Macro-to-micro quantum mapping and the emergence of nonlinearity

Hybrid Quantum-Classical Algorithm for Hydrodynamics

“…The key is to consider more general quantum walks and quantum automata. Self-interacting walks and automata [35][36][37] are of particular interest because they are a relatively easy tool to model arbitrary equations of state and can probably be realized using Bose-condensates [38,39].…”

Reductions in finite-dimensional quantum mechanics: from symmetries to operator algebras and beyond

“…Similar adaptations of the classical notion of coarse-graining in quantum theory have been explored in [37,34,30] (for other approaches to the quantum notion of coarse-graining see [89,32,35]). Our main contribution is in deriving the general operational meaning of such notion of coarse-graining in quantum theory, and rigorously demonstrating its relation to the analogous classical notion.…”

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

“…From an operational perspective, when assembling an effective preparation , which is accessed through a coarsegraining map Λ, and with properties O, microscopically we are in fact sampling from the set Ω Λ (O). Due to the linearity of the expectation value, this perspective suggests an averaging map A Λ : O → L(H D ) that assigns the appropriate description to the microscopic ensemble [32]:…”

“…While in principle one could use the MEP to assign a description to the microscopic state, when studying the effective dynamics that might emerge from a coarse-grained dynamics [32], an assignment map naturally surfaced. Consider the set of all states which are consistent with the coarse-grained data, i.e., the set…”

“…(1) As in the foundations of the MEP, in Ref. [32] it was suggested to assign to the underlying system the description given by the uniform average of the states, Ω Λ (O) ψ . The map A Λ : O → L(H D ) that takes the known coarse-grained data and assigns to the system a uniform average among all the fine-grained descriptions that agree with the data was named Average Assignment Map (AAM) -more details below.…”