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We consider entangled state production utilizing a full optomechanicalarrangement, based on which we create entanglement between two far three-levelV-type atoms using a quantum repeater protocol. At first, we consider eightidentical atoms (1; 2;...; 8), while adjacent pairs (i; i + 1) with i = 1; 3;5; 7 have been prepared in entangled states and the atoms 1, 8 are the twotarget atoms. The three-level atoms (1,2,3,4) and (5,6,7,8) distinctly becomeentangled with the system including optical and mechanical modes by performingthe interaction in optomechanical cavities between atoms (2,3) and (6,7),respectively. Then, by operating appropriate measurements, instead of Bellstate measurement which is a hard task in practical works, the entangled statesof atoms (1,4) and (5,8) are achieved. Next, via interacting atoms (4,5) of thepairs (1,4) and (5,8) and operating proper measurement, the entangled state oftarget atoms (1,8) is obtained. In the continuation, entropy and successprobability of the produced entangled state are then evaluated. It is observedthat the time period of entropy is increased by increasing the mechanicalfrequency and by decreasing optomechanical coupling strength to the fieldmodes. Also, in most cases, the maximum of success probability is increased bydecreasing G and via decreasing.

Distributed entangled state production by using quantum repeater protocol