Bounds on Information Combining With Quantum Side Information

"Bounds on information combining" are entropic inequalities that determine how the information (entropy) of a set of random variables can change when these are combined in certain prescribed ways. Such bounds play an important role in classical information theory, particularly in coding and Shannon theory; entropy power inequalities are special instances of them. The arguably most elementary kind of information combining is the addition of two binary random variables (a CNOT gate), and the resulting quantities play an important role in Belief propagation and Polar coding. We investigate this problem in the setting where quantum side information is available, which has been recognized as a hard setting for entropy power inequalities. Our main technical result is a non-trivial, and close to optimal, lower bound on the combined entropy, which can be seen as an almost optimal "quantum Mrs. Gerber's Lemma". Our proof uses three main ingredients: (1) a new bound on the concavity of von Neumann entropy, which is tight in the regime of low pairwise state fidelities; (2) the quantitative improvement of strong subadditivity due to Fawzi-Renner, in which we manage to handle the minimization over recovery maps; (3) recent duality results on classical-quantum-channels due to Renes et al. We furthermore present conjectures on the optimal lower and upper bounds under quantum side information, supported by interesting analytical observations and strong numerical evidence. We finally apply our bounds to Polar coding for binary-input classical-quantum channels, and show the following three results: (A) Even non-stationary channels polarize under the polar transform. (B) The blocklength required to approach the symmetric capacity scales at most sub-exponentially in the gap to capacity. (C) Under the aforementioned lower bound conjecture, a blocklength polynomial in the gap suffices.Comment: 23 pages, 6 figures; v2: small correction

Combining relevance information in a synchronous collaborative information retrieval environment

Traditionally information retrieval (IR) research has focussed on a single user interaction modality, where a user searches to satisfy an information need. Recent advances in both web technologies, such as the sociable web of Web 2.0, and computer hardware, such as tabletop interface devices, have enabled multiple users to collaborate on many computer-related tasks. Due to these advances there is an increasing need to support two or more users searching together at the same time, in order to satisfy a shared information need, which we refer to as Synchronous Collaborative Information Retrieval. Synchronous Collaborative Information Retrieval (SCIR) represents a significant paradigmatic shift from traditional IR systems. In order to support an effective SCIR search, new techniques are required to coordinate users' activities. In this chapter we explore the effectiveness of a sharing of knowledge policy on a collaborating group. Sharing of knowledge refers to the process of passing relevance information across users, if one user finds items of relevance to the search task then the group should benefit in the form of improved ranked lists returned to each searcher. In order to evaluate the proposed techniques we simulate two users searching together through an incremental feedback system. The simulation assumes that users decide on an initial query with which to begin the collaborative search and proceed through the search by providing relevance judgments to the system and receiving a new ranked list. In order to populate these simulations we extract data from the interaction logs of various experimental IR systems from previous Text REtrieval Conference (TREC) workshops

Combining Supernovae and LSS Information with the CMB

Observations of the Cosmic Microwave Background (CMB), large scale structure (LSS) and standard candles such as Type 1a Supernovae (SN) each place different constraints on the values of cosmological parameters. We assume an inflationary Cold Dark Matter model with a cosmological constant, in which the initial density perturbations in the universe are adiabatic. We discuss the parameter degeneracies inherent in interpreting CMB or SN data, and derive their orthogonal nature. We then present our preliminary results of combining CMB and SN likelihood functions. The results of combining the CMB and IRAS 1.2 Jy survey information are given, with marginalised confidence regions in the H_0, Omega_m, b_IRAS and Q_rms-ps directions assuming n=1, Omega_Lambda+Omega_m=1 and Omega_b h^2=0.024. Finally we combine all three likelihood functions and find that the three data sets are consistent and suitably orthogonal, leading to tight constraints on H_0, Omega_m, b_IRAS and Q_rms-ps, given our assumptions.Comment: 7 pages, 4 figures, submitted to ``The CMB and the Planck Mission'', proceedings of the workshop held in Santander, Spain, June 199

Hybrid XML Retrieval: Combining Information Retrieval and a Native XML Database

This paper investigates the impact of three approaches to XML retrieval: using Zettair, a full-text information retrieval system; using eXist, a native XML database; and using a hybrid system that takes full article answers from Zettair and uses eXist to extract elements from those articles. For the content-only topics, we undertake a preliminary analysis of the INEX 2003 relevance assessments in order to identify the types of highly relevant document components. Further analysis identifies two complementary sub-cases of relevance assessments ("General" and "Specific") and two categories of topics ("Broad" and "Narrow"). We develop a novel retrieval module that for a content-only topic utilises the information from the resulting answer list of a native XML database and dynamically determines the preferable units of retrieval, which we call "Coherent Retrieval Elements". The results of our experiments show that -- when each of the three systems is evaluated against different retrieval scenarios (such as different cases of relevance assessments, different topic categories and different choices of evaluation metrics) -- the XML retrieval systems exhibit varying behaviour and the best performance can be reached for different values of the retrieval parameters. In the case of INEX 2003 relevance assessments for the content-only topics, our newly developed hybrid XML retrieval system is substantially more effective than either Zettair or eXist, and yields a robust and a very effective XML retrieval.Comment: Postprint version. The editor version can be accessed through the DO