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EnglishA short review of algebraic geometry tools for the decomposition of tensors and polynomials is given from the point of view of applications to quantum and atomic physics. Examples of application to assemblies of indistinguishable two-level bosonic atoms are discussed using modern formulations of the classical Sylvester algorithm for the decomposition of homogeneous polynomials in two variables. In particular, the symmetric rank and symmetric border rank of spin squeezed states are calculated as well as their Schrödinger-cat-like decomposition as the sum of macroscopically different coherent spin states; Fock states provide an example of states for which the symmetric rank and the symmetric border rank are different
Algebraic geometry tools for the study of entanglement: an application to spin squeezed states / Bernardi, Alessandra; Carusotto, Iacopo. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - 45:10(2012), pp. 10530401-10530413.
| Titolo: | Algebraic geometry tools for the study of entanglement: an application to spin squeezed states |
| Autori: | Bernardi, Alessandra; Carusotto, Iacopo |
| Autori Unitn: | |
| Titolo del periodico: | JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL |
| Anno di pubblicazione: | 2012 |
| Numero e parte del fascicolo: | 10 |
| Codice identificativo Scopus: | 2-s2.0-84857942948 |
| Codice identificativo Pubmed: | 10.1088/1751-8113/45/10/10530 |
| Codice identificativo ISI: | WOS:000300985600013 |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1088/1751-8113/45/10/105304 |
| Handle: | http://hdl.handle.net/11572/134885 |
| Citazione: | Algebraic geometry tools for the study of entanglement: an application to spin squeezed states / Bernardi, Alessandra; Carusotto, Iacopo. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - 45:10(2012), pp. 10530401-10530413. |
| Appare nelle tipologie: | 03.1 Articolo su rivista (Journal article) |
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|---|---|---|---|---|
| 407811Rev27Jan12.pdf | Post-print referato (Refereed author’s manuscript) | Tutti i diritti riservati (All rights reserved) | Open Access Visualizza/Apri |
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