The multidimensional transporter device is a device native to this universe that is capable of transporting a person from one universe into another.
In 2371, Miles 'Smiley' O'Brien used the device visit the mirror universe for an unknown purpose. It is possible he was seeking assistance for the Terran Rebellion from Captain Sisko of that universe. (TTLG)
In 2372, Jennifer Sisko also visited the mirror universe using another version of the device. She brought a device for Benjamin Sisko (mirror) to join her and Jake Sisko in this universe. It was programmed to only allow Sisko to use it. (SM)
In the mirror universe, Miles O'Brien somehow obtained schematics for this device which he gave to Rom to study. In 2375, Rom left a PADD out containing the schematics; Grand Nagus Zek found the PADD and duplicated the interdimensional transporting process. Zek then used the device, entering this universe in hopes of establishing commercial relations. Ezri Tigan used the device to cross over and recruit Quark (mirror) in a plan to rescue Zek. (TENC)