Rank of a tensor and quantum entanglement. (English) Zbl 07901773
This is a survey aimed to mathematicians or people with a strong mathematical background) of the use of tensor rank, symmetric tensor rank and similar concepts for the study of quantum entanglement with most examples and quoted results for 3-tensors. Even for matrices (and often physicists reduce their problems to the matrix case using flattenings) would find something interesting related to asymptotic rank. The algebraist will find not only the main language of entanglement, but also the norms (nuclear and spectral norms) needed to go from an integer, e.g., the tensor rank, to a real number to measure the quantum entanglement.
Reviewer: Edoardo Ballico (Povo)
MSC:
| 14N07 | Secant varieties, tensor rank, varieties of sums of powers |
| 15A69 | Multilinear algebra, tensor calculus |
| 65K10 | Numerical optimization and variational techniques |
| 81P40 | Quantum coherence, entanglement, quantum correlations |
| 90C27 | Combinatorial optimization |
Keywords:
tensor rank; symmetric tensor rank; entanglement; multipartite quantum systems; nuclear and spectral norms; nuclear rank; quantum entanglement; quantum statesSoftware:
BertiniReferences:
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