Dimension-Independent Positive-Partial-Transpose Probability Ratios
| dc.creator | Slater, Paul B. | |
| dc.date | 2005-05-13 | |
| dc.date.accessioned | 2026-07-07T06:12:46Z | |
| dc.date.available | 2026-07-07T06:12:46Z | |
| dc.description | We conduct quasi-Monte Carlo numerical integrations in two very high (80 and 79)-dimensional domains -- the parameter spaces of rank-9 and rank-8 qutrit-qutrit (9 x 9) density matrices. We, then, estimate the ratio of the probability -- in terms of the Hilbert-Schmidt metric -- that a generic rank-9 density matrix has a positive partial transpose (PPT) to the probability that a generic rank-8 density matrix has a PPT (a precondition to separability/nonentanglement). Close examination of the numerical results generated -- despite certain large fluctuations -- indicates that the true ratio may, in fact, be 2. Our earlier investigation (eprint quant-ph/0410238) also yielded estimates close to 2 of the comparable ratios for qubit-qubit and qubit-qutrit pairs (the only two cases where the PPT condition fully implies separability). Therefore, it merits conjecturing (as Zyczkowski was the first to do) that such Hilbert-Schmidt (rank-NM/rank-(NM-1)) PPT probability ratios are 2 for all NM-dimensional quantum systems. | |
| dc.description | 8 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0505093 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0505093 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/92887 | |
| dc.subject | Quantum Physics | |
| dc.title | Dimension-Independent Positive-Partial-Transpose Probability Ratios | |
| dc.type | text |