Methods and systems for a 2-qubit multi-user quantum key distribution protocol

A method for an operator O to generate and distribute a multi-user shared key to a receiver A and to a receiver B, comprising:

• preparing pairs of entangled qubits in sequence, each pair of entangled qubits in a state of 2-qubit entanglement;
• sending from each pair of entangled qubits, one entangled qubit to a receiver A and the other entangled qubit to a receiver B;
• receiving a reply from each of receiver A and receiver B;
• sending the multi-user shared key to each of receiver A and receiver B, wherein sending the multi-user shared key to each of receiver A and receiver B comprises:
• sending to receiver A, a list of encoded bits from receiver B, for deriving a key according to receiver A's list of measured bits, and receiver A's list of encoded bits;
• sending to receiver B, a list of encoded bits from receiver A, for deriving a key according to receiver B's list of measured bits, and receiver B's list of encoded bits;
• receiving, through respective authenticated classical channels-receiver A's derived key and receiver B's derived key;
• and
• performing quantum correlation between receiver A's derived key and receiver B's derived key using an entanglement inequality, wherein deriving a key comprises rejecting pairs of bits that were not entangled according to the entanglement inequality;
• discarding a derived key and aborting communication, if entanglement between receiver A's derived key and receiver B's derived key is insufficient to ensure security.