A final requires just 2 teams
A semifinal requires 4 teams (the 2 wining trams make it to the final)
A quarter final must deliver 4 teams to compete in the semi final and thus there need to be 8 teams competing - no more, no less.
This is true for ALL "finals" of two team sports, no matter how large the competition.
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There are a total of 8 teams, singles or pairs at the quarter-finals of a tournament.