Abstract
In this work we investigate how to quantify the coherence of quantum measurements. First, we establish a resource theoretical framework to address the coherence of measurement and show that any statistical distance can be adopted to define a coherence monotone of measurement. For instance, the relative entropy fulfills all the required properties as a proper monotone. We specifically introduce a coherence monotone of measurement in terms of off-diagonal elements of positive-operator-valued measure components. This quantification provides a lower bound on the robustness of measurement-coherence that has an operational meaning as the maximal advantage over all incoherent measurements in state discrimination tasks. Finally, we propose an experimental scheme to assess our quantification of measurement-coherence and demonstrate it by performing an experiment using a single qubit on IBM Q processor.
Highlights
With the development of quantum technologies, it has been widely perceived that quantum physics can offer enormous advantages in operational tasks
We assume a pure probe state for analysis in Eq (17) (Eq (14) in the revised version), and importantly, this procedure will only underestimate the coherence of measurement, thereby providing a reliable lower bound for robustness, if the noise occurring is strictly incoherent operation (SIO): When we introduced the properties of our monotone of coherence, we proved that the SIO does not increase the coherence measure
A resource theory generally consists of two ingredients, free resources and free operations
Summary
With the development of quantum technologies, it has been widely perceived that quantum physics can offer enormous advantages in operational tasks. This led to extensive investigations of its role in computation [11, 12], thermodynamics [13, 14] and metrology [15, 16] It was studied how closely quantum coherence is related to other fundamental notions such as entanglement [17], correlations [18] and nonclassicality [19] The resource theoretical approach for coherent operations was employed in [33] It considered a quantum measurement as an operation that maps a quantum state to a statistical distribution according to the Gleason’s theorem [34], which was demonstrated experimentally via detector tomography. We introduce a readily computable coherence monotone of measurement which takes into account the off-diagonal elements of each POVM component We show that this monotone gives a lower bound on the general robustness that is closely related to the maximal advantage over all incoherent measurements in the state discrimination task [35]. The key benefit of this approach may be its simplicity and directness as it avoids a computationally demanding post-processing that becomes challenging for high dimensional systems
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
