Advanced Attacks On Qubit-Ensemble Based Quantum Coins

Abstract: We present and characterize an ensemble based quantum token protocol that allows for implementing non-clonable tokens containing ensembles of identically prepared qubits. Multiple differently initialized tokens with ensembles are realizing a quantum coin that can be issued by a bank. A sophisticated attempt to copy the token 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 proof the security of the ensemble based protocol under these conditions and provide detailed expressions on how the quantum coin must be designed to fulfill desired security requirements. We have used realistic parameters of the IBM Quantum Platforms and verified our numerical simulations with experimental data for advanced attacks using brute force optimization, direct inversion tomography, maximum likelihood and Bayesian method. Full message passing interface parallelized source code is provided to allow for adjusting to other hardware platforms. Interestingly, our results deviate from predictions provided by quantum state tomography. This can be attributed to the fact that an attacker's goal is not to get an optimal estimate of an unknown quantum state, but to mislead the bank into accepting the counterfeit quantum coin. Finnally, we prove that an arbitrary level of security can be obtained by adding an increasing amount of quantum tokens into a quantum coin.