Quantum Secure Direct Communication with Private Dense Coding Using a General Preshared Quantum State

We study quantum secure direct communication by using a general preshared state and generalization of dense coding. In this scenario, Alice is allowed to apply unitary on the encode her message, set unitaries forms group. To decode Bob measurement across his own system he receives. worst we guarantee that Eve obtains no information for message even when access joint between she intercepts original state. For practical application, propose concrete protocol derive an upper bound leakage in finite-length setting. also discuss how our scenario case with discrete Weyl-Heisenberg representation unknown.