Measure of macrocoherence

Abstract: Macrocoherence is the concept of quantum mechanics being scaled up to the macroscopic level where everyday physical systems should inhibit quantum mechanical properties, however this is not what is observed. Through the use of Leggett-Garg inequalities, one can infer if there is a fundamental quantum mechanical behavior of the system being observed. Then, using violations of these inequalities, this paper discusses the possibility of extracting useful measures of how macroscopic a system can be. Utilizing an analogy with the measures of locality through Bell's inequalities, the scope of what a measure should consist of is discussed. A measure should be proper in the sense that a baseline of 0 should be obtained from system that never violates an LGI. Further, it is proposed that a measure should extend naturally to all orders of LGIs without ranking quantum systems differently. With these in mind two measures are proposed, one utilizing the integral over the violated area of a LGI over time whereas the other uses inner products over a matrix defined elementwise as a specified LGI. The measures scopes are discussed and their applications are showcased for some analytical quantum systems. Though functional, the measures are found to lack a resource tied to its value complicating the conceptualization of what is being measured. It is concluded that a new effort to find a true measure of macrocoherence should start from the concept of a resource.