Recently-crowned US Open champion Novak Djokovic's decision to opt out of the playoffs along with world number 33 Filip Krajinovic has raised hopes of an equal contest between the two teams.
Bhambri, who is world No 96 lost 3-6 6-7 (3-7) 5-7 to Frenchman Herbert in a match that lasted nearly two and half hours.
The Indian, ranked 85, lost his first round 6-2 3-6 3-6 2-6 in two hour and 38 minutes to the Italian.
AITA had exempted the country's top singles player Yuki considering that playing at the Grand Slams is crucial to secure ranking points, which would earn him a direct entry into the Tokyo Olympics.
Sanjita, who won a gold in women's 53kg class in the Gold Coast CWG in April, had tested positive for an anabolic steroid in a test conducted during the World Championships in USA in November last year.
Leander Paes returned to the Indian team for the Asian Games while the country's top player Yuki Bhambri was exempted as the AITA announced a 12-member squad.
Yuki, ranked 93, has told AITA that if he gets direct entry into the last Grand Slam of the season, he won't be available.
In the round of 32, which lasted around an hour and 17 minutes, the Indian pair were outplayed in straight sets 5-7, 3-6.
Bhambri and Sharan, who had also teamed up at the inaugural Maharashtra Open, sent Raja and Martin packing with a 6-3, 5-7 and 6-4 win in the opening round of the Roland Garros.
Bopanna and his French partner Roger-Vasselin began their Roland Garros campaign with a comfortable win over the American team of Taylor Fritz and Frances Tiafoe.
Rohan Bopanna began his men's doubles campaign with an easy win along with French partner Edouard Roger-Vasselin in Paris on Tuesday.
Yuki earned 125 ranking points and a prize purse of USD 21,600 while Ramkumar got 75 points and USD 12,720 for his effort.
India will face China in the Asia/Oceania Group 1 second round at Tianjin, China on April 6-7.
Yuki will now meet world No 11 and eighth-seeded American Jack Sock in the second round of the tournament, having come through the qualifying round.
In his second and final ATP Miami Masters qualifying match, the 25-year-old eased past Ymer 7-5, 6-2 in a one-sided clash that lasted almost one and a half hour.
Yuki, who qualified for the Indian Wells Masters and went on to scalp world number 12 Lucas Puille, dispatched Argentina's Olivo 6-4 6-1 in the opening round of the USD 7,972,535 hard court event.
It has been a great tournament for Bhambri, who knocked out players of the calibre of two-time doubles Grand Slam winner Nicolas Mahut and world number 12 Lucas Pouille en route the third round.
In a stunning performance, the 110th ranked Yuki, who qualified for the main draw, dispatched the ninth seed Frenchman 6-4 6-4 in one hour and 19 minutes.
In his opening round in the main draw, Yuki will fight it out with fellow qualifier Nicolas Mahut, ranked 101, and if he manages to cross the first hurdle he will be up against world number 12 Lucas Pouille.
Yuki, seeded ninth, edged past America's Dennis Novikov 7-5, 7-5 while Ramkumar defeated Michael Mmoh 6-3, 7-5 in his first-round match in the qualifiers on Wednesday.
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