CPR HS1000 DEV ALT AFTER ARTCC CTLR MISSES INCORRECT READBACK ARRIVING PSP.

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I WAS ENRTE FROM SMF TO PSP. I WAS PIC OF ACFT. I WAS IN R SEAT. A JUNIOR CAPT WAS FLYING IN THE L SEAT. WE WERE IN A SLOW DSCNT FROM FL330. ATC WAS VERY BUSY. WE WERE GIVEN DSCNTS IN 1000 FT INCREMENTS IN A VERY RHYTHMIC FASHION JUST PRIOR TO LEVELING AT THE PRESCRIBED ALT. PRIOR TO LEVELING AT FL210. ATC GAVE US WHAT WE LATER FOUND OUT WAS A TFC RPT. 'TFC 10-11 O'CLOCK; 2 MI; FL200.' WE THOUGHT ATC TOLD US TO DSND AND MAINTAIN FL200. WE PROVIDED THE STANDARD READBACK; 'ROGER; DSND AND MAINTAIN FL200.' ATC DID NOT CATCH OUR MISTAKE; NOR DID WE. WE PROCEEDED PAST FL210 TO FL200. AFTER A FEW SECONDS OF QUIET; ATC ASKED US TO VERIFY OUR ALT OF FL210. I REPLIED; 'WAS CLRED TO FL200; BUT WE WILL RETURN TO FL210.' HE REPLIED (ATC); 'MAINTAIN FL210; TFC 10-11 O'CLOCK; B737; 2 MI.' WE WERE BACK AT FL210 BY THEN AND REPLIED; 'NO JOY; LEVEL FL210.' BOTTOM OF ALTDEV WAS FL203. AUTOPLT WAS ON THE WHOLE TIME EXCEPT FOR ALT CORRECTION. AS SOON AS WE REPLIED LEVEL FL210; ATC CLRED US TO 'DSND AND MAINTAIN FL200.' ONCE ON THE GND; PSP ATC ASKED US TO CALL ZLA. ZLA OPERATIONAL SUPVR SPOKE TO ME. INFORMED ME OF THE DETAILS OF THE TAPE. ACFT IN LOSS OF SEPARATION WAS LOST. AFTER REVIEWING TAPES; IT WAS CLR WE MISTOOK THE TFC RPT FOR ANOTHER 1000 FT DSCNT AND THE CTLR DID NOT CATCH THE FAULTY READBACK FROM ME. THE CTLR WAS IMMEDIATELY TAKEN OFF DUTY FOR 'RETRAINING.' MY FO AND I WERE ALSO TAKEN OFF FLT STATUS AND BROUGHT BACK TO HEADQUARTERS FOR DEBRIEFING AND POSSIBLE/CERTAIN RETRAINING. I FEEL BOTH PARTIES ARE VERY PROACTIVE IN REMEDYING THIS SIT.