Why was not a peace treaty signed between the USSR and Japan?

The quarrel over the Kuril Islands, the territory of Japan annexed by the USSR in 1945, spoiled relations between the USSR and Japan. Tokyo says it is ready to sign a peace treaty in exchange for surrendering two of the four disputed islands.
In February 1946, Moscow declares that the Kuriles are currently part of the territory of the Soviet Union. The population of the island was deported to Kazakhstan. Tokyo authorities continued to condition the signing of the peace treaty after the return of the southern Kuriles: Kunashir, Iturup, Shikotan and Habomai.
Both countries formalized the resumption of negotiations on the basis of an agreement between the USSR and Japan signed in 1956, but they never followed through.