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In this note we construct an explicit optimal (negative-weight) adversary matrix for the element distinctness problem, given that the size of the alphabet is sufficiently large.
Quantum cryptanalysis of hash and claw-free functions
G. Brassard, P. Høyer, and A. Tapp · 1998
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Quantum lower bounds by polynomials
R. Beals, H. Buhrman, R. Cleve, M. Mosca, and R. de Wolf · 2001
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Quantum lower bounds by quantum arguments
A. Ambainis · 2002
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Polynomial degree vs. quantum query complexity
A. Ambainis · 2003
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Quantum lower bounds for the collision and the element distinctness problems
S. Aaronson and Y. Shi · 2004
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Quantum lower bounds for collision and element distinctness with small range
A. Ambainis · 2005
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Quantum lower bound for the collision problem with small range
S. Kutin · 2005
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On the power of ambainis lower bounds
S. Zhang · 2005
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All quantum adversary methods are equivalent
R. Špalek and M. Szegedy · 2006
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Quantum walk algorithm for element distinctness
A. Ambainis · 2007
Later among the works it cites.
Negative weights make adversaries stronger
P. Høyer, T. Lee, and R. Špalek · 2007
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Quantum query complexity of the state conversion problem
T. Lee, R. Mittal, B. Reichardt, R. Špalek, and M. Szegedy · 2011
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Reflections for quantum query algorithms
B. Reichardt · 2011
Later among the works it cites.
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