On the Geometric Probability of Entangled Mixed States
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| 024 | 7 | 0 | |a 10.1007/s10958-015-2542-y |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10958-015-2542-y | ||
| 245 | 0 | 0 | |a On the Geometric Probability of Entangled Mixed States |h [Elektronische Daten] |c [A. Khvedelidze, I. Rogojin] |
| 520 | 3 | |a The state space of a composite quantum system, the set of density matrices P $$ \mathfrak{P} $$ +, is decomposable into the space of separable states S $$ \mathfrak{S} $$ + and its complement, the space of entangled states. An explicit construction of such a decomposition constitutes the so-called separability problem. If the space P $$ \mathfrak{P} $$ + is endowed with a certain Riemannian metric, then the separability problem admits a measuretheoretic formulation. In particular, one can define the "geometric probability of separability” as the relative volume of the space of separable states S $$ \mathfrak{S} $$ + with respect to the volume of all states. In the present note, using the Peres-Horodecki positive partial transposition criterion, we discuss the measure-theoretic aspects of the separability problem for bipartite systems composed either of two qubits or of a qubit-qutrit pair. Necessary and sufficient conditions for the separability of a two-qubit state are formulated in terms of local SU(2) ⊗ SU(2) invariant polynomials, the determinant of the correlation matrix, and the determinant of the Schlienz-Mahler matrix. Using the projective method of generating random density matrices distributed according to the Hilbert-Schmidt or Bures measure, we calculate the probability of separability (including that of absolute separability) of a two-qubit and qubit-qutrit pair. Bibliograhpy: 47 titles. | |
| 540 | |a Springer Science+Business Media New York, 2015 | ||
| 700 | 1 | |a Khvedelidze |D A. |u A. Razmadze Mathematical Institute, Tbilisi, Georgia |4 aut | |
| 700 | 1 | |a Rogojin |D I. |u Joint Institute for Nuclear Research, Dubna, Russia |4 aut | |
| 773 | 0 | |t Journal of Mathematical Sciences |d Springer US; http://www.springer-ny.com |g 209/6(2015-09-01), 988-1004 |x 1072-3374 |q 209:6<988 |1 2015 |2 209 |o 10958 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10958-015-2542-y |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10958-015-2542-y |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Khvedelidze |D A. |u A. Razmadze Mathematical Institute, Tbilisi, Georgia |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Rogojin |D I. |u Joint Institute for Nuclear Research, Dubna, Russia |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Journal of Mathematical Sciences |d Springer US; http://www.springer-ny.com |g 209/6(2015-09-01), 988-1004 |x 1072-3374 |q 209:6<988 |1 2015 |2 209 |o 10958 | ||