Nilpotent quantum mechanics, qubits, and flavors of entanglement
| dc.creator | Frydryszak, Andrzej M. | |
| dc.date | 2008-10-16 | |
| dc.date.accessioned | 2026-07-07T10:10:52Z | |
| dc.date.available | 2026-07-07T10:10:52Z | |
| dc.description | We address the question of description of qubit system in a formalism based on the nilpotent commuting variables. In this formalism qubits exhibit properties of composite objects being subject of the Pauli exclusion principle, but otherwise behaving boson-like. They are not fundamental particles. In such an approach the classical limit yields the nilpotent mechanics. Using the space of $η$-wavefunctions, generalized Schrödinger equation etc. we study properties of pure qubit systems and also properties of some composed, hybrid models: fermion-qubit, boson-qubit. The fermion-qubit system can be truly supersymmetric, with both SUSY partners having identical spectra. It is new and very interesting that SUSY transformations relate here only nilpotent object. The $η$-eigenfunctions for the qubit-qubit system give the set of Bloch vectors as a natural basis. Then the $η$-formalism is applied to the description of the pure state entanglement. Nilpotent commuting variables were firstly used in this context in [A. Mandilara, et. al., Phys. Rev. A \textbf{74}, 022331 (2006)], we generalize and extend approach presented there. Our main tool for study the entanglement or separability of states are Wronskians of $η$-functions. The known invariants and entanglement monotones for systems of $n=2,3,4$ qubits are expressed in terms of the Wronskians. This approach gives criteria for separability of states and insight into the flavor of entanglement of the system and simplifies description. | |
| dc.description | 50 pages, 3 tables, 1 figure | |
| dc.identifier | https://arxiv.org/abs/0810.3016 | |
| dc.identifier | http://arxiv.org/abs/0810.3016 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/171720 | |
| dc.subject | Quantum Physics | |
| dc.title | Nilpotent quantum mechanics, qubits, and flavors of entanglement | |
| dc.type | text |