A What is a 'Quantum Coherence'?

Summary
I'm unsure of what it means for a system or state to have various 'quantum coherences' which can be selected.
I have recently been reading some stuff on quantum information in the physics literature which refers to 'a mechanism by which a measurement in A determines quantum coherences in B', where A and B are subsystems of a larger system.

I am aware of the meaning of the terms 'decoherence' and 'coherent state', but could someone clarify for me what it means for a system to have several 'quantum coherences' which can be chosen from?

Also in a paper 'On the role of complex phases in the quantum statistics of weak measurements', I have seen the following quotation:
''As early as 1995, Steinberg pointed out that weak measurements provide a natural definition of conditional probabilities in quantum mechanics. However, the mathematically consistent definition of such weak conditional probabilities results in complex numbers originating from the quantum coherences of the initial and final states''.


Again, could someone explain what it means for the initial and final states to have 'quantum coherences'?
 
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The reference is the paper you mention https://arxiv.org/abs/1104.0062, the other quotation was from correspondence with someone working in the area so I cannot really reference it.
 

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