Mathematical Physics (MP)http://hdl.handle.net/20.500.11824/162024-02-22T23:10:11Z2024-02-22T23:10:11ZThe theory of F-rational signatureSmirnov, I.Tucker, K.http://hdl.handle.net/20.500.11824/17712024-02-20T23:20:30Z2024-01-01T00:00:00ZThe theory of F-rational signature
Smirnov, I.; Tucker, K.
2024-01-01T00:00:00ZCorrelation constraints and the Bloch geometry of two qubitsMorelli, S.Eltschka, C.Huber, M.Siewert, J.http://hdl.handle.net/20.500.11824/17472024-02-13T23:19:41Z2024-01-19T00:00:00ZCorrelation constraints and the Bloch geometry of two qubits
Morelli, S.; Eltschka, C.; Huber, M.; Siewert, J.
We present an inequality on the purity of a bipartite state depending solely on the length difference of the local Bloch vectors. For two qubits this inequality is tight for all marginal states and so extends the previously known solution for the two-qubit marginal problem. With this inequality we construct a three-dimensional Bloch model of the two-qubit quantum state space in terms of Bloch lengths, providing a pleasing visualization of this high-dimensional state space. This allows to characterize quantum states by a strongly reduced set of parameters and to investigate the interplay between local properties of the marginal systems and global properties encoded in the correlations.
2024-01-19T00:00:00ZModerately discontinuous homotopyFernández de Bobadilla, J.Heinze, S.Pe Pereira, M.http://hdl.handle.net/20.500.11824/17412024-02-02T23:19:28Z2022-12-01T00:00:00ZModerately discontinuous homotopy
Fernández de Bobadilla, J.; Heinze, S.; Pe Pereira, M.
2022-12-01T00:00:00ZSturm–Liouville systems for the survival probability in first-passage time problemsPagnini, G.Dahlenburg, M.http://hdl.handle.net/20.500.11824/17092023-11-22T23:19:29Z2023-11-15T00:00:00ZSturm–Liouville systems for the survival probability in first-passage time problems
Pagnini, G.; Dahlenburg, M.
We derive a Sturm–Liouville system of equations for the exact calculation of the survival probability in first-passage time problems. This system is the one associated with the Wiener–Hopf integral equation obtained from the theory of random walks. The derived approach is an alternative to the existing literature and we tested it against direct calculations from both discrete- and continuous-time random walks in a manageable, but meaningful, example. Within this framework, the Sparre Andersen theorem results to be a boundary condition for the system.
2023-11-15T00:00:00Z