How Quantum Theory is Developing the Field of Information Retrieval
D. Song1, M. Lalmas2, C.J. van Rijsbergen2, I. Frommholz2, B. Piwowarski2, J. Wang1, P. Zhang1, G. Zuccon2, P.D. Bruza4
S. Arafat2, L. Azzopardi2, E. Di Buccio5, A. Huertas-Rosero2, Y. Hou6, M. Melucci5, S. RÄuger3
1The Robert Gordon University, UK; 2University of Glasgow, UK; 3The Open University, UK;
4Queensland University of Technology, Australia; 5University of Padua, Italy; 6Tianjin University, China
Abstract
This position paper provides an overview of work conducted
and an outlook of future directions within the field of In-
formation Retrieval (IR) that aims to develop novel models,
methods and frameworks inspired by Quantum Theory (QT).
Introduction
The goal of IR is to predict which documents can help users
in satisfying their information needs, i.e. to measure the rel-
evance of the documents. Consider this search scenario: “I
am looking for information about children activities in Cam-
bridge; this is usually listed at the top of documents; I also
want documents containing images. It is raining so I need in-
door activities”. This information need contains contextual
components (local search and weather), which may evolve
over time, e.g. after the user has seen some documents. It
also contains multimodal components, specifying where the
relevant information can be found in the document, and re-
quests text and non-text results. This type of complex but re-
alistic information needs cannot yet be satisfied with today’s
IR technologies. To address these challenges, we believe
that a radically new IR paradigm is needed.
Relationships between formal methods in IR and QT has
been shown to exist (van Rijsbergen 2004). In addition,
a growing body of literature is supporting the notion that
quantum-like phenomena exist in human natural language
and text, cognition and decision making, all related to key
aspects of the IR process. Corresponding to these quantum-
like phenomena are non-classical probabilities that the tradi-
tional IR models are insufficient to support. All the evidence
suggests that QT provides suitable building blocks for a non-
classical approach that could address these challenges.
An on-going international collaboration, through the
UK Engineering and Physical Sciences Research Council
funded Renaissance project1, is attempting to develop novel
IR models, methods and frameworks inspired by QT. Build-
ing upon the Renaissance project, a new EU funded project,
QONTEXT, through the Marie-Curie International Research
Staff Exchange Scheme, has recently started, aiming to con-
solidate and extend this collaboration.
Copyright c° 2010, Association for the Advancement of Artificial
Intelligence (www.aaai.org). All rights reserved.
1http://renaissance.dcs.gla.ac.uk/start
Research Hypothesis and Objectives
We hypothesise that QT provides innovation and inspiration
into circumventing the emerging context and multimodality
issues in IR. Specifically, our main objectives are:
² Development of a generic QT-based paradigm for IR, with
special focus on three key themes: (1) Frameworks: gen-
eral frameworks and operational methods for contextual
and multimodal IR; (2) Spaces: geometrical represen-
tation and characterisation of context through semantic
spaces; (3) Interferences: the interferences among doc-
uments, topics and user’s cognitive status in contextual
relevance measurement process.
² Implementation, application and evaluation of the QT-
based IR methods to suitable IR tasks, such as ad-hoc re-
trieval, interactive retrieval, and multimedia retrieval.
In the following sections, we report the progress achieved
in these three key themes.
Frameworks Theme
Interactive IR Framework
The probabilistic formalism of QT provides a sound ba-
sis for building a principled interactive IR framework, as
proposed in (Piwowarski et al. 2010). In this framework,
events, e.g. document relevance, correspond to subspaces,
in an “information need space”. These provide a means
to compute the probability of any event, and to update this
probability when the event is realised, e.g. a document is
judged relevant. These updates, capturing interaction, are
performed on density operators that represent the state of a
user’s information need. After each interaction, a new den-
sity is computed and then used to re-rank documents. A
main challenge is the construction of appropriate subspaces
and initial density operators. A methodology to construct
those from a document collection has been proposed. Cur-
rent developments include a structured query language to
compute the initial information need density, experiments
with interaction, multimedia, and polyrepresentation, and
the validation of the proposed construction methodology.
Polyrepresentation Framework
Polyrepresentation for IR postulates that a document can be
characterised by several different representations. In cross-
media retrieval, a document can be represented by textual

and visual features. A document can be looked from dif-
ferent viewpoints, e.g. its authors, its content, user-given re-
views, ratings. Each of these properties characterises the
document with respect to different representations. If there
is a ranking w.r.t. each representation, the intersection of
it (i.e. documents appearing in all rankings) is called the
“cognitive overlap”. Polyrepresentation suggests that rel-
evant documents are at the cognitive overlap of the docu-
ments representations. Our aim is to support polyrepresenta-
tion in a QT-inspired interactive IR framework, as proposed
in (Frommholz et al. 2010). Each distinct representation is
described within a Hilbert space, similar to the aforemen-
tioned information need space. We define a product Hilbert
space of the single representation spaces. Instead of com-
bining the ranking scores independently from different rep-
resentations, states in this space may be correlated or non-
separable due to interrelations between representations. The
ranking scores are then computed in a way analogous to the
expected outcome of a quantum measurement (Wang, Song,
and Kaliciak 2010). Initial experiment has shown a promis-
ing performance of the approach in image retrieval.
Logical Imaging
Logic-based models played a fundamental role in the devel-
opment of IR research. van Rijsbergen (2004) provided the
basis for describing logic-based IR models within a quan-
tum formalism, and in particular within Hilbert spaces. Zuc-
con, Azzopardi and van Rijsbergen (2008) proposed a con-
crete formulation of a well-known logic-based IR technique,
i.e. Logical Imaging, in terms of QT. Logical Imaging (LI)
is a technique for updating the probability that a document is
relevant to a query by exploiting inter-document term rela-
tionships. The new formalisation of LI in terms of QT devel-
ops from an analogy between states of a quantum system and
terms in documents. In particular, the dynamics of a physi-
cal system is associated with the kinematics of probabilities
generated by LI. By placing LI within the quantum frame-
work, a mathematical basis is provided to capture, model
and use the contextual information associated with a term to
understand its meaning in a specific context. The latter was
not dealt with in the original LI model.
Quantum Based Measurements for Documents
The problem of representing text documents within an IR
system is formulated as an analogy to that of represent-
ing the quantum states of a physical system. In (Huertas-
Rosero, Azzopardi, and van Rijsbergen 2008), lexical mea-
surements of text are proposed as a way of representing doc-
uments which are akin to physical measurements on quan-
tum states. The representation of the text is only known af-
ter measurements have been made, because the process of
measuring may destroy parts of the text. Thus, the docu-
ment is characterised through erasure. We define the Selec-
tive Erasers as a model of lexical measurement and explore
ways of using them to obtain information from documents.
Amongst these characteristics are those suitable for using as
term weights, based on e.g. occurrence frequencies and dis-
tances between occurrences. Erasers are explored as ways
of obtaining information about how one term is used with
respect to another, like various co-occurrence quantification
methods, and distances between neighbouring occurrences.
Mathematical structures like lattices and algebras can be de-
fined to generate composite operations able to capture se-
mantic information from text (Huertas-Rosero, Azzopardi,
and van Rijsbergen 2009). This research has produced a
mathematical foundation for a quantum-like representation
of text and provides a basis for indexing and retrieval within
a QT-inspired IR system.
Search Simulation Framework
In addition to a mathematical framework, QT provides ab-
stract concepts describing the physical world that may be
suitable metaphors for describing IR phenomena. Following
this premise, we studied the application of QT concepts to
address some foundational issues in search (Arafat and van
Rijsbergen 2007). Initially, the problem was to define the
concept and process of search and to differentiate it from
other processes. This then led to forming a model of search
that spurred investigation of problems related to incorpo-
rating models of user cognition and interaction within this
search model. One conclusion from this work is that, in or-
der to fully benefit from the formalisation tools from QT,
a methodological shift in the approach to evaluation in IR is
required. Specifically, interactive search scenario simulation
would require to be considered. The implications of such a
shift are currently under investigation.
Spaces Theme
Context Spaces
Capturing context requires exploiting different sources of
evidence involved in the IR process. These sources are the
properties of the different entities involved when retrieving
and accessing information, where examples of entities in-
clude document, task, user, or location. To exploit the vari-
ety of entities and sources, it is necessary to model the re-
lationships existing between the entities and those existing
between the properties of the entities. Such relationships are
themselves possible sources that can be used to predict rele-
vance. In (Di Buccio, Lalmas, and Melucci ), we proposed
a methodology that supports the design of an IR system able
to model in a uniform way the properties of the entities in-
volved, the properties of their relationships and the relation-
ships between the different properties. Sources and relation-
ships are modeled and then exploited through a geometric
framework (Melucci 2008), which provides a uniform and
concrete representation in terms of vector subspaces. For
instance, the degree to which a modeled source occurs in a
document can be measured as the distance between the vec-
tor representation of the document and the subspace mod-
eling the source(s) spanned by the vector space basis. This
motivates the trace-based function proposed in (van Rijsber-
gen 2004). Using trace in IR, and in particular the density
operators, provides the means to establish a link between
geometry and probability in vector spaces.

Semantic Subspaces
A major IR challenge is how to represent documents to sup-
port the retrieval of those relevant to a user query without
retrieving documents that are instead irrelevant. In the vec-
tor space model for IR, a document is represented as a vec-
tor whose components indicate the (weighted) presence or
absence of a term in the document itself. Documents are
then matched against a user query, represented as a vector as
well, by means of the inner product. Zuccon, Azzopardi and
van Rijsbergen (2009b) proposed an alternative approach:
documents are represented as subspaces, which encode the
semantic of the document itself. However, assuming that a
user picks a document, and thus its associated subspace, to
represent the query, how could documents be compared to
discriminate between relevant and irrelevant? This problem
is reformulated as how to distinguish preparations of differ-
ent quantum systems, where preparations are represented by
semantic (sub)spaces. With this in mind, the subspace dis-
tance is introduced. Empirical experiments showed that the
subspace representation of documents together with the sub-
space distance provide a technique for separating relevant
documents from irrelevant ones.
Non-separability in Human Semantic Space A theory
and associated experimental apparatus has been developed
for testing whether concept combinations are non-separable
in human memory in (Bruza et al. 2009). For instance,
the term “bat” can be modelled in a two dimensional vec-
tor space as a vector that expresses the intuition that “bat”
is a linear combination of two possible senses e.g. “sport”
and “animal” (which correspond to vector space basis). The
same can be said for the term “boxer” which also has two
senses, one dealing with the sport of boxing and the other re-
lating to the breed of dog. As both terms can be represented
as a superposition between the basis states corresponding to
“sport” and “animal”, this opens the possibility to represent
the concept combination “boxer bat” following the quan-
tum formalism. In QT, interacting systems are formalised
via a tensor product of the individual systems, representing
the concept combination “boxer bat” as the outer product
of the two vectors. The state of “boxer bat” is decompos-
able, if it can be established as a product of the state “boxer”
with the state “bat”. Such a decomposable state of the inter-
acting systems is termed as being separable. We are inter-
ested in the non-separability of concept combinations. This
has been investigated using a basic quantum-like model of
concept combinations. An empirical framework for testing
whether such non-separable combinations actually manifest
in cognition and some initial results for bi-ambiguous con-
cept combinations are given in (Bruza et al. 2010). Thus far,
preliminary results suggest many concept combinations are
“pseudo-classically” non-separable meaning the combina-
tion cannot be modelled by probability distributions across
the senses of the individual words. There are some concept
combinations, however, which appear quantum-like entan-
gled but more empirical experimentation is needed to verify
this. The non-separability of concept combinations suggests
that for an IR system to effectively represent concepts, the
representations used should be non-compositional. For ex-
ample, this rules out using mixture models to represent con-
cept combinations as such models are clearly compositional.
Deriving Pure High-order Semantic Associations
from Semantic Spaces
The classical bag-of-words vector space model (VSM)
fails to capture high-order semantic associations (interac-
tions) between terms. Initial evidence has shown that the
phenomenon of quantum-like entanglement (e.g. as non-
separable associations) exists in a semantic space and can
potentially play a crucial role in determining the embedded
semantics. We propose to consider pure high-order inter-
actions (e.g. the terms “invasion”, “Napoleon” and “Spain”
form a high-level semantic entity) that cannot be reduced
to the compositional effect of lower-order ones (e.g. the
co-occurrence of “invasion” and “Napoleon” and the co-
occurrence of “Spain” and “Napoleon”), as an indicator of
non-separable high-level semantic entities. To characterize
the intrinsic order of interactions and distinguish pure high-
order interactions from lower-order ones, we developed a
set of methods (Hou and Song 2009), upon which we pro-
pose an extended vector space model (EVSM) that involves
context-sensitive high-order information and aims at char-
acterizing high-level retrieval contexts. Compared with the
direct incorporation of classical statistical dependence in
VSM, our methods have proved mathematically more rig-
orous. An extensive empirical evaluation is on-going.
Interference Theme
Interference in Document Ranking
Document ranking in response to a user query is usually pro-
duced according to the Probability Ranking Principle (PRP),
i.e. by ordering the documents according to decreasing prob-
ability of relevance. Documents relevance judgements are
assumed to be independent from other documents. This is
an unreal assumption. In (Zuccon, Azzopardi, and van Ri-
jsbergen 2009a), an analogy between the document ranking
scenario in IR and the double slit experiment has been sug-
gested. Through this analogy, it was shown that the PRP
resorts to model the ranking scenario as Kolmogorovian
probability theory models the double slit experiment. As it
is known from empirical observations, the Kolmogorovian
predictions for the double slit experiment are inadequate,
while those obtained through quantum probability theory
correctly reassemble the empirical observations of the phys-
ical experiment. This suggests to model the document rank-
ing scenario in IR by adopting quantum probability theory.
The resultant is a novel quantum probability ranking princi-
ple (QPRP), where interference plays a key role, represent-
ing interdependent document relevance. QPRP is able to
model situations where a document relevance assessment is
influenced by other documents. Empirical validations have
consolidated QPRP as the state of the art criteria for ranking
documents under interdependent document relevance.
Cognitive Interference
The concept of interference is applied to relevance assess-
ments, aiming to explain and predict user behaviour rather

than the utility of a particular document ranking.
Cognitive Interference in Document Relevance Measure-
ment Cognitive interference occurs when users change
their relevance measurement result for one document af-
ter they have measured other documents. For example, if
users only measure document d0, they may think it is highly
relevant. However, after having viewed another document
which is more relevant than d0, they may now regard d0 as
partially relevant only. We adopt the probabilistic automaton
(PA) and its quantum counterpart, quantum finite automaton
(QFA), to represent the transition of the measurement states
(the relevance degrees of the document judged by users) and
dynamically model the cognitive interference of users when
they are judging a list of documents (Zhang et al. 2010).
The research is inspired by recent work from cognitive sci-
ence, where QT is employed to model interference in hu-
man decision probability measurements which leads to the
violation of the classic law of total probability. We are in-
vestigating this direction through user relevance judgment
data collected from a task-based user study. We also aim to
extend it to standard IR tasks and experiments.
Experimental Issues on Cognitive Interference and
Quantum Probability In (van Rijsbergen 2004) and re-
lated literature, it was hypothesised that a QT-based frame-
work and the quantum probability would be suitable for go-
ing beyond classical retrieval models. A IR scenario, in
which such a framework can be a necessary, was discussed,
and corresponding experiments were carried out in (Melucci
2010). The necessity of considering quantum probability
stemmed from the experimental observation that the best
terms for query expansion have a probability that does not
obey classical probability and instead can be defined within
a quantum probability function.
Conclusions and Future Work
This paper reports an ongoing international collaborative re-
search agenda in applying Quantum Theory to develop the
field of Information Retrieval and the promising progress
that has been made. Current research has been focused
on three main themes: Frameworks, Spaces and Interfer-
ence. We have developed novel QT-based IR frameworks
that aim to address two challenging issues: context and mul-
timodality. Common to these frameworks are the construc-
tion of appropriate subspaces, their interactions and evolu-
tions, and measurement of document relevance. To facili-
tate the frameworks, the Spaces theme aims at developing
a geometrical representation of context, which can be de-
rived from different sources, and characterising context in
terms of semantic subspaces, high-order and non-separable
concept associations. The Interference theme aims to model
and utilise a fundamental quantum-like phenomenon (as a
specific type of contextual effect), namely the interference,
in the document ranking and relevance judgment process.
Our future research will be focused on integration and
evaluation. Due to the high exploratory nature of this line
of research, so far we have taken a bottom-up approach. As
a result, the proposed methods in the three themes are still
largely fragmented. For instance, exploiting meaning in se-
mantic spaces and incorporating interference in document
relevance judgement are means to deal with the context is-
sue, whereas combining evidences and polyrepresentation
are to deal with the multimodality issue. Integrating them to
form a comprehensive model will be the next step to fully
realise the potential of QT-based IR. Further, the current ex-
perimental results, carried out separately for different meth-
ods, albeit promising, have not yet shown the full extent of
using QT for IR. To this end, we will develop a common
evaluation methodology and platform, where proper cogni-
tion and interaction aspects should be taken into account,
and carry out more extensive empirical evaluations.
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