Quantum direct communication with authentication

We propose two quantum direct communication (QDC) protocols with user authentication. Users can identify each other by checking the correlation of Greenberger-Horne-Zeilinger (GHZ) states. Alice can directly send a secret message to Bob without any previously shared secret using the remaining GHZ states after authentication. Our second QDC protocol can be used even though there is no quantum link between Alice and Bob. The security of the transmitted message is guaranteed by properties of entanglement of GHZ states.

Figure 1

Procedures of authentication 0 (prerequisite). Alice and Bob register their secret identities and hash functions with Trent. (1) Trent generates GHZ states $\mid \Psi ⟩=(1∕\sqrt{2})({\mid 000⟩}_{ATB}+{\mid 111⟩}_{ATB})$. (2) Trent makes unitary operations on $\mid \Psi ⟩$ with Alice’s and Bob’s authentication keys. (3) Trent distributes GHZ particles to Alice and Bob. (4) Alice and Bob make reverse unitary operations on their qubits with their authentication keys. (5) Alice and Bob choose a subset of GHZ states, make local measurements in the $z$ basis on them, and compare the results.

Figure 2

Procedures of the first direct communication protocol (GHZ states were distributed as depicted in Fig. 1). (1) Alice chooses a subset of GHZ states and a random bit string. Alice performs unitary transformations both on the qubits selected for the check process following this random bit string and on the remaining qubits following the secret message. For example if the bit is 0, she makes a Hadamard operation $H$; otherwise a bit-flip operation and a Hadamard operation, $HX$. (2) Alice sends the qubits to Bob. (3) Bob makes Bell measurements on pairs of particles consisting of his qubit and Alice’s qubit. (4) Trent makes von Neumann measurements on his GHZ particles and reveals the results. (5) Alice and Bob compare the check bits.

Figure 3

Procedures of the second direct communication protocol (GHZ states were distributed as depicted in Fig. 1). (1) Alice chooses the position of check bits and a random bit string. Alice performs unitary transformations on the qubits selected for the check process following this random bit string and on the remaining qubits following the secret message. For example if the bit is 0, she makes a Hadamard operation $H$; otherwise a bit-flip operation and a Hadamard operation, $HX$. (2) Alice sends the encoded qubits to Trent. (3) Trent makes Bell measurements on pairs of particles consisting of his qubit and Alice’s qubit. (4) Trent reveals the measurement outcomes. (5) Bob makes von Neumann measurements on his GHZ particles. (6) Alice and Bob compare the check bits.