LESS THAN STANDARD SEPARATON AND NMAC BETWEEN COMMUTER AND SMA ACFT. OPERATIONAL ERROR.

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UPON REACHING MADISON VOR WE REQUESTED CLRNC DIRECT TO PVD AND WERE ADVISED BY BOS CENTER THAT QUONSET WOULD ISSUE THAT CLRNC. WE CONTACTED QUONSET TRACON ON 133.85; REQUESTED AND WERE GRANTED 'DIRECT PVD.' AS OUR POS WAS SOMEWHAT S AND W OF THE ARPT; AND THE LNDG RWYS WERE 23L/23R; WE WERE GIVEN A VECTOR ON A 050 DEG HDG AND TOLD TO DSND TO 5000'; AT WHICH TIME ALL LNDG LIGHTS WERE ILLUMINATED. WE WERE THEN CLRED TO 2500'. UPON REACHING THE SITUATE RESERVOIR; APPROX 7 MI W OF THE ARPT; WE WERE TURNED OVER TO ANOTHER QUONSET CTLR ON 124.5. WE ADVISED THE CTLR THAT WE HAD THE ARPT IN SIGHT. HE TOLD US WE WERE CLRED FOR THE VISUAL TO RWY 23L AND TO STAY WITH HIM. AT THIS TIME; WE WERE ADVISED THAT THERE WAS TFC 2 MI N OF THE ARPT AT 1800'. NO FURTHER INFO ABOUT THIS ACFT WAS GIVEN. WE PROCEEDED INBND TO THE ARPT ON APPROX A 070 DEG HDG. AT THIS POINT WE WERE APPROX 1-2 NM W OF THE ARPT AND WERE UNABLE TO CONTACT THE CTLR WHO WAS TALKING TO ANOTHER ACFT. AT A POINT APPROX 2 MI N OF THE ARPT; AND ON APPROX A 075 DEG HDG; WE SAW SMA Y; APPARENTLY A TFC RPTR. AT THE TIME I SAW ACFT Y HE WAS AT OUR 12 O'CLOCK POS AND LESS THAN 1 MI; AT THE SAME ALT; OPP DIRECTION. WE ALTERED COURSE TO THE LEFT AND PASSED BY THE ACFT. AS SOON AS THIS HAD OCCURRED; QUONSET ADVISED US TO CONTACT PVD TWR FOR LNDG CLRNC. NO MENTION ABOUT ACFT Y. WHEN WE CAME UP ON THE TWR FREQ; 120.70; THE PLT OF Y WAS TALKING TO THE TWR ABOUT US. WE CALLED THE TWR; ADVISED THAT WE HAD JUST BEEN TURNED OVER TO HIM BY QUONSET. WE WERE CLRED TO LAND. AFTER LNDG; I CALLED BOTH PVD TWR AND QUONSET TRACON. THE TWR PERSONNEL SEEMED RATHER PUT OUT THAT QUONSET HAD NOT TURNED OUR FLT OVER TO THE TWR EARLIER. AT QUONSET TRACON I SPOKE TO THE WATCH SUPVR AND WAS ADVISED THAT A TRNEE HAD BEEN ON THE POS AND HAD BEEN RELIEVED SHORTLY AFTER THE INCIDENT.