Experimental mutual coherence from separable coherent qubits

Quantum coherence is a fundamental resource in modern quantum physics with important applications in quantum technologies. In composite quantum systems, various forms of coherence emerge and play an important role, such as the global coherence, coherence of local subsystems, and the recently introduced mutual coherence. We investigate states that maximize the mutual coherence in various subspaces of the overall two-qubit Hilbert space and discover a nontrivial asymmetric optimal state in the three-dimensional subspace. We experimentally generate this optimal state from two factorized photonic qubits by a strictly incoherent probabilistic quantum operation that projects the input state onto the desired three-dimensional subspace. For comparison, we also experimentally test the preparation of states with maximal mutual coherence by unitary transformations of input product states. These proof-of-principle tests demonstrate the initial steps of control of mutual quantum coherence in qubit systems.