Geometric and Quantum Methods for Information Retrieval by Yaoyong Li and Hamish Cunningham.
Abstract:
This paper reviews the recent developments in applying geometric and quantum mechanics methods for information retrieval and natural language processing. It discusses the interesting analogies between components of information retrieval and quantum mechanics. It then describes some quantum mechanics phenomena found in the conventional data analysis and in the psychological experiments for word association. It also presents the applications of the concepts and methods in quantum mechanics such as quantum logic and tensor product to document retrieval and meaning of composite words, respectively. The purpose of the paper is to give the state of the art on and to draw attention of the IR community to the geometric and quantum methods and their potential applications in IR and NLP.
More complex models can (may?) lead to better IR methods, but:
Moreover, as Hilbert space is the mathematical foundation for quantum mechanics (QM), basing IR on Hilbert space creates an analogy between IR and QM and may usefully bring some concepts and methods from QM into IR. (p.24)
is a dubious claim at best.
The “analogy” between QM and IR makes the point:
QM IR a quantum system a collection of object for retrieval complex Hilbert space information space state vector objects in collection observable query measurement search eigenvalues relevant or not for one object probability of getting one eigenvalue relevance degree of object to query
The authors are comparing apples and oranges. For example, “complex Hilbert space” and “information space.”
A “complex Hilbert space” is a model that has been found useful with another model, one called quantum mechanics.
An “information space,” on the other hand, encompasses models known to use “complex Hilbert spaces” and more. Depends on the information space of interest.
Or the notion of “observable” being paired with “query.”
Complex Hilbert spaces may be quite useful for IR, but tying IR to quantum mechanics isn’t required to make use of it.