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There has been a surge of progress in recent years in developing algorithms for testing and learning quantum states that achieve optimal copy complexity.
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Barycentric decomposition of quantum measurements in finite dimensions
Giulio Chiribella, Giacomo Mauro D’Ariano, and Dirk Schlingemann · 2010
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Practical characterization of quantum devices without tomography
Marcus P da Silva, Olivier Landon-Cardinal, and David Poulin · 2011
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Sébastien Bubeck and Nicolo Cesa-Bianchi · 2012
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John Wright · 2016
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Roksana Baleshzar, Deeparnab Chakrabarty, Ramesh Krishnan S Pallavoor, Sofya Raskhodnikova, and C Seshadhri · 2017
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Clément L Canonne · 2017
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Xi Chen, Erik Waingarten, and Jinyu Xie · 2017
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Boolean unateness testing with O ~ ( n 3 / 4 ) \tilde{O}(n^{3/4}) adaptive queries
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Jayadev Acharya, Clément L Canonne, and Gautam Kamath · 2014
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Siu-On Chan, Ilias Diakonikolas, Paul Valiant, and Gregory Valiant · 2014
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Clément Canonne, Dana Ron, and Rocco A Servedio · 2014
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Ilias Diakonikolas, Daniel M Kane, and Vladimir Nikishkin · 2014
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Clément L Canonne, Dana Ron, and Rocco A Servedio · 2015
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Introduction to property testing
Oded Goldreich · 2017
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Sample-optimal tomography of quantum states
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Property testing of joint distributions using conditional samples
Rishiraj Bhattacharyya and Sourav Chakraborty · 2018
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Adaptive lower bound for testing monotonicity on the line
Aleksandrs Belovs · 2018
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Testing shape restrictions of discrete distributions
Clément L Canonne, Ilias Diakonikolas, Themis Gouleakis, and Ronitt Rubinfeld · 2018
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Measuring quantum entropy
Jayadev Acharya, Ibrahim Issa, Nirmal V Shende, and Aaron B Wagner · 2019
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