  The coherent superposition of quantum states is an important resource for
quantum information processing which distinguishes quantum dynamics and
information from their classical counterparts. In this article we determine the
coherence requirements to communicate quantum information in a broad setting
encompassing monitored quantum dynamics and quantum error correction codes. We
determine these requirements by considering hybrid circuits that are generated
by a quantum information game played between two opponents, Alice and Eve, who
compete by applying unitaries and measurements on a fixed number of qubits.
Alice applies unitaries in an attempt to maintain quantum channel capacity,
while Eve applies measurements in an attempt to destroy it. By limiting the
coherence generating or destroying operations available to each opponent, we
determine Alice's coherence requirements. When Alice plays a random strategy
aimed at mimicking generic monitored quantum dynamics, we discover a
coherence-tuned phase transitions in entanglement and quantum channel capacity.
We then derive a theorem giving the minimum coherence required by Alice in any
successful strategy, and conclude by proving that coherence sets an upper bound
on the code distance in any stabelizer quantum error correction codes. Such
bounds provide a rigorous quantification of the coherence resource requirements
for quantum communication and error correction.
