Identifying And Modeling Quantum Entanglements In Quantum Language Models

Recently,quantum theory has a profound impact on multidisciplinary studies,such as Philosophy,Psychology,Cognition,Physics and Information Retrieval,and so on.In 2004,van Rijsbergen firstly stated that quantum theory can be regarded as a formal language that can be used for describing objects and processes in information retrieval.Following this pioneering work,quantum theory has a great effect on information retrieval.In 2013,quantum language model has been proposed to model term dependencies upon the quantum theory framework and successively applied in information retrieval.However,quantum language model's dependency is based on co-occurrence of terms and has not yet taken into account the quantum entanglement.Quantum entanglement which is a mysterious phenomenon is a core concept in quantum theory,and is also an important research direction in modern society.From the form of mathematics,a system is entangled if and only if the system's state cannot be decomposed into the tensor product of sub-systems' states.The entangled particles in EPR pair which seemed to be spooky action at a distance embody the non-locality and inseparability.Besides,quantum Entanglement has a significant cognitive implication.In cognitive filed,Pauli and Jung,the famous psychologist and philosopher,argued that the recognition of the unconscious state is akin to the quantum measurement on the entangled state.Importantly,an entangled state can provide a more complete description for the nature of realities,and determine intrinsic correlations of considered objects globally,rather than those co-occurrences on the surface.In this paper,we expected to identify and model the quantum entanglement in the quantum language model.It is,however,a real challenge to determine and measure the quantum entanglement using the classical statics of texts in a post-measurement configuration.In order to circumvent this problem,we theoretically prove the connection between quantum entanglement and statistically unconditional pure dependence.Since unconditional pure dependence has an implementable deciding algorithm,we can in turn characterize quantum entanglement by extracting the unconditional pure dependence patterns from texts.This leads to a measurable quantum entanglement,based on which we further advance the existing quantum language model framework.Finally,we empirically compare our model with the original quantum language model and the Markov random filed model based on the unconditional pure dependence,and the experimental results demonstrate the effectiveness and usefulness of our model.Specifically,we illuminate our work from the following key points:(1)compare the differences between the classical propositional logic system and the quantum theory framework,thus show the advantage of quantum theory framework;(2)explain the cognitive implications of quantum entanglement and the necessity of modeling quantum entanglements in information retrieval;(3)how to infer the occurrence of quantum entanglement in a post-measurement configuration;(4)apply the measureable quantum entanglement into the quantum language model framework and conduct experiments on the documents re-ranking task.