Controlled bidirectional quantum secure direct communication with hyperentangled Bell states

Abstract This paper presents a groundbreaking protocol for controlled bidirectional quantum secure direct communication based on hyperentangled Bell states, involving two longitudinal momentum and polarization degrees of freedom. In this protocol, the controller Charlie governs bidirectional communication between two legitimate participants. Participants encode their secret messages using 64 unitary operations. However, without Charlie’s permission, specifically without publishing the final measurement results, participants cannot exchange secret messages. Security analysis are conducted to prevent eavesdropper Eve from obtaining users’ secret messages through illegitimate means. Compared with previously proposed controlled bidirectional quantum secure direct communication, the proposed protocol significantly improves transmission efficiency because each pair of photons can transmit 12 bits of classical information. The protocol achieves a remarkable qubit efficiency, reaching up to 85.7%. However, when we don’t take into account the number of qubits consumed by the decoy particles, we can theoretically achieve an efficiency of 200%.