| 1 |
JohnstonN,MacLeanO.Pairwise completely positive matrices and conjugate local diagonal unitary invariant quantum states[J].Electronic Journal of Linear Algebra,2019,35,156-180.
doi: 10.13001/1081-3810.3842
|
| 2 |
SinghS.Entanglement detection in triangle-free quantum states[J].Physical Review A,2021,103(3):032436.
doi: 10.1103/PhysRevA.103.032436
|
| 3 |
SinghS,NechitaI.Diagonal unitary and orthogonal symmetries in quantum theory[J].Journal of Physics. A. Mathematical and Theoretical,2022,55(25):255302.
doi: 10.1088/1751-8121/ac7017
|
| 4 |
NechitaI,SinghS.A graphical calculus for integration over random diagonal unitary matrices[J].Linear Algebra and its Applications,2021,613,46-86.
doi: 10.1016/j.laa.2020.12.014
|
| 5 |
BermanA,Shaked-MondererN.Completely Positive Matrices[M].River Edge:World Scientific,2003.
|
| 6 |
DickinsonP J,GijbenL,HanD.On the computational complexity of membership problems for the completely positive cone and its dual[J].Computational Optimization and Applications,2014,57(2):403-415.
doi: 10.1007/s10589-013-9594-z
|
| 7 |
ArimaN,KimS,KojimaM.A quadratically constrained quadratic optimization model for completely positive cone programming[J].SIAM Journal on Optimization,2013,23(4):2320-2340.
doi: 10.1137/120890636
|
| 8 |
BurerS.On the copositive representation of binary and continuous nonconvex quadratic programs[J].Mathematical Programming,2009,120(2):479-495.
doi: 10.1007/s10107-008-0223-z
|
| 9 |
de KlerkE,PasechnikD V.Approximation of the stability number of a graph via copositive programming[J].SIAM Journal on Optimization,2002,12(4):875-892.
doi: 10.1137/S1052623401383248
|
| 10 |
DukanovicI,RendlF.Copositive programming motivated bounds on the stability and the chromatic numbers[J].Mathematical Programming,2010,121(2):249-268.
doi: 10.1007/s10107-008-0233-x
|
| 11 |
GühneO,TothG.Entanglement detection[J].Physics Reports,2009,474(1-6):1-75.
doi: 10.1016/j.physrep.2009.02.004
|
| 12 |
GvozdenovićN,LaurentM.The operator Ψ for the chromatic number of a graph[J].SIAM Journal on Optimization,2008,19(2):572-591.
doi: 10.1137/050648237
|
| 13 |
ZhouA,FanJ.The CP-matrix completion problem[J].SIAM Journal on Matrix Analysis and Applications,2014,35(1):127-142.
doi: 10.1137/130919490
|
| 14 |
DahlG,LeinaasJ M,MyrheimJ,et al.A tensor product matrix approximation problem in quantum physics[J].Linear Algebra and its Applications,2007,420(2-3):711-725.
doi: 10.1016/j.laa.2006.08.026
|
| 15 |
WernerR F.Quantum states with Einstein-Podolsky-Rosen correlations admitting a hiddenvariable model[J].Physical Review A,1989,40(8):4277-4281.
doi: 10.1103/PhysRevA.40.4277
|
| 16 |
GharibianS.Strong NP-hardness of the quantum separability problem[J].Quantum Information and Computation,2010,10(3-4):343-360.
|
| 17 |
Gurvits L. Classical deterministic complexity of Edmonds' problem and quantum entanglement[C]//Proceedings of the Thirty-Fifth Annual ACM Symposium on Theory of Computing, 2003: 10-19.
|
| 18 |
QiL,DaiH,HanD.Conditions for strong ellipticity and M-eigenvalues[J].Frontiers of Mathematics in China,2009,4(2):349-364.
doi: 10.1007/s11464-009-0016-6
|
| 19 |
DohertyA C,ParriloP A,SpedalieriF M.Complete family of separability criteria[J].Physical Review A,2004,69(2):022308.
doi: 10.1103/PhysRevA.69.022308
|
| 20 |
GurvitsL,BarnumH.Largest separable balls around the maximally mixed bipartite quantum state[J].Physical Review A,2002,66(6):062311.
doi: 10.1103/PhysRevA.66.062311
|
| 21 |
HorodeckiR,HorodeckiP,HorodeckiM,et al.Quantum entanglement[J].Reviews of Modern Physics,2009,81(2):865-942.
doi: 10.1103/RevModPhys.81.865
|
| 22 |
NieJ,ZhangX.Positive maps and separable matrices[J].SIAM Journal on Optimization,2016,26(2):1236-1256.
doi: 10.1137/15M1018514
|
| 23 |
PutinarM.Positive polynomials on compact semi-algebraic sets[J].Indiana University Mathematics Journal,1993,42(3):969-984.
doi: 10.1512/iumj.1993.42.42045
|
| 24 |
NieJ.Optimality conditions and finite convergence of Lasserre's hierarchy[J].Mathematical Programming,2014,146(1-2):97-121.
doi: 10.1007/s10107-013-0680-x
|
| 25 |
LasserreJ B.Completely positive matrices associated with M-matrices[J].Linear and Multilinear Algebra,1994,37(4):303-310.
doi: 10.1080/03081089408818334
|
| 26 |
Laurent M. Sums of squares, moment matrices and optimization over polynomials[M]//Putinar M, Sullivant S (eds.). Emerging Applications of Algebraic Geometry, New York: Springer, 2009: 157-270.
|
| 27 |
NieJ.Moment and Polynomial Optimization[M].Philadelphia:Society for Industrial and Applied Mathematics,2023.
|
| 28 |
CurtoR,FialkowL.Truncated K-moment problems in several variables[J].Journal of Operator Theory,2005,54(1):189-226.
|
| 29 |
NieJ.The $\mathcal{A}$-truncated K-moment problem[J].Foundations of Computational Mathematics,2014,14(6):1243-1276.
doi: 10.1007/s10208-014-9225-9
|
| 30 |
NieJ.Certifying convergence of Lasserre's hierarchy via flat truncation[J].Mathematical Programming,2013,142(1-2):485-510.
doi: 10.1007/s10107-012-0589-9
|
| 31 |
NieJ.Linear optimization with cones of moments and nonnegative polynomials[J].Mathematical Programming,2015,153(1):247-274.
doi: 10.1007/s10107-014-0797-6
|
| 32 |
HenrionD,LasserreJ B,LoefbergJ.GloptiPoly 3: Moments, optimization and semidefinite programming[J].Optimization Methods and Software,2009,24(4-5):761-779.
doi: 10.1080/10556780802699201
|
| 33 |
SturmJ F.Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones[J].Optimization Methods and Software,1999,11/12(1-4):625-653.
|
| 34 |
DemmelJ W.Applied Numerical Linear Algebra[M].Philadelphia:Society for Industrial and Applied Mathematics,1997.
|
| 35 |
GolubG H,Van Loan,CharlesF.Matrix Computations[M].Baltimore:Johns Hopkins University Press,1996.
|
| 36 |
Henrion D, Lasserre J B. Detecting global optimality and extracting solutions in GloptiPoly[M]//Henrion D, Garulli A (eds.) Positive Polynomials in Control, Berlin: Saunders, 2005: 293-310.
|
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