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Volumn 53, Issue 7, 2012, Pages

Comment on some results of Erdahl and the convex structure of reduced density matrices

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EID: 84864740259     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.4736842     Document Type: Article
Times cited : (30)

References (26)
  • 1
    • 47749122552 scopus 로고    scopus 로고
    • The Pauli principle revisited
    • 10.1007/s00220-008-0552-z
    • Altunbulak M. Klyachko A. The Pauli principle revisited. Commun. Math. Phys. 2008, 282:287-322. 10.1007/s00220-008-0552-z.
    • (2008) Commun. Math. Phys. , vol.282 , pp. 287-322
    • Altunbulak, M.1    Klyachko, A.2
  • 3
    • 29144464785 scopus 로고    scopus 로고
    • The spectra of quantum states and the Kronecker coefficients of the symmetric group
    • 10.1007/s00220-005-1435-1
    • Christandl M. Mitchison G. The spectra of quantum states and the Kronecker coefficients of the symmetric group. Commun. Math. Phys. 2006, 261:789-797. 10.1007/s00220-005-1435-1.
    • (2006) Commun. Math. Phys. , vol.261 , pp. 789-797
    • Christandl, M.1    Mitchison, G.2
  • 4
    • 36149015994 scopus 로고
    • Structure of fermion density matrices
    • 10.1103/RevModPhys.35.668
    • Coleman A.J. Structure of fermion density matrices. Rev. Mod. Phys. 1963, 35:668-686. 10.1103/RevModPhys.35.668.
    • (1963) Rev. Mod. Phys. , vol.35 , pp. 668-686
    • Coleman, A.J.1
  • 5
    • 69649108540 scopus 로고    scopus 로고
    • Three-party pure quantum states are determined by two two-party reduced states
    • 10.1103/PhysRevA.70.010302
    • Diósi L. Three-party pure quantum states are determined by two two-party reduced states. Phys. Rev. A 2004, 70(1):010302. 10.1103/PhysRevA.70.010302.
    • (2004) Phys. Rev. A , vol.70 , Issue.1 , pp. 010302
    • Diósi, L.1
  • 6
    • 0001253566 scopus 로고
    • The convex structure of the set of N-representable reduced 2-Matrices
    • 10.1063/1.1665885
    • Erdahl R.M. The convex structure of the set of N-representable reduced 2-Matrices. J. Math. Phys. 1972, 13:1608-1621. 10.1063/1.1665885.
    • (1972) J. Math. Phys. , vol.13 , pp. 1608-1621
    • Erdahl, R.M.1
  • 7
    • 0000647855 scopus 로고
    • Reduction of the N-particle variational problem
    • 10.1063/1.1704098
    • Garrod C. Percus J.K. Reduction of the N-particle variational problem. J. Math. Phys. 1964, 5:1756-1776. 10.1063/1.1704098.
    • (1964) J. Math. Phys. , vol.5 , pp. 1756-1776
    • Garrod, C.1    Percus, J.K.2
  • 8
    • 18444380877 scopus 로고    scopus 로고
    • Parts of quantum states
    • 10.1103/PhysRevA.71.012324
    • Jones N.S. Linden N. Parts of quantum states. Phys. Rev. A 2005, 71:012324. 10.1103/PhysRevA.71.012324.
    • (2005) Phys. Rev. A , vol.71 , pp. 012324
    • Jones, N.S.1    Linden, N.2
  • 9
    • 12344273636 scopus 로고    scopus 로고
    • Quantum marginal problem and representations of the symmetric group
    • e-print arXiv:quant-ph/0409113.
    • Klyachko A. Quantum marginal problem and representations of the symmetric group. e-print arXiv:quant-ph/0409113.
    • Klyachko, A.1
  • 10
    • 33646436427 scopus 로고    scopus 로고
    • Quantum marginal problem and N-representability
    • 10.1088/1742-6596/36/1/014
    • Klyachko A. Quantum marginal problem and N-representability. J. Phys.: Conf. Ser. 2006, 36:72-86. 10.1088/1742-6596/36/1/014.
    • (2006) J. Phys.: Conf. Ser. , vol.36 , pp. 72-86
    • Klyachko, A.1
  • 11
    • 0000761608 scopus 로고
    • Linear inequalities and the pauli principle
    • 10.1002/zamm.19610410711
    • Kuhn H. Linear inequalities and the pauli principle. Combinatorial Analysis, Proc. Symp. Appl. Math. 1960, 10:141-147. 10.1002/zamm.19610410711.
    • (1960) Combinatorial Analysis, Proc. Symp. Appl. Math. , vol.10 , pp. 141-147
    • Kuhn, H.1
  • 12
    • 0000881958 scopus 로고
    • N-representability problem for reduced density matrices
    • 10.1063/1.1705122
    • Kummer H. N-representability problem for reduced density matrices. J. Math. Phys. 1967, 8:2063-2081. 10.1063/1.1705122.
    • (1967) J. Math. Phys. , vol.8 , pp. 2063-2081
    • Kummer, H.1
  • 13
    • 4243299985 scopus 로고    scopus 로고
    • Almost every pure state of three qubits is completely determined by its two-particle reduced density matrices
    • 10.1103/PhysRevLett.89.207901
    • Linden N. Popescu S. Wootters W.K. Almost every pure state of three qubits is completely determined by its two-particle reduced density matrices. Phys. Rev. Lett. 2002, 89:207901. 10.1103/PhysRevLett.89.207901.
    • (2002) Phys. Rev. Lett. , vol.89 , pp. 207901
    • Linden, N.1    Popescu, S.2    Wootters, W.K.3
  • 14
    • 0242545144 scopus 로고    scopus 로고
    • The parts determine the whole in a generic pure quantum state
    • 10.1103/PhysRevLett.89.277906
    • Linden N. Wootters W.K. The parts determine the whole in a generic pure quantum state. Phys. Rev. Lett. 2002, 89:277906. 10.1103/PhysRevLett.89.277906.
    • (2002) Phys. Rev. Lett. , vol.89 , pp. 277906
    • Linden, N.1    Wootters, W.K.2
  • 15
    • 33947266941 scopus 로고    scopus 로고
    • Quantum computational complexity of the N-representability problem: QMA complete
    • 10.1103/PhysRevLett.98.110503
    • Liu Y.-K. Christandl M. Verstraete F. Quantum computational complexity of the N-representability problem: QMA complete. Phys. Rev. Lett. 2007, 98(11):110503. 10.1103/PhysRevLett.98.110503.
    • (2007) Phys. Rev. Lett. , vol.98 , Issue.11 , pp. 110503
    • Liu, Y.-K.1    Christandl, M.2    Verstraete, F.3
  • 16
    • 79952578062 scopus 로고    scopus 로고
    • Quantum codes give counterexamples to the unique preimage conjecture of the N-representability problem
    • 10.1103/PhysRevLett.106.110501
    • Ocko S.A. Chen X. Zeng B. Yoshida B. Ji Z. Ruskai M.B. Chuang I.L. Quantum codes give counterexamples to the unique preimage conjecture of the N-representability problem. Phys. Rev. Lett. 2011, 106(11):110501. 10.1103/PhysRevLett.106.110501.
    • (2011) Phys. Rev. Lett. , vol.106 , Issue.11 , pp. 110501
    • Ocko, S.A.1    Chen, X.2    Zeng, B.3    Yoshida, B.4    Ji, Z.5    Ruskai, M.B.6    Chuang, I.L.7
  • 17
    • 0002296079 scopus 로고    scopus 로고
    • Some theorems on uniqueness and reconstruction of higher-order density matrices
    • J. Cioslowski, in , edited by (Springer)
    • Rosina M. Some theorems on uniqueness and reconstruction of higher-order density matrices. Many-Electron Densities and Reduced Density Matrices 2000, J. Cioslowski, in edited by (Springer)
    • (2000) Many-Electron Densities and Reduced Density Matrices
    • Rosina, M.1
  • 18
    • 0000057792 scopus 로고
    • N-representability problem: particle-hole equivalence
    • 10.1063/1.1665118
    • Ruskai M.B. N-representability problem: particle-hole equivalence. J. Math. Phys. 1970, 11(11):3218-3224. 10.1063/1.1665118.
    • (1970) J. Math. Phys. , vol.11 , Issue.11 , pp. 3218-3224
    • Ruskai, M.B.1
  • 19
    • 35548968929 scopus 로고    scopus 로고
    • Connecting N-representability to Weyl's problem: the one-particle density matrix for N = 3 and R = 6
    • 10.1088/1751-8113/40/45/F01
    • Ruskai M.B. Connecting N-representability to Weyl's problem: the one-particle density matrix for N = 3 and R = 6. J. Phys. A 2007, 40:F961-F967. 10.1088/1751-8113/40/45/F01.
    • (2007) J. Phys. A , vol.40
    • Ruskai, M.B.1
  • 20
    • 0000455749 scopus 로고
    • N-representability problem for fermion density matrices. I. The second-order density matrix with N = 3
    • 10.1063/1.1701504
    • Smith D.W. N-representability problem for fermion density matrices. I. The second-order density matrix with N = 3. J. Chem. Phys. 1965, 43:258. 10.1063/1.1701504.
    • (1965) J. Chem. Phys. , vol.43 , pp. 258
    • Smith, D.W.1
  • 21
    • 36149026119 scopus 로고
    • Concept of off-diagonal long-range order and the quantum phases of liquid he and of superconductors
    • 10.1103/RevModPhys.34.694
    • Yang C.N. Concept of off-diagonal long-range order and the quantum phases of liquid he and of superconductors. Rev. Mod. Phys. 1962, 34:694-704. 10.1103/RevModPhys.34.694.
    • (1962) Rev. Mod. Phys. , vol.34 , pp. 694-704
    • Yang, C.N.1
  • 22
    • 84864776667 scopus 로고    scopus 로고
    • Note
    • It is ironic that there is a typesetting error in the title of this section so that what was intended as "In Finite Dimensions ..." appears as "INFINITE DIMENSIONS ..." rather than "IN FINITE DIMENSIONS.".
  • 23
    • 84864776666 scopus 로고    scopus 로고
    • N(W)]⊥
    • N(W)]⊥
  • 24
    • 84864776663 scopus 로고    scopus 로고
    • j , much less a set with unit norm.
    • j , much less a set with unit norm.
  • 25
    • 84864780508 scopus 로고    scopus 로고
    • Here, we use the fact that a linear map is continuous and interpret open as relatively open.
    • Here, we use the fact that a linear map is continuous and interpret open as relatively open.
  • 26
    • 84864767628 scopus 로고    scopus 로고
    • 2
    • 2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.