage of the H-H bond in the sub-femtosecond timescale is accompanied by larger energy transfer (by about 3%) than conventional theory predicts. It is proposed to interpreted the results by considering the neutron-proton collisional system as an entangled open quantum system being subject to decoherence owing to the interactions with the “environment” (i.e., two electrons plus second proton of H2).

The sphynx's new riddle : how to relate the canonical formula of myth to quantum interaction

We introduce Claude Lévi Strauss' canonical formula (CF), an attempt to rigorously formalise the general narrative structure of myth. This formula utilises the Klein group as its basis, but a recent work draws attention to its natural quaternion form, which opens up the possibility that it may require a quantum inspired interpretation. We present the CF in a form that can be understood by a non-anthropological audience, using the formalisation of a key myth (that of Adonis) to draw attention to its mathematical structure. The future potential formalisation of mythological structure within a quantum inspired framework is proposed and discussed, with a probabilistic interpretation further generalising the formula