  One of the fundamental tasks in information theory is the compression of
information. To achieve this in the quantum domain, quantum autoencoders that
aim to compress quantum states to low-dimensional ones have been proposed. When
taking a pure state as the reference state, there exists an upper bound for the
encoding fidelity. This bound limits the compression rate for high-rank states
that have high entropy. To overcome the entropy inconsistency between the
initial states and the reconstructed states, we allow the reference state to be
a mixed state. A new cost function that combines the encoding fidelity and the
quantum mutual information is proposed for compressing general input states. In
particular, we consider the reference states to be a mixture of maximally mixed
states and pure states. To achieve efficient compression for different states,
two strategies for setting the ratio of mixedness (in the mixture of maximally
mixed states and pure states) are provided based on prior knowledge about
quantum states or observations obtained from the training process. Numerical
results on thermal states of the transverse-field Ising model, Werner states,
and maximally mixed states blended with pure states illustrate the
effectiveness of the proposed method. In addition, quantum autoencoders using
mixed reference states are experimentally implemented on IBM Quantum devices to
compress and reconstruct thermal states and Werner states.
