Complementarity Relation for Coherence and Disturbance

Abstract

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.

7 pages, 3 figures

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• Uncertainty of quantum channels via modified generalized variance and modified generalized Wigner-Yanase-Dyson skew information
• Coherence and realism in the Aharonov-Bohm effect
• Measurement sharpness and disturbance tradeoff
• Quantum Coherence, Coherent Information and Information Gain in Quantum Measurement
• Experimental demonstration of complementarity relations between quantum steering criteria
• Uncertainty-disturbance relations and applications