Ablaberdyeva studied at the Moscow Conservatoire under Nina Dorliak.
She also toured the USSR, Czech Republic, Hungary, Cuba, Sweden, and France during this time.
Ablaberdyeva has made several recordings including Stravinsky's Les Noces, several cantatas by Giovanni Battista Pergolesi and Antonio Vivaldi, art songs by various Russian composers, and numerous works by J.S.
Bach, Henry Purcell and George Frideric Handel, mostly on the Melodiya label.
A CD of songs by Tchaikovsky was made at All Saints Church, Tudely, Kent, UK.