Complementarity Relation for Coherence and Disturbance. (arXiv:1708.03090v1 [quant-ph])

Quantum measurements necessarily disturb the state of physical system. Once
we perform a complete measurement, the system undergoes decoherence and loses
its coherence. If there is no disturbance, the state retains all of its
coherence. It is therefore natural to ask if there is trade-off between
disturbance caused to a state and its coherence. We present a coherence
disturbance complementarity relation using the relative entropy of coherence.
For bipartite states we prove a complementarity relation between the quantum
coherence, entanglement and disturbance. Similar relation also holds for
quantum coherence, quantum discord and disturbance for a bipartite state. We
illustrate the trade-off between the coherence and the disturbance for single
qubit state for various quantum channels.

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