Your definition of 'Private' is interesting.
Tokyo Metro is owned by... the national and local government.
Tokyo Metro is owned by... the national and local government.
From Wikipedia: [1]
The Japan Railways Group, more commonly known as JR Group (JRグループ Jeiāru Gurūpu), consists of seven for-profit companies that took over most of the assets and operations of the government-owned Japanese National Railways on April 1, 1987. Most of the liability of the JNR was assumed by the JNR Settlement Corporation.