TASHKENT, Uzbekistan—Step after tentative step, Uzbekistan—one of the world’s most closed societies—is beginning to open up.

The most-populous post-Soviet nation in Central Asia had become increasingly repressive during the quarter-century rule of former President Islam Karimov, who died a year ago. Freedom House, which ranks countries by political rights and civil liberties, has consistently put Uzbekistan among the planet’s five worst offenders, alongside North Korea.

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