The paper shows that ranking information units by quantum probability differs from ranking them by classical probability provided the same data used for parameter estimation. As probability of detection (also known as recall or power) and probability of false alarm (also known as fallout or size) measure the quality of ranking, we point out and show that ranking by quantum probability yields higher probability of detection than ranking by classical probability provided a given probability of false alarm and the same parameter estimation data. As quantum probability provided more effective detectors than classical probability within other domains that data management, we conjecture that, the system that can implement subspace-based detectors shall be more effective than a system which implements a set-based detectors, the effectiveness being calculated as expected recall estimated over the probability of detection and expected fallout estimated over the probability of false alarm.
The paper shows that ranking information units by quantum probability differs from ranking them by classical probability provided the same data used for parameter estimation. As probability of detection (also known as recall or power) and probability of false alarm (also known as fallout or size) measure the quality of ranking, we point out and show that ranking by quantum probability yields higher probability of detection than ranking by classical probability provided a given probability of false alarm and the same parameter estimation data. As quantum probability provided more effective detectors than classical probability within other domains that data management, we conjecture that, the system that can implement subspace-based detectors shall be more effective than a system which implements a set-based detectors, the effectiveness being calculated as expected recall estimated over the probability of detection and expected fallout estimated over the probability of false alarm.
According to the probability ranking principle, the document set with the highest values of probability of relevance optimizes information retrieval effectiveness given the probabilities are estimated as accurately as possible. The key point of this principle is the separation of the document set into two subsets with a given level of fallout and with the highest recall. If subsets of set measures are replaced by subspaces and space measures, we obtain an alternative theory stemming from Quantum Theory. That theory is named after vector probability because vectors represent event like sets do in classical probability. The paper shows that the separation into vector subspaces is more effective than the separation into subsets with the same available evidence. The result is proved mathematically and verified experimentally. In general, the paper suggests that quantum theory is not only a source of rhetoric inspiration, but is a sufficient condition to improve retrieval effectiveness in a principled way.
Indexing is a core process of an information retrieval (IR) system (IRS). As indexing can neither be exhaustive nor precise, the decision taken by an IRS about the relevance of the content of a document to an information need is subject to uncertainty. It is our hypothesis that one of the reasons that IRSs are unable to optimally respond to every query is that the document collections and the posting lists are modeled as sets of documents. In contrast, if vector spaces replace sets along the way given by quantum mechanics, it is possible to define a quantum information retrieval basis (QIRB) that at least in principle yields more effective document ranking than the ranking yielded by the current principles, with effectiveness being measured in terms of recall at every level of fallout. To this end, we show that the probability ranking principle and the Neyman–Pearson Lemma (NPL) are equivalent. The rest of the article follows from this result. In particular, we introduce the QIRB, link it to a generalization of the NPL and demonstrate its superiority through a concise mathematical analysis and an empirical study. The challenges posed by this basis and the research directions that would be opened are also discussed.
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 IR 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. While PRP explicitly assumes that the relevancy of a document is independent of that of other documents, we suggest that qPRP implicitly models interdependent document relevance through quantum interference and thus is suited to those document ranking tasks where the independence assumption fails. Throughout the thesis, we also suggest how quantum interference can be estimated for effective document ranking. 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 than or comparable to alternative ranking approaches. However, when evaluation contexts that account for interdependent document relevance are examined (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), 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 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 of future research. These include investigating estimations and approximations of quantum interference in qPRP, exploiting complex numbers for the representation of documents and queries, and applying the concepts underlying qPRP to tasks other than document ranking. This dissertation was completed at School of Computing Science, University of Glasgow under the advise of Dr. Leif Azzopardi and Prof. Keith van Rijsbergen. Prof. Norbert Fuhr, Dr. Iadh Ounis, and Dr. John O'Donnell served as dissertation committee members. For the full dissertation, visit: http://theses.gla.ac.uk/3463.
In this paper we address the problem of using one probability space for estimating parameters and predicting future data when the observed data come from multiple contexts and thus from distinct spaces. We explain that a set-based probabilistic space might be suboptimal in the case of multiple contexts. To overcome suboptimality and reconcile multiple contexts in one space, the paper introduces the Quantum Probability Space (QPS). We also present an algorithm to calculate the QPS for data observed from multiple contexts and provide a web application that implements the algorithm. The QPS has application in Information Retrieval (IR), Machine Learning (ML) and in any domain where items should optimally be ranked and classified by some properties but under conditions of uncertainty due to context.
Leakage from a known encoding subspace can be detected by projection. However, the corresponding projector is unavailable when the encoding subspace is not classically specified. Here we show how independent quantum references prepared by the same encoder enable leakage detection without a classical description of the encoding. A coherent measurement on the references and a single message leaves every state within the two-dimensional encoding subspace, including its entanglement with a remote system, exactly unchanged. We derive the exact detection law for M ideal references and prove optimality among tests with zero false alarm for every encoding. For orthogonal leakage, the miss probability is asymptotic to 4/M, independent of the ambient dimension d. Measuring all references first, even collectively, gives zero detection at every finite budget under the same zero-false-alarm requirement. For a fixed detection target between zero and one, the optimal measurement-first cost is Θ(d/ε) at sufficiently small tolerance ε on normal false alarm and conditional disturbance; a dimension-independent coherent budget suffices. For one logical qubit encoded in three physical qubits, seven coherent references achieve at least 50% orthogonal-leakage detection, whereas any measurement-first receiver needs at least 588 under the same 1% normal tolerances. Quantum references thus support leakage checks without classical reconstruction, with a sample advantage exponential in the number of physical qubits.
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.