Hilbert-Schmidt Geometry of n-Level Jakobczyk-Siennicki Two-Dimensional Quantum Systems
| dc.creator | Slater, Paul B. | |
| dc.date | 2005-08-30 | |
| dc.date | 2005-12-20 | |
| dc.date.accessioned | 2026-07-07T06:43:41Z | |
| dc.date.available | 2026-07-07T06:43:41Z | |
| dc.description | Jakobczyk and Siennicki studied two-dimensional sections of a set of (generalized) Bloch vectors corresponding to n x n density matrices of two-qubit systems (that is, the case n = 4). They found essentially five different types of (nontrivial) separability regimes. We compute the Euclidean/Hilbert-Schmidt (HS) separability probabilities assigned to these regimes, and conduct parallel two-dimensional sectional analyses for the higher-level cases n=6,8,9 and 10. Making use of the newly-introduced capability for integration over implicitly defined regions of version 5.1 of Mathematica -- also fruitfully used in our n=4 three-parameter entropy-maximization-based study quant-ph/0507203 -- we obtain a wide-ranging variety of exact HS-probabilities. For n>6, the probabilities are those of having a partial positive transpose (PPT). For the n=6 case, we also obtain biseparability probabilities; in the n=8,9 instances, bi-PPT probabilities; and for n=8, tri-PPT probabilities. By far, the most frequently recorded probability for n>4 is π/4 = 0.785398. We also conduct a number of related analyses, pertaining to the (one-dimensional) boundaries (both exterior and interior) of the separability and PPT domains, and attempt (with limited success) some exact calculations pertaining to the 9-dimensional (real) and 15-dimensional (complex) convex sets of two-qubit density matrices -- for which HS-separability probabilities have been conjectured, but not verified. | |
| dc.description | 45 pages, moderate rewriting | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0508227 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0508227 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/102511 | |
| dc.subject | Quantum Physics | |
| dc.title | Hilbert-Schmidt Geometry of n-Level Jakobczyk-Siennicki Two-Dimensional Quantum Systems | |
| dc.type | text |