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The characterization of physical systems relies on the observable propertieswhich are measured, and how such measurements are performed. Here we analyzetwo ways of assigning a description to a quantum system assuming that we onlyhave access to coarse-grained properties. More specifically, we compare theMaximum Entropy Principle method, with the Bayesian-inspired recently proposedAverage Assignment Map method [P. S. Correia et al, Phys. Rev. A 103, 052210(2021)]. Despite the fact that the assigned descriptions by both methodsrespect the measured constraints, and that they share the same conceptualfoundations, the descriptions differ in scenarios that go beyond thetraditional system-environment structure. The Average Assignment Map is thusshown to be a more sensible choice for the ever more prevalent scenario ofcomplex quantum systems. We discuss the physics behind such a difference, andfurther exploit it in a quantum thermodynamics process.

Quantum state inference from coarse-grained descriptions: analysis and an application to quantum thermodynamics