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The overlap measurement scheme accomplishes to evaluate the overlap of twoinput quantum states by only measuring an introduced auxiliary qubit,irrespective of the complexity of the two input states. We find acounterintuitive phenomenon that no quantum dissonance can be found, eventhough the auxiliary qubit might be entangled, classically correlated or evenuncorrelated with the two input states based on different types of inputstates. In principle, this provides an opposite but supplementary example tothe remarkable algorithm of the deterministic quantum computation with onequbit in which no entanglement is present. Finally, we consider a simpleoverlap measurement model to demonstrate the continuous change (includingpotential sudden death of quantum discord) with the input states from entangledto product states by only adjusting some simple initial parameters.

Quantum Dissonance Is Rejected in an Overlap Measurement Scheme