Concierge is Key Witness in Kim Kardashian Robbery

The concierge who was taken up Kim Kardashian's private elevator and opened the door to a $10 million jewelry heist has become the critical witness ... sources connected to the case tell TMZ.

We're told Kim has downloaded Paris cops about her interactions with the concierge. We've learned on Tuesday Kim had an extensive interview with cops by phone and told them the following:

-- The concierge was handcuffed when he opened the door to her apartment.

-- As she put it, "He opened the door and led them [the robbers] up and was in there the whole time."

-- Kim told police she engaged the concierge in conversation, saying, "Are we gonna die?" He calmly responded, "I don't know."

-- Kim, we're told, made a point to cops that the concierge was extremely calm, despite being cuffed and held at gunpoint.

-- Kardashian says when the robbers left the apartment they took the concierge with them and deposited him in the lobby where his hands were still cuffed.