Classifying spaces and tensor products for manifolds with $\R$-actions
Tensors, manifolds and differential geometry: applications in mechanics and relati...
| Full text | |
| Author(s): |
Guerini, Leonardo
;
Baraviera, Alexandre
Total Authors: 2
|
| Document type: | Journal article |
| Source: | LINEAR & MULTILINEAR ALGEBRA; v. N/A, p. 14-pg., 2022-12-29. |
| Abstract | |
Quantum measurements can be interpreted as a generalization of probability vectors, in which non-negative real numbers are replaced by positive semi-definite operators. We extrapolate this analogy to define a generalization of doubly stochastic matrices that we call doubly normalized tensors (DNTs), and investigate a corresponding version of Birkhoff-von Neumann's theorem, which states that permutations are the extremal points of the set of doubly stochastic matrices. We prove that joint measurability appears naturally as a mathematical feature of DNTs in this context and that this feature is necessary and sufficient for a characterization similar to Birkhoff-von Neumann's. Conversely, we also show that DNTs arise from a particular instance of a joint measurability problem, remarking the relevance of this quantum-theoretical property in general operator theory. (AU) | |
| FAPESP's process: | 18/04208-9 - Quantum measurement simulability and applications to Bell nonlocality |
| Grantee: | Leonardo Guerini de Souza |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 16/01343-7 - ICTP South American Institute for Fundamental Research: a regional center for theoretical physics |
| Grantee: | Nathan Jacob Berkovits |
| Support Opportunities: | Special Projects |