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A fundamental problem in statistics and learning theory is to test properties of distributions.
A mathematical theory of communication
Claude E. Shannon · 1948
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On measures of entropy and information
Alfréd Rényi · 1961
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Quantum computation and quantum information
Michael A. Nielsen and Isaac L. Chuang · 2000
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Testing random variables for independence and identity
Tuğkan Batu, Eldar Fischer, Lance Fortnow, Ravi Kumar, Ronitt Rubinfeld, and Patrick White · 2001
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Quantum fingerprinting
Harry Buhrman, Richard Cleve, John Watrous, and Ronald de Wolf · 2001
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Quantum amplitude amplification and estimation
Gilles Brassard, Peter Høyer, Michele Mosca, and Alain Tapp · 2002
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Estimation of entropy and mutual information
Liam Paninski · 2003
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Estimating entropy on m bins given fewer than m samples
Liam Paninski · 2004
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The complexity of approximating the entropy
Tuğkan Batu, Sanjoy Dasgupta, Ravi Kumar, and Ronitt Rubinfeld · 2005
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A coincidence-based test for uniformity given very sparsely sampled discrete data
Liam Paninski · 2008
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New results on quantum property testing
Sourav Chakraborty, Eldar Fischer, Arie Matsliah, and Ronald de Wolf · 2010
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Quantum algorithms for testing properties of distributions
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Testing closeness of discrete distributions
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Optimal algorithms for testing closeness of discrete distributions
Siu-On Chan, Ilias Diakonikolas, Gregory Valiant, and Paul Valiant · 2014
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Minimax estimation of functionals of discrete distributions
Jiantao Jiao, Kartik Venkat, Yanjun Han, and Tsachy Weissman · 2015
Optimal quantum sample complexity of learning algorithms
Srinivasan Arunachalam and Ronald de Wolf · 2017
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Costin Bădescu, Ryan O’Donnell, and John Wright · 2017
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Introduction to property testing
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Efficient quantum tomography II
Ryan O’Donnell and John Wright · 2017
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Two new results about quantum exact learnings
Srinivasan Arunachalam, Sourav Chakraborty, Troy Lee, and Ronald de Wolf · 2018
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A new approach for testing properties of discrete distributions
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Hamiltonian simulation by qubitization
Guang Hao Low and Isaac L. Chuang · 2016
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Ryan O’Donnell and John Wright · 2016
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Minimax rates of entropy estimation on large alphabets via best polynomial approximation
Yihong Wu and Pengkun Yang · 2016
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A unified maximum likelihood approach for estimating symmetric properties of discrete distributions
Jayadev Acharya, Hirakendu Das, Alon Orlitsky, and Ananda Theertha Suresh
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The polynomial method strikes back: Tight quantum query bounds via dual polynomials
Mark Bun, Robin Kothari, and Justin Thaler · 2018
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Shantanav Chakraborty, András Gilyén, and Stacey Jeffery · 2018
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András Gilyén, Yuan Su, Guang Hao Low, and Nathan Wiebe · 2018
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Quantum query complexity of entropy estimation
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A note on the quantum query complexity of permutation symmetric functions
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A Survey of Quantum Property Testing
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