Compatibility between agents as a tool for coarse-grained descriptions of quantum systems

Abstract

Shedding a new light in the coarse-graining scenario, in this contribution we came up with different necessary and sufficient conditions for the existence of a well-defined coarse-grained state. For doing so, we had to break apart with the usual quantum channels perspective and assume a more decision-theoretical posture. Broadly speaking, we reinterpret the coarse-graining problem in the language of quantum state pooling, and by making an extensive use of the conditional quantum states toolkit, we have been able to derive more tangible conditions for the emergence of a compatible effective coarse-grained state.

Investigating Coarse-Grainings and Emergent Quantum Dynamics with Four Mathematical Perspectives

“…1, as it has been done in ref. [40]. Another dimension that can also be explored ties back to the SDP characteri-sation of the problem, as we think it is also possible to write down the emergent map (or the Choi-Jamio lkowski image of it) whenever such map happens to exist.…”

Quantum walks via quantum cellular automata

“…In the following we apply the coarse-graining local map to the operator (10), getting a general expression for the coarse-grained density operator in level L + 1. To get this general form, note that we can distinguish three different cases: (i) x = x and a = a , (ii) a = a , for all for x = x and (iii) x = x .…”

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

“…In order to deal with this new class of phenomena, quantum channels with the output dimension smaller than the input dimension, dubbed coarse-graining channels, were used to obtain a system's effective description [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. In this formalism, a coarse-graining map is thus a completely positive map…”