According to this post on the Asahi Shimbun, the Ministry of Affairs and Communications (MIC) has a proposal to run an experiment later this year, across the country using 2,000 cellphone volunteers, to record potential encounters between people infected with a contagious disease. From what we can tell, the proposed trial will track and collect GPS data for time and location so if someone is found later to be infected the agency, with some help from the telecom operators, would be able to identify and notify people who had may have had recent contact.
While theoretically this sounds at least possible, we can imagine the privacy issues that would be raised if it were to approach actual commercialization. Must be slow news day Golden Week in Japan!
Update: Then again maybe folks could just check with this handy online tool instead.. 
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