7,530 research outputs found
Investigating Bell Inequalities for Multidimensional Relevance Judgments in Information Retrieval
Relevance judgment in Information Retrieval is influenced by multiple factors. These include not only the topicality of the documents but also other user oriented factors like trust, user interest, etc. Recent works have identified and classified these various factors into seven dimensions of relevance. In a previous work, these relevance dimensions were quantified and user's cognitive state with respect to a document was represented as a state vector in a Hilbert Space, with each relevance dimension representing a basis. It was observed that relevance dimensions are incompatible in some documents, when making a judgment. Incompatibility being a fundamental feature of Quantum Theory, this motivated us to test the Quantum nature of relevance judgments using Bell type inequalities. However, none of the Bell-type inequalities tested have shown any violation. We discuss our methodology to construct incompatible basis for documents from real world query log data, the experiments to test Bell inequalities on this dataset and possible reasons for the lack of violation
Looking at Vector Space and Language Models for IR using Density Matrices
In this work, we conduct a joint analysis of both Vector Space and Language
Models for IR using the mathematical framework of Quantum Theory. We shed light
on how both models allocate the space of density matrices. A density matrix is
shown to be a general representational tool capable of leveraging capabilities
of both VSM and LM representations thus paving the way for a new generation of
retrieval models. We analyze the possible implications suggested by our
findings.Comment: In Proceedings of Quantum Interaction 201
Raman quantum memory based on an ensemble of nitrogen-vacancy centers coupled to a microcavity
We propose a scheme to realize optical quantum memories in an ensemble of
nitrogen-vacancy centers in diamond that are coupled to a micro-cavity. The
scheme is based on off-resonant Raman coupling, which allows one to circumvent
optical inhomogeneous broadening and store optical photons in the electronic
spin coherence. This approach promises a storage time of order one second and a
time-bandwidth product of order 10. We include all possible optical
transitions in a 9-level configuration, numerically evaluate the efficiencies
and discuss the requirements for achieving high efficiency and fidelity
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
Structured random measurements in signal processing
Compressed sensing and its extensions have recently triggered interest in
randomized signal acquisition. A key finding is that random measurements
provide sparse signal reconstruction guarantees for efficient and stable
algorithms with a minimal number of samples. While this was first shown for
(unstructured) Gaussian random measurement matrices, applications require
certain structure of the measurements leading to structured random measurement
matrices. Near optimal recovery guarantees for such structured measurements
have been developed over the past years in a variety of contexts. This article
surveys the theory in three scenarios: compressed sensing (sparse recovery),
low rank matrix recovery, and phaseless estimation. The random measurement
matrices to be considered include random partial Fourier matrices, partial
random circulant matrices (subsampled convolutions), matrix completion, and
phase estimation from magnitudes of Fourier type measurements. The article
concludes with a brief discussion of the mathematical techniques for the
analysis of such structured random measurements.Comment: 22 pages, 2 figure
The quantum probability ranking principle for information retrieval
While the Probability Ranking Principle for Information Retrieval provides the basis for formal models, it makes a very strong assumption regarding the dependence between documents. However, it has been observed that in real situations this assumption does not always hold. In this paper we propose a reformulation of the Probability Ranking Principle based on quantum theory. Quantum probability theory naturally includes interference effects between events. We posit that this interference captures the dependency between the judgement of document relevance. The outcome is a more sophisticated principle, the Quantum Probability Ranking Principle, that provides a more sensitive ranking which caters for interference/dependence between documents’ relevanc
Nambu-Goldstone Effective Theory of Information at Quantum Criticality
We establish a fundamental connection between quantum criticality of a
many-body system, such as Bose-Einstein condensates, and its capacity of
information-storage and processing. For deriving the effective theory of modes
in the vicinity of the quantum critical point we develop a new method by
mapping a Bose-Einstein condensate of -particles onto a sigma model with a
continuous global (pseudo)symmetry that mixes bosons of different momenta. The
Bogolyubov modes of the condensate are mapped onto the Goldstone modes of the
sigma model, which become gapless at the critical point. These gapless
Goldstone modes are the quantum carriers of information and entropy. Analyzing
their effective theory, we observe the information-processing properties
strikingly similar to the ones predicted by the black hole portrait. The energy
cost per qubit of information-storage vanishes in the large- limit and the
total information-storage capacity increases with either exponentially or
as a power law. The longevity of information-storage also increases with ,
whereas the scrambling time in the over-critical regime is controlled by the
Lyapunov exponent and scales logarithmically with . This connection reveals
that the origin of black hole information storage lies in the quantum
criticality of the graviton Bose-gas, and that much simpler systems that can be
manufactured in table-top experiments can exhibit very similar
information-processing dynamics.Comment: 25 pages, 6 figure
Improved Lower Bounds for Locally Decodable Codes and Private Information Retrieval
We prove new lower bounds for locally decodable codes and private information
retrieval. We show that a 2-query LDC encoding n-bit strings over an l-bit
alphabet, where the decoder only uses b bits of each queried position of the
codeword, needs code length m = exp(Omega(n/(2^b Sum_{i=0}^b {l choose i})))
Similarly, a 2-server PIR scheme with an n-bit database and t-bit queries,
where the user only needs b bits from each of the two l-bit answers, unknown to
the servers, satisfies t = Omega(n/(2^b Sum_{i=0}^b {l choose i})). This
implies that several known PIR schemes are close to optimal. Our results
generalize those of Goldreich et al. who proved roughly the same bounds for
linear LDCs and PIRs. Like earlier work by Kerenidis and de Wolf, our classical
lower bounds are proved using quantum computational techniques. In particular,
we give a tight analysis of how well a 2-input function can be computed from a
quantum superposition of both inputs.Comment: 12 pages LaTeX, To appear in ICALP '0
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