Train EB applied when departing BSD TB3.Alarm in ATS showed "CBTC applied EB due to train moved wit hout authorization" and " Train door 0 status lost while tra in is moving". TC confirmed EB applied due to cab door at 'B ~~~~~ 3724 Train EB applied when departing BSD TB3. Alarm in ATS showed "CBTC applied EB due to train moved without authorization" and " Train door 0 status lost while train is moving". TC confirmed EB applied due to 'B' side cab door opened by itself when departing BSD TB3. TC assisted to close cab door and reset EB - ok. Train continued in AM to the next station.  3724 B/S cab door found having free play. Readjusted the double lock latch. Resecured the locking mechanism. Security/Function check - OK.  Kana 44154