LESS THAN STANDARD SEPARATION BETWEEN 2 GA-TWIN ENGINE ACFT. PLT DEVIATION.

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WORKING APCH; DEP AND HDOF AT THE SIOUX FALLS ARPT; I EXPERIENCED AN OPERROR IN WHICH 2 SMT ACFT LOST SEP. SMT X WAS HANDED OFF FROM ZMP AT 11000'; MY CTL APPROX 40 MI W. ON INITIAL CONTACT WITH X I TOLD HIM TO DSND AT PLT'S DISCRETION AND MAINTAIN 4000'; TURN RIGHT HDG 120 DEGS FOR VECTORS TO THE VOR DME RWY 33 FINAL APCH COURSE. APPROX 4 MINS LATER X REQUESTED A CONTACT APCH; WHEN HE WAS APPROX 20 MI W. I TOLD HIM IT WOULD BE LESS DELAY TO BE VECTORED FOR THE APCH. APPROX 5 MINS LATER X RPTED THE ARPT IN SIGHT. I CLRED X FOR A VISUAL APCH TO RWY 33. IMMEDIATELY FOLLOWING THAT ACFT Y RPTED THE ARPT IN SIGHT. I TOLD HIM TO 'CONTINUE PRESENT HDG; YOU'RE FOLLOWING AN SMT AT 12 O'CLOCK AND 6 MI; EBND AT 3400.' APPROX 2 MINS LATER I OBSERVED X TRACK TO BE NBOUND TOWARD ACFT Y AND NOT TOWARD THE ARPT. I ISSUED A TURN TO Y TO THE SW AND ISSUED TFC AS SMT X; 12 O'CLOCK; 4 MI DSNDING OUT OF 3100'; THEN ISSUED A TURN FARTHER TO THE SW TO Y. BECAUSE OF X'S TURN TO THE N; SEP DECREASED TO APPROX 2 MI LAT AND 700' VERT. I BELIEVE THAT X DID NOT ACTUALLY HAVE THE ARPT IN SIGHT AND TURNED TO FOLLOW THE INTERSTATE TO THE ARPT CAUSING THIS ERROR. THE ACFT DID NOT MAKE A NORMAL TRACK TO THE ARPT/RWY. DURING THIS ENTIRE PERIOD; OUR RADAR MAP WAS FADING IN AND OUT; CAUSING SOME CONFUSION AND PROBS VECTORING FOR THE APCH.