Complementarity Relation for Coherence and Disturbance

TL;DR

This paper establishes a fundamental trade-off relation between quantum coherence and disturbance caused by measurements, extending to bipartite states involving entanglement and discord, with illustrative examples on single qubits.

Contribution

It introduces a coherence disturbance complementarity relation using relative entropy of coherence, applicable to bipartite states and various quantum channels.

Findings

Derived a coherence disturbance complementarity relation.

Proved relations involving coherence, entanglement, and disturbance.

Illustrated trade-offs for single qubit states under different channels.

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.