Creation of quantum coherence with general measurement processes

Quantum measurement not only can destroy coherence but also can create it. Here, we estimate the maximum amount of coherence, one can create under a complete non-selective measurement process. For our analysis, we consider projective as well as POVM measurements. Based on our observations, we characterize the measurement processes into two categories, namely, the measurements with the ability to induce coherence and the ones without this ability. Our findings also suggest that the more POVM elements present in a measurement that acts on the quantum system, the less will be its coherence creating ability. We also introduce the notion of raw coherence in the POVMs that helps to create quantum coherence. Finally, we find a trade-off relation between the coherence creation, entanglement generation between system and apparatus, and the mixedness of the system in a general measurement setup.

Automated summary

Quantum measurement can both destroy and create coherence. In this study, we determine the maximum amount of coherence that can be created under a complete non-selective measurement process. We categorize measurement processes into two types based on their ability to induce coherence. Our findings indicate that the presence of more POVM elements in a measurement reduces its coherence creating ability. We introduce the concept of raw coherence in POVMs to aid in the creation of quantum coherence. Additionally, we identify a trade-off relationship between coherence creation, generation of entanglement, and system mixedness in a general measurement setup.