Quantum autoencoders using mixed reference states

One of the fundamental tasks in quantum information theory is quantum data compression, which can be realized via quantum autoencoders that first compress quantum states to low-dimensional ones and then recover to the original ones with a reference state. When taking a pure reference state, there exists an upper bound for the encoding fidelity, which limits the compression of states with high entropy. To overcome the entropy inconsistency, we allow the reference state to be a mixed state and propose a cost function that combines the encoding fidelity and the quantum mutual information. We consider the reference states to be a mixture of maximally mixed states and pure states and propose three strategies for setting the ratio of mixedness. Numerical simulations of different states and experimental implementations on IBM quantum devices illustrate the effectiveness of our approach.