Seminars
Quantum Permutations as Genuine Quantum Coordinate Transformations
by
→
Europe/Rome
Grassano
Grassano
Description
Quantum reference frame transformations embody a quantization of the notion of coordinate systems through using a superposition of classical coordinate systems. In this talk I will show that this can be extended to a notion of quantum coordinate transformations more general than superposition of classical ones. This more general notion will be ``locally quantum", as opposed to the current known QRFs, which are only ``globally quantum": similarly to the transition from special to general relativity. To do this we will import a mathematical object called quantum permutations (aka `magic unitaries') into physics, showing that it can form a notion of quantum coordinate systems that includes quantum reference frames as a small subset. This is the subset of quantum-controlled permutations. The control basis is in turn global, i.e. space(time) independent: otherwise different branches would not correspond to different classical coordinate transformations. By including an important principle of quantum theory — non-commutativity — one can get out of this small subset and thus generalize quantum reference frames to the entirety of the set of quantum permutations. This unlocks \emph{local} quantum coordinate systems, which control on different bases at different space(time) points, while of course still being a unitary transformation. We showcase the implications of this extension, using the "local quantumness" to localize a particle in a superposition without delocalizing another particle in a definite location, a feat impossible with the currently known QRF transformations.