Two Tensor Optimization Problems From Quantum Information
summary
Two tensor problems are the focus: deciding transformability under local linear maps via restriction/degeneration and optimizing asymptotic resource rates. Claims include that triple reduced spectra form entanglement polytopes (convex, six classes for three qubits) and that Brion/moment-map methods plus Schur–Weyl duality let one turn occurrence obstructions into entropy optimizations whose values are multiplicative. Tools are algebraic geometry, GCT ideas and Shannon entropy on polytopes. A concrete payoff is a more efficient tensor‑network description of the resonating valence bond state, and the entanglement test has been implemented in the lab.
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chapters (11)
- 0:00Introduction
- 3:12Quantum Information
- 5:22Thebourns Rule
- 9:00Quantum Operations
- 10:53Restrictions
- 20:05Resource Theory
- 25:13Entanglement Polytope
- 27:45Dual Characterization
- 31:38Entanglement Test
- 32:42Information Theory
- 57:29Physics
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