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The area of property testing tries to design algorithms that can efficiently handle very large amounts of data: given a large object that either has a certain property or is somehow "far" from having that property, a tester should efficiently distinguish between these two cases.
Proposed experiment to test local hidden-variable theories
John F. Clauser, Michael A. Horne, Abner Shimony, and Richard A. Holt · 1969
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Stephen M. Barnett and Sarah Croke · 1970
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Linear transformations which preserve trace and positive semidefiniteness of operators
A. Jamiołkowski · 1972
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Bounds for the quantity of information transmitted by a quantum communication channel
Alexander S. Holevo · 1973
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Completely positive linear maps on complex matrices
Man-Duen Choi · 1975
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Quantum detection and estimation theory
Carl W. Helstrom · 1976
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Probabilistic computations: Toward a unified measure of complexity
Andrew C-C. Yao · 1977
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Some complexity questions related to distributive computing
Andrew C-C. Yao · 1979
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Quantum generalizations of Bell’s inequality
Boris S. Cirel’son · 1980
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The Theory of Error-Correcting Codes
F. J. MacWilliams and N. J. A. Sloane · 1983
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Maximal violation of Bell’s inequalities is generic in quantum field theory
Stephen J. Summers and Reinhard Werner · 1987
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Daniel M. Greenberger, Michael A. Horne, and Anton Zeilinger · 1989
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Matthew McKague · 1989
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Non-deterministic exponential time has two-prover interactive protocols
László Babai, Lance Fortnow, and Carsten Lund · 1991
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Maximal violation of Bell inequalities for mixed states
Samuel L. Braunstein, Ady Mann, and Michael Revzen · 1992
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The probabilistic communication complexity of set intersection
Bala Kalyanasundaram and Georg Schnitger · 1992
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Which states violate Bell’s inequality maximally?
Sandu Popescu and Daniel Rohrlich · 1992
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On the distributional complexity of disjointness
Alexander A. Razborov · 1992
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Self-testing/correcting with applications to numerical problems
Manuel Blum, Michael Luby, and Ronitt Rubinfeld · 1993
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Some results and problems on quantum Bell-type inequalities
Boris S. Tsirelson · 1993
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Linearity testing in characteristic two
Mihir Bellare, Don Coppersmith, Johan Håstad, Marcos Kiwi, and Madhu Sudan · 1996
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A fast quantum mechanical algorithm for database search
Lov K. Grover · 1996
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Stabilization of quantum computations by symmetrisation
Adriano Barenco, André Berthiaume, David Deutsch, Artur Ekert, Richard Jozsa, and Chiara Macchiavello · 1997
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Quantum computation of Fourier transforms over symmetric groups
Robert Beals · 1997
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Strengths and weaknesses of quantum computing
Charles H. Bennett, Ethan Bernstein, Gilles Brassard, and Umesh Vazirani · 1997
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Quantum complexity theory
Ethan Bernstein and Umesh Vazirani · 1997
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An exact quantum polynomial-time algorithm for Simon’s problem
Gilles Brassard and Peter Høyer · 1997
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Communication Complexity
Eyal Kushilevitz and Noam Nisan · 1997
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Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer
Peter W. Shor · 1997
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On the power of quantum computation
Daniel R. Simon · 1997
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Proof verification and the hardness of approximation problems
Sanjeev Arora, Carsten Lund, Rajeev Motwani, Madhu Sudan, and Mario Szegedy · 1998
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Property testing and its connection to learning and approximation
Oded Goldreich, Shafi Goldwasser, and Dana Ron · 1998
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Quantum cryptography with imperfect apparatus
Dominic Mayers and Andrew C-C. Yao · 1998
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Optimal state estimation for
Dagmar Bruß and Chiara Macchiavello · 1999
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Stabilizer Codes and Quantum Error Correction
Daniel Gottesman · 1999
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Coding theorem and strong converse for quantum channels
Andreas Winter · 1999
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On testing expansion in bounded-degree graphs
Oded Goldreich and Dana Ron · 2000
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An improved quantum Fourier transform algorithm and applications
Lisa Hales and Sean Hallgren · 2000
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Parallelization, amplification, and exponential time simulation of quantum interactive proof systems
Alexei Kitaev and John Watrous · 2000
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Continuity bounds for entanglement
Michael A. Nielsen · 2000
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Quantum Computation and Quantum Information
Michael A. Nielsen and Isaac L. Chuang · 2000
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Statistical distinguishability between unitary operations
Antonio Acín · 2001
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Testing random variables for independence and identity
Tuǧkan Batu, Lance Fortnow, Eldar Fischer, Ravi Kumar, Ronitt Rubinfeld, and Patrick White · 2001
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Quantum lower bounds by polynomials
Robert Beals, Harry Buhrman, Richard Cleve, Michele Mosca, and Ronald de Wolf · 2001
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Quantum fingerprinting
Harry Buhrman, Richard Cleve, John Watrous, and Ronald de Wolf · 2001
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Quantum state discrimination
Anthony Chefles · 2001
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The art of uninformed decisions
Eldar Fischer · 2001
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Estimating the spectrum of a density operator
M. Keyl and R. F. Werner · 2001
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Quantum lower bounds by quantum arguments
Andris Ambainis · 2002
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Quantum amplitude amplification and estimation
Gilles Brassard, Peter Høyer, Michele Mosca, and Alain Tapp · 2002
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Complexity measures and decision tree complexity: A survey
Harry Buhrman and Ronald de Wolf · 2002
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Property testing in bounded degree graphs
Oded Goldreich and Dana Ron · 2002
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The Quantum Fourier Transform and Extensions of the Abelian Hidden Subgroup Problem
Lisa Hales · 2002
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Classical and Quantum Computation
A. Yu. Kitaev, A. H. Shen, and M. N. Vyalyi · 2002
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A new proof of the channel coding theorem via hypothesis testing in quantum information theory
Tomohiro Ogawa and Hiroshi Nagaoka · 2002
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Classical deterministic complexity of Edmonds’ problem and quantum entanglement
Leonid Gurvits · 2003
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Property testing of data dimensionality
Robert Krauthgamer and Ori Sasson · 2003
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Measurement-based quantum computation with cluster states
Robert Raussendorf, Dan Browne, and Hans Briegel · 2003
Cited alongside, same era.
Quantum lower bounds for the collision and the element distinctness problems
Scott Aaronson and Yaoyun Shi · 2004
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Measuring polynomial functions of states
Todd A. Brun · 2004
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A lower bound for testing juntas
Hana Chockler and Dan Gutfreund · 2004
Cited alongside, same era.
All entangled states are useful for channel discrimination
Marco Piani and John Watrous · 2009
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Ben W. Reichardt · 2009
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BQP and the Polynomial Hierarchy
Scott Aaronson · 2010
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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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Eldar Fischer, Guy Kindler, Dana Ron, Samuel Safra, and Alex Samorodnitsky · 2004
Cited alongside, same era.
Self testing quantum apparatus
Dominic Mayers and Andrew C-C. Yao · 2004
Cited alongside, same era.
Quantum State Estimation
Matteo Paris and Jaroslav Řeháček, editors · 2004
Cited alongside, same era.
Testing Reed-Muller codes
Noga Alon, Tali Kaufman, Michael Krivelevich, Simon Litsyn, and Dana Ron · 2005
Cited alongside, same era.
No signaling and quantum key distribution
Jonathan Barrett, Lucien Hardy, and Adrian Kent · 2005
Cited alongside, same era.
Efficient testing of groups
Katalin Friedl, Gábor Ivanyos, and Miklos Santha · 2005
Cited alongside, same era.
Marcus Cramer, Martin B. Plenio, Steven T. Flammia, Rolando Somma, David Gross, Stephen D. Bartlett, Olivier Landon-Cardinal, David Poulin, and Yi-Kai Liu · 2010
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Strong NP-hardness of the quantum separability problem
Sevag Gharibian · 2010
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Almost commuting matrices with respect to normalized Hilbert-Schmidt norm, 2010
Lev Glebsky · 2010
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Property Testing: Current Research and Surveys
Oded Goldreich, editor · 2010
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Quantum state tomography via compressed sensing
David Gross, Yi-Kai Liu, Steven T. Flammia, Stephen Becker, and Jens Eisert · 2010
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Ashley Montanaro and Tobias Osborne · 2010
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Computational distinguishability of degradable and antidegradable channels
William Rosgen · 2010
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Quantum property testing for bounded-degree graphs
Andris Ambainis, Andrew M. Childs, and Yi-Kai Liu · 2011
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Quantum algorithms for testing properties of distributions
Sergey Bravyi, Aram W. Harrow, and Avinatan Hassidim · 2011
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Direct fidelity estimation from few Pauli measurements
Steven T. Flammia and Yi-Kai Liu · 2011
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Quantum tests for the linearity and permutation invariance of Boolean functions
Mark Hillery and Erika Andersson · 2011
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Quantum property testing of group solvability
Yoshifumi Inui and Francois Le Gall · 2011
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Rahul Jain, Zhengfeng Ji, Sarvagya Upadhyay, and John Watrous · 2011
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Quantum interpolation of polynomials
Daniel M. Kane and Samuel A. Kutin · 2011
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Testing periodicity
Oded Lachish and Ilan Newman · 2011
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Quantum query complexity of state conversion
Troy Lee, Rajan Mittal, Ben W. Reichardt, Robert Špalek, and Mario Szegedy · 2011
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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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Testing symmetric properties of distributions
Paul Valiant · 2011
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Property testing of unitary operators
Guoming Wang · 2011
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Property testing lower bounds via communication complexity
Eric Blais, Joshua Brody, and Kevin Matulef · 2012
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Sparse and lopsided set disjointness via information theory
Anirban Dasgupta, Ravi Kumar, and D. Sivakumar · 2012
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Quantum tomography via compressed sensing: Error bounds, sample complexity, and efficient estimators
Steven T. Flammia, David Gross, Yi-Kai Liu, and Jens Eisert · 2012
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A multi-prover interactive proof for NEXP sound against entangled provers
Tsuyoshi Ito and Thomas Vidick · 2012
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Robust self-testing of the singlet
Matthew McKague, Tzyh Haur Yang, and Valerio Scarani · 2012
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Certifiable quantum dice: or, true random number generation secure against quantum adversaries
Umesh Vazirani and Thomas Vidick · 2012
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Property testing of quantum measurements, 2012
Guoming Wang · 2012
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Dorit Aharonov, Itai Arad, and Thomas Vidick · 2013
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Testing closeness of discrete distributions
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Improved quantum test for linearity of a Boolean function, 2013
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Property testing for cyclic groups and beyond
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