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According to Wikipedia:
“The main qualifying criteria were the ATP and WTA ranking lists published on 8 June 2020. The players entering were formally submitted by the International Tennis Federation. The ATP and WTA rankings were based on performances from the previous 52 weeks, and there were several tournaments in the two-month period between the time of the rankings being frozen for entry and the beginning of the tennis events at the Olympics. Players had to be part of a nominated team for three Fed Cup (women) or Davis Cup (men) events between the 2016 and 2020 Olympics. This requirement was reduced to two Fed/Davis Cup events during the Olympic cycle from 2016 to 2020 if their nation competed at the Zone Group round robin level for three of the four years or if the player had represented their nation at least twenty times. All players were required to have been part of a nominated team for a Fed/Davis Cup event in 2019 or 2020, and to have had a good standing with their National Olympic Committee.[1][2]
Each National Olympic Committee (NOC) could enter 6 male and 6 female athletes, with a maximum of 4 entries in the individual events, and 2 pairs in the doubles events.
For the singles competitions, the top 56 players in the world rankings on June 8, 2020 of the WTA and ATP tours are qualified for the Olympics. However, entry has been limited to four players from a country. This means that players who are ranked in the top 56 but represent the NOCs with four higher-ranked players already participating do not qualify, allowing players who are ranked outside of the top 56 but from countries with fewer than four players already qualified to compete. A player could only participate if he or she has made him- or herself available to be drafted to represent the player's country in Davis Cup or Fed Cup for two of the following years: 2017, 2018, 2019, and 2020, with one of the years being either 2019 or 2020. Six of the remaining eight slots will be allocated by continent: two in the 2019 Pan American Games, one in the 2018 Asian Games, one in the 2019 African Games, and one each for Europe and Oceania for the highest-ranked athlete from an NOC with no other qualifiers. The final two spots are reserved, one for the host nation and one for a previous Olympic gold medalist or Grand Slam champion.”
