Gharahighahi, Masoud (2022) Classifying Entanglement by Algebraic Geometry. [Tesi di dottorato]
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| Item Type: | Tesi di dottorato |
|---|---|
| Resource language: | English |
| Title: | Classifying Entanglement by Algebraic Geometry |
| Creators: | Creators Email Gharahighahi, Masoud masoud.gharahi@gmail.com |
| Date: | 1 November 2022 |
| Number of Pages: | 157 |
| Institution: | Università degli Studi di Napoli Federico II |
| Department: | Fisica |
| Dottorato: | Quantum Technologies (Tecnologie Quantistiche) |
| Ciclo di dottorato: | 35 |
| Coordinatore del Corso di dottorato: | nome email Tafuri, Francesco francesco.tafuri@unina.it |
| Tutor: | nome email Mancini, Stefano UNSPECIFIED |
| Date: | 1 November 2022 |
| Number of Pages: | 157 |
| Keywords: | Entanglement - Classification - Algebraic Geometry - Secant variety - l multilinear rank - tensor rank - border rank |
| Settori scientifico-disciplinari del MIUR: | Area 02 - Scienze fisiche > FIS/02 - Fisica teorica, modelli e metodi matematici |
| Date Deposited: | 13 Jan 2023 19:08 |
| Last Modified: | 09 Apr 2025 13:33 |
| URI: | http://www.fedoa.unina.it/id/eprint/14716 |
Collection description
Quantum Entanglement is one of the key manifestations of quantum mechanics that separate the quantum realm from the classical one. Characterization of entanglement as a physical resource for quantum technology became of uppermost importance. While the entanglement of bipartite systems is already well understood, the ultimate goal to cope with the properties of entanglement of multipartite systems is still far from being realized. This dissertation covers characterization of multipartite entanglement using algebraic-geometric tools. Firstly, we establish an algorithm to classify multipartite entanglement by k-secant varieties of the Segre variety and `-multilinear ranks that are invariant under Stochastic Local Operations with Classical Communication (SLOCC). We present a fine-structure classification of multiqubit and tripartite entanglement based on this algorithm. Another fundamental problem in quantum information theory is entanglement transformation that is quite challenging regarding to multipartite systems. It is captivating that the proposed entanglement classification by algebraic geometry can be considered as a reference to study SLOCC and asymptotic SLOCC interconversions among different resources based on tensor rank and border rank, respectively. In this regard, we also introduce a new class of tensors that we call persistent tensors and construct a lower bound for their tensor rank. We further cover SLOCC convertibility of multipartite systems considering several families of persistent tensors.
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