Towards Quantum-Based DB+IR Processing
Based on the Principle of Polyrepresentation
David Zellhöfer1, Ingo Frommholz2, Ingo Schmitt1, Mounia Lalmas3,
and Keith van Rijsbergen2
1 Brandenburg University of Technology Cottbus, Department of Computer Science
Postfach 10 13 44, 03013 Cottbus, Germany
david.zellhoefer@tu-cottbus.de
http://dbis.informatik.tu-cottbus.de/
2 University of Glasgow, School of Computing Science
18 Lilybank Gardens, Glasgow G12 8QQ, Scotland
ingo.frommholz@glasgow.ac.uk
http://ir.dcs.gla.ac.uk/
3 Yahoo! Research, Spain
mounia@acm.org
Abstract. The cognitively motivated principle of polyrepresentation
still lacks a theoretical foundation in IR. In this work, we discuss two
competing polyrepresentation frameworks that are based on quantum
theory. Both approaches support different aspects of polyrepresentation,
where one is focused on the geometric properties of quantum theory while
the other has a strong logical basis. We compare both approaches and
outline how they can be combined to express further aspects of polyrep-
resentation.
1 Introduction
The core idea behind the principle of polyrepresentation of documents [2] is that
a document is defined by different representations that can be combined to de-
termine the cognitive overlap where it is assumed highly relevant documents are
likely to be contained. Examples of different representations of the same doc-
ument are user-given ratings, reviews and comments, the author-given textual
content or non-textual features of a multimedia document.
Inspired by van Rijsbergen’s idea of applying the mathematics behind quan-
tum theory for IR, seamlessly combining geometry, probability theory and log-
ics [5], recent frameworks have approached polyrepresentation from different
viewpoints. While in [1] a geometric framework is proposed which has a proba-
bilistic interpretation, [9] comes from the database domain and has a quantum
logic-based background [6], which can also be interpreted probabilistically. These
approaches are complementary in the sense that they focus on different aspects
of polyrepresentation on the one hand, and in its viewpoint of the underlying
theory (geometrical vs. logic-based) on the other hand, with geometry as their
common mathematical ground. Our intention in this study is therefore to learn
from both approaches and figure out the potential we can gain from combining
them.
P. Clough et al. (Eds.): ECIR 2011, LNCS 6611, pp. 729–732, 2011.
c
© Springer-Verlag Berlin Heidelberg 2011

730 D. Zellhöfer et al.
2 Quantum-Based Frameworks for Polyrepresentation
Van Rijsbergen argues in his seminal work [5] in support of a quantum mechanic/
logic-based interpretation of IR. He outlines how probability theory, logic, and
geometry relate in the context of quantum theory. In the following subsections,
we will discuss two approaches which are based on these findings. Both ap-
proaches reflect different aspects of the principle of polyrepresentation.
2.1 The IQIR Framework
The motivation behind the IQIR framework (Interactive Quantum-based IR) is
to provide means for (interactive) information retrieval on the ground of quan-
tum mechanics [1]. The framework is based on the assumption that there is an
information need (IN) space, which is a real-valued Hilbert space. The user’s IN
is represented by a set of unit state vectors, reflecting the uncertainty the sys-
tem has about the user’s IN. The event that a document is relevant is modelled
as a subspace. The probability of relevance is now determined by the squared
length of the projections of the vectors onto the document subspace. To support
polyrepresentation, a separate Hilbert space for each document representation is
created. To determine the cognitive overlap, the single representation spaces and
their state vectors are combined using the tensor product, which establishes a
polyrepresentation space. Geometric means are provided to weight single repre-
sentations according to their importance to the user and to control the cognitive
overlap. Within the polyrepresentation space, a non-separable (or entangled)
state expresses dependencies between document representations from the user’s
point of view. Another inherent feature of the framework is that the vectors rep-
resenting the user’s IN can dynamically be transformed to reflect several forms
of user interaction and information need drifts. This is motivated by the fact
that information needs are indeed dynamic by nature [2].
2.2 CQQL
In contrast to the aforementioned approach, the commuting quantum query lan-
guage (CQQL) [6] models the IN as a subspace of a hypothetical real-valued
Hilbert space on which documents, represented as vectors, will be projected in
order to determine their probability of relevance. Again, polyrepresentation and
the creation of the cognitive overlap is supported by combining the isolated
Hilbert spaces, each describing the attributes of a single document represen-
tation, by means of the tensor product. Because of CQQL’s background in DB
theory, it differentiates between attribute values that will be modelled by orthog-
onal state vectors mirroring Boolean values and probability values that rely on
non-orthogonal vectors. Although quantum logic itself does not form a Boolean
algebra (because the law of distributivity is violated), the commuting projector
describing the IN subspace is consistent with these rules. To guarantee this –
generally speaking – CQQL restricts the query to not use more than one prob-
ability condition on one attribute, e.g, title ≈ ”polyrepresentation” ∨ title ≈
”quantum logic”. If this restriction is accepted, an IN can be modelled using the
full structural power of a Boolean algebra, i.e, conjunctions, disjunctions, and

Towards Quantum-Based DB+IR Processing 731
negations. Note that this does not mean the re-introduction of the shortcomings
of Boolean retrieval models such as unordered result sets or the absence of term
weighting. Instead, CQQL fully supports weighted logical connectors in order to
adjust a query according to the user’s needs [8], i.e, to construct the cognitive
overlap. Given a structured query that models the cognitive overlap expressing
the user’s IN, the relevance of all documents can be assessed.
3 Probabilities, Geometry and Logics for
Polyrepresentation – Opportunities and Challenges
Because of their conceptual similarities, it is tempting to combine both ap-
proaches into one quantum-based DB and IR query model that supports the
principle of polyrepresentation. Regarding a polyrepresentative query model,
IQIR lacks the opportunity to express highly structured queries. Such queries
relying on Boolean connectors are shown to support the polyrepresentation prin-
ciple best [3]. CQQL offers means to incorporate such queries into the query
model. An interesting result from the utilisation of quantum theory for IR in
IQIR is the potential to introduce concepts like non-separable (entangled) states
reflecting inter-relationships between parts of a query, the representation of the
system’s uncertainty about the user’s IN and the possibility to reflect user in-
teraction by means of quantum measurement. The first idea is not supported
in CQQL so far. CQQL addresses the latter by a machine-based learning rele-
vance feedback approach in order to adjust the present condition weights that
eventually determine the cognitive overlap [7,8].
Both approaches have in common that they rely on weights to steer the influ-
ence of different representations onto the cognitive overlap. IQIR offers so-called
"don’t care" aspects whereas CQQL equips all logical connectors with weights
in order to personalise a query. Hence, both methods use – in a way – pseudo
features to express different grades of importance for terms or parts of a query. A
combination of both approaches would give us the possibility to create a frame-
work that is able to reflect the system’s uncertainty about the user’s IN, react
on IN drifts and represent interrelations between document representations, in
combination with powerful querying mechanisms provided by a query language
that supports concepts from databases and IR. This way, complex and possibly
interactive retrieval strategies, as structured queries to given knowledge base of
polyrepresented documents combining factual and content-oriented aspects, are
supported.
One of the biggest open challenges to achieve this goal is the dual way docu-
ments and information needs are represented in both frameworks. In IQIR, the
unit vectors represent the user’s IN and subspaces represent documents, whereas
in CQQL, these vectors describe one representation of a document and the user
state (the query) is reflected by a projector/subspace. In CQQL, the document
is considered the dynamic part that is measured against the projector, which
resembles the viewpoint taken in [4]. Although somewhat dual, there is no stan-
dard way to translate one view into the other. A solution may be to regard the
set of unit vectors in IQIR as an average or a probability distribution of projec-
tors in CQQL. This may impose some restrictions on how we can model these

732 D. Zellhöfer et al.
vectors; we may for a start just deal with the case that the user’s IN is repre-
sented by one vector only. As both approaches rely on weights to incorporate
the dynamics of the user’s search goal and the weights in CQQL already affect
the projector it seems appropriate to pursue this idea further.
4 Conclusion
In this study we analysed two polyrepresentation frameworks that are based on
the mathematical formalism of quantum mechanics. We have shown that both
approaches are complementary when it comes to polyrepresentation, with ge-
ometry as common mathematical grounds. A combination of both approaches
would lead to a powerful theoretical and also practical framework for polyrep-
resentation, giving rise to supporting complex retrieval strategies. One of the
biggest challenges is the dual nature of both approaches, which we are going to
address in our future work.
Acknowledgements
This research was supported by an Engineering and Physical Sciences Research
Council grant (Grant Number EP/F015984/2). This paper was written when
Mounia Lalmas was a Microsoft Research/RAEng Research Professor.
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