Security analysis of ensemble-based quantum token protocol under advanced attacks

We present and characterize advanced attacks on an ensemble-based quantum token protocol that allows for implementing non-clonable quantum coins. Multiple differently initialized tokens of identically prepared qubit ensembles are combined to a quantum coin that can be issued by a bank. A sophisticated attempt to copy tokens can assume that measurements on sub-ensembles can be carried through and that even individual qubits can be measured. Even though such an advanced attack might be perceived as technically unfeasible, we prove the security of the protocol under these conditions. We performed numerical simulations and verified our results by experiments on the IBM quantum platforms for different types of advanced attacks. Finally, we demonstrate that the security of the quantum coin can be made high by increasing the number of tokens. This paper in conjunction with provided numerical simulation tools verified against experimental data from the IBM quantum platforms allows for securely implementing our ensemble-based quantum token protocol with arbitrary quantum systems.