Entanglement/Asymmetry correspondence for internal quantum reference frames

Quantum conformal symmetries for spacetimes in superposition

“…To see this, consider two general solutions φ = aφ and φ = aϕ of the Minkowski KG equation, related to the curved solutions via the scale factor a, through transformation (12). Using the definitions ( 13) and (18) of the pseudo inner products, one can show that ( φ, φ) η = (aφ, aϕ) η = (φ, ϕ) g .…”

“…These symmetry principles are implemented within the framework of quantum reference frame (QRF) transformations. Initially seen as changes between the perspectives of quantum systems [6][7][8][9][10][11][12][13][14][15][16][17][18][19], the interpretation of QRF changes has broadened to encompass a more abstract understanding in the sense of changes of quantum coordinate systems (e.g. [1,3,5,17,20]).…”

A model of quantum spacetime

“…As already mentioned, this is because, calculating the conditioned state of S to a certain value x j on R through (18), we find no contributions from different positions x i = x j , and so interference phenomena are not present even if the position states are not orthogonal. Rather f (x j − x i ) is related to the spread of the coefficients appearing in the global state |Ψ and this fact shows us a condition for a good functioning of our framework: a large spread in the coefficients within the global state in the expansion (8) is needed in order to distinguish states of S projected to closer values of R [27].…”

“…the value t m on C. For such a state, through (27) and the relative state definition, it is easy to find the time evolution with respect to the clock C: (31) where |φ(t 0 ) R,S = √ d C t 0 |Ψ is the state of R + S conditioned on t 0 that is the value of the clock taken as initial time. Equation (31) shows, as expected, the simultaneous evolution of R and S over time.…”

“…Looking at the relative state (in Everett sense [6]) of the subsystem S, PaW show that the dynamical Schrödinger evolution can be recovered with respect to the clock values. This approach has recently attracted a large interest and has stimulated several generalizations (see for example [7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29]), including an experimental illustration [30]. The PaW framework can be read as an internalization of the time reference frame, with the clock being an appropriately chosen physical system and time is considered as "what is shown on a quantum clock".…”