Bidirectional Controlled Quantum Teleportation of Three-Qubit State by a New Entangled Eleven-Qubit State

Abstract

In this paper, an improved controlled bidirectional quantum teleportation protocol of the special three-qubit state is proposed. In a little bit more detail, under the control of the third supervisor Charlie, Alice wants to send one special three-qubit entangled state to Bob, and at the meantime, Bob also wants to transmit another special three-qubit entangled state to Alice. In other words, both Alice and Bob can be the sender and receiver simultaneously. To achieve this aim, a specific eleven-qubit entangled state is shared among Alice, Bob and Charlie in advance acting as the quantum channel. Then, Alice and Bob first implement the GHZ-state measurement and Bell-state measurement respectively, and following Charlie’s single-qubit measurement. Finally, upon the foregoing measurement results, Alice and Bob can respectively implement the specific unitary operators on their local particles to recover the initial state transmitted by the other.

Appendix

Table 1 The collapsed states of qubits {B₃, B₄, a₃, A₂, B₅, A₃, A₄, b₃, B₂, A₅, C} under Alice’s and Bob’s GHZ-state measurement results

Table 2 On the base of that Alice’s and Bob’s GHZ-state measurement result are ${\left|{\phi}^{+}\right\rangle}_{{\mathrm{a}}_1{\mathrm{a}}_2{\mathrm{A}}_1}$ and ${\left|{\gamma}^{+}\right\rangle}_{{\mathrm{b}}_1{\mathrm{b}}_2{\mathrm{B}}_1}$ of Step 1 in subsection 2.2, the collapsed states of qubits {B₃, B₄, B₅, A₃, A₄, A₅, C} correspond to Alice’s and Bob’s Bell-state measurement results of Step 2 in subsection 2.2

Table 3 On the base of that Alice’s and Bob’s GHZ-state measurement result are ${\left|{\phi}^{+}\right\rangle}_{{\mathrm{a}}_1{\mathrm{a}}_2{\mathrm{A}}_1}$ and ${\left|{\gamma}^{+}\right\rangle}_{{\mathrm{b}}_1{\mathrm{b}}_2{\mathrm{B}}_1}$ of Step 1 in subsection 2.2, the specific unitary transformation employed to transmit collapsed states of qubits {B₃, B₄, B₅, A₃, A₄, A₅} into the desired state shown in Eq. (16) correspond to Alice’s and Bob’s Bell-states measurement results, and Charlie’s single-qubit measurement results