Information leak and incompatibility of physical context: A modified approach

A beautiful idea about the incompatibility of Physical Context(IPC) was introduced in Phys. Rev. A 102, 050201(R) (2020). Here, a context is defined as a set of a quantum state and two sharp rank-one measurements, and the incompatibility of physical context is defined as the leakage of information while implementing those two measurements successively in that quantum state. In this work, we show the limitations in their approach. The three primary limitations are that, (i) their approach is not positive operator-valued measurements and (ii), they restrict information-theoretic agents Alice, Eve and Bob to specific quantum operations and do not consider most general quantum operations i.e., quantum instruments and (iii), their measure of IPC can take negative values in specific cases in a more general scenario which implies the limitation of their information measure. Thereby, we have introduced a generalization and modification to their approach in more general and convenient way, such that this idea is well-defined for generic measurements, without these limitations. We also present a comparison of the measure of the IPC through their and our method. Lastly, we show, how the IPC reduces in the presence of memory using our modification, which further validates our approach.