Compressibility of Positive Semidefinite Factorizations and Quantum Models

We investigate compressibility of the dimension of positive semidefinite matrices, while approximately preserving their pairwise inner products. This can either be regarded as compression of positive semidefinite factorizations of nonnegative matrices or (if the matrices are subject to additional no...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 62; no. 5; pp. 2867 - 2880
Main Authors: Stark, Cyril J., Harrow, Aram W.
Format: Journal Article
Language:English
Published: New York IEEE 01.05.2016
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Communication
Communication systems
Complexity theory
Compression algorithms
Computational modeling
Data analysis
Data models
Information theory
Mathematical functions
Mathematical programming
Probability distribution
Quantum computing
Quantum mechanics
Quantum theory
Data analysis
Quantum mechanics
Compression algorithms
Mathematical programming
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Summary:We investigate compressibility of the dimension of positive semidefinite matrices, while approximately preserving their pairwise inner products. This can either be regarded as compression of positive semidefinite factorizations of nonnegative matrices or (if the matrices are subject to additional normalization constraints) as compression of quantum models. We derive both lower and upper bounds on compressibility. Applications are broad and range from the analysis of experimental data to bounding the one-way quantum communication complexity of Boolean functions.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2016.2538278