Convex set of quantum states with positive partial transpose analysed by hit and run algorithm
The convex set of quantum states of a composite K×K system with positive partial transpose is analysed. A version of the hit and run algorithm is used to generate a sequence of random points covering this set uniformly and an estimation for the convergence speed of the algorithm is derived. For K⩾3...
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| Published in | Journal of physics. A, Mathematical and theoretical Vol. 50; no. 25; pp. 255206 - 255217 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
IOP Publishing
23.06.2017
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1751-8113 1751-8121 |
| DOI | 10.1088/1751-8121/aa70f5 |
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| Abstract | The convex set of quantum states of a composite K×K system with positive partial transpose is analysed. A version of the hit and run algorithm is used to generate a sequence of random points covering this set uniformly and an estimation for the convergence speed of the algorithm is derived. For K⩾3 this algorithm works faster than sampling over the entire set of states and verifying whether the partial transpose is positive. The level density of the PPT states is shown to differ from the Marchenko-Pastur distribution, supported in [0, 4] and corresponding asymptotically to the entire set of quantum states. Based on the shifted semi-circle law, describing asymptotic level density of partially transposed states, and on the level density for the Gaussian unitary ensemble with constraints for the spectrum we find an explicit form of the probability distribution supported in [0, 3], which describes well the level density obtained numerically for PPT states. |
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| AbstractList | The convex set of quantum states of a composite K×K system with positive partial transpose is analysed. A version of the hit and run algorithm is used to generate a sequence of random points covering this set uniformly and an estimation for the convergence speed of the algorithm is derived. For K⩾3 this algorithm works faster than sampling over the entire set of states and verifying whether the partial transpose is positive. The level density of the PPT states is shown to differ from the Marchenko-Pastur distribution, supported in [0, 4] and corresponding asymptotically to the entire set of quantum states. Based on the shifted semi-circle law, describing asymptotic level density of partially transposed states, and on the level density for the Gaussian unitary ensemble with constraints for the spectrum we find an explicit form of the probability distribution supported in [0, 3], which describes well the level density obtained numerically for PPT states. |
| Author | yczkowski, Karol Szyma ski, Konrad Szarek, Tomasz Collins, Benot |
| Author_xml | – sequence: 1 givenname: Konrad surname: Szyma ski fullname: Szyma ski, Konrad email: konrad.szymanski@uj.edu.pl organization: Jagiellonian University Institute of Physics, Cracow, Poland – sequence: 2 givenname: Benot surname: Collins fullname: Collins, Benot email: collins@math.kyoto-u.ac.jp organization: CNRS , France – sequence: 3 givenname: Tomasz surname: Szarek fullname: Szarek, Tomasz email: szarek@intertele.pl organization: Gda sk University of Technology Faculty of Physics and Applied Mathematics, ul. Gabriela Narutowicza 11/12, 80-233 Gda sk, Poland – sequence: 4 givenname: Karol surname: yczkowski fullname: yczkowski, Karol email: karol@tatry.if.uj.edu.pl organization: Center for Theoretical Physics , Polish Academy of Sciences, Warsaw |
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| Cites_doi | 10.1103/PhysRevA.76.052325 10.1007/978-1-4612-0019-2 10.1103/PhysRevA.58.883 10.1142/S2010326312500013 10.1017/CBO9780511535048 10.1515/9781400835416 10.1088/0305-4470/34/35/335 10.1088/0305-4470/37/35/004 10.1103/physreva.93.062112 10.1002/rsa.20135 10.1103/PhysRevA.88.062330 10.1103/PhysRevA.58.826 10.26421/QIC15.7-8-10 10.1016/j.laa.2014.11.031 10.1103/PhysRevA.85.062331 10.1070/sm1967v001n04abeh001994 10.1016/S0375-9601(96)00706-2 10.1103/PhysRevA.73.022109 10.1088/0305-4470/39/5/L02 10.1103/PhysRevE.77.041108 10.1007/BF01883625 10.1063/1.2841325 10.1142/S2010326312500025 10.1155/2015/621353 10.1016/j.jcss.2004.06.003 10.1103/PhysRevA.66.062311 10.1103/PhysRevA.63.032307 10.1063/1.3595693 10.1093/biomet/57.1.97 10.1103/RevModPhys.81.865 10.1088/0305-4470/38/47/011 10.4171/OWR/2004/01 10.1137/S009753970544727X 10.1103/PhysRevA.64.012316 |
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| References | 22 24 27 Arunachalam S (35) 2015; 15 28 29 Doeblin W (25) 1937; 39 Sommers H-J (26) 2004; 37 Życzkowski K (8) 2001; 34 31 10 32 11 33 12 34 13 Collins B (20) 2017; 24 14 36 15 37 16 18 Szarek S (23) 2006; 39 19 Grabowski J (4) 2005; 38 Vempala S (17) 2005; 52 1 2 3 Forrester P J (30) 2010 5 6 7 9 21 |
| References_xml | – ident: 32 doi: 10.1103/PhysRevA.76.052325 – ident: 1 doi: 10.1007/978-1-4612-0019-2 – ident: 10 doi: 10.1103/PhysRevA.58.883 – ident: 13 doi: 10.1142/S2010326312500013 – ident: 5 doi: 10.1017/CBO9780511535048 – year: 2010 ident: 30 publication-title: Log-gases and Random matrices doi: 10.1515/9781400835416 – volume: 34 start-page: 7111 issn: 0305-4470 year: 2001 ident: 8 publication-title: J. Phys. A: Math. Gen. doi: 10.1088/0305-4470/34/35/335 – volume: 37 start-page: 8457 issn: 0305-4470 year: 2004 ident: 26 publication-title: J. Phys. A: Math. Gen. doi: 10.1088/0305-4470/37/35/004 – ident: 29 doi: 10.1103/physreva.93.062112 – volume: 39 start-page: 57 issn: 1220-3858 year: 1937 ident: 25 publication-title: Bull. Math. Soc. Roum. Sci. – ident: 19 doi: 10.1002/rsa.20135 – ident: 33 doi: 10.1103/PhysRevA.88.062330 – ident: 28 doi: 10.1103/PhysRevA.58.826 – volume: 15 start-page: 0694 issn: 1533-7146 year: 2015 ident: 35 publication-title: Quant. Inf. Comput. doi: 10.26421/QIC15.7-8-10 – ident: 36 doi: 10.1016/j.laa.2014.11.031 – ident: 14 doi: 10.1103/PhysRevA.85.062331 – ident: 22 doi: 10.1070/sm1967v001n04abeh001994 – ident: 7 doi: 10.1016/S0375-9601(96)00706-2 – ident: 12 doi: 10.1103/PhysRevA.73.022109 – volume: 39 start-page: L119 issn: 0305-4470 year: 2006 ident: 23 publication-title: J. Phys. A: Math. Gen. doi: 10.1088/0305-4470/39/5/L02 – ident: 15 doi: 10.1103/PhysRevE.77.041108 – ident: 2 doi: 10.1007/BF01883625 – ident: 34 doi: 10.1063/1.2841325 – ident: 37 doi: 10.1142/S2010326312500025 – ident: 27 doi: 10.1155/2015/621353 – volume: 52 start-page: 573 year: 2005 ident: 17 publication-title: Comb. Comput. Geom. MSRI Publ. – ident: 21 doi: 10.1016/j.jcss.2004.06.003 – ident: 11 doi: 10.1103/PhysRevA.66.062311 – volume: 24 start-page: 3 issn: 0944-6532 year: 2017 ident: 20 publication-title: J. Convex Anal. – ident: 3 doi: 10.1103/PhysRevA.63.032307 – ident: 9 doi: 10.1063/1.3595693 – ident: 24 doi: 10.1093/biomet/57.1.97 – ident: 6 doi: 10.1103/RevModPhys.81.865 – volume: 38 start-page: 10217 issn: 0305-4470 year: 2005 ident: 4 publication-title: J. Phys. A: Math. Gen. doi: 10.1088/0305-4470/38/47/011 – ident: 16 doi: 10.4171/OWR/2004/01 – ident: 18 doi: 10.1137/S009753970544727X – ident: 31 doi: 10.1103/PhysRevA.64.012316 |
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| SubjectTerms | gaussian unitary ensemble Marchenko-Pastur distribution positive partial transpose separable states spectral density |
| Title | Convex set of quantum states with positive partial transpose analysed by hit and run algorithm |
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