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We study whether one can write a Matrix Product Density Operator (MPDO) as the Gibbs state of a quasi-local parent Hamiltonian.
Gibbs states of a one dimensional quantum lattice
H. Araki · 1969
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Markov field on finite graphs and lattices
J.M. Hammersley and P.E. Clifford · 1971
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Completely positive maps and entropy inequalities
G. Lindblad · 1975
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Relative entropy and the wigner-yanase-dyson-lieb concavity in an interpolation theory
A. Uhlmann · 1977
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The Contraction Mapping Approach to the Perron-Frobenius Theory: Why Hilbert’s Metric?
E. Kohlberg and J. W. Pratt · 1982
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Sufficient subalgebras and the relative entropy of states of a von Neumann algebra
D. Petz · 1986
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Rigorous results on valence-bond ground states in antiferromagnets
I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki · 1987
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Sufficiency of channels over Von Neumann algebras
D. Petz · 1988
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sufficiency of channels over von neumann algebras
D. Petz · 1988
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Finitely correlated states on quantum spin chains
M. Fannes, B. Nachtergaele, and R. F. Werner · 1992
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E. Knill, R. Laflamme, and L. Viola · 2000
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Carathéodory theorem
G. E. D.-Uchida · 2001
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Theory of operator algebras. I
M. Takesaki · 2002
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Operations that do not disturb partially known quantum states
M. Koashi and N. Imoto · 2002
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Completely Bounded Maps and Operator Algebras
V. Paulsen · 2003
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Renormalization algorithms for quantum-many body systems in two and higher dimensions,
F. Verstraete and J. I. Cirac · 2004
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Matrix product density operators: Simulation of finite-temperature and dissipative systems
F. Verstraete, J. J. García-Ripoll, and J. I. Cirac · 2004
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Structure of States Which Satisfy Strong Subadditivity of Quantum Entropy with Equality
P. Hayden, R. Jozsa, D. Petz, and A. Winter · 2004
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The simplest proof of Burnside’s theorem on matrix algebras
V. Lomonosov and P. Rosenthal · 2004
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Sets of nonnegative matrices without positive products
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Matrix-product operators and states: Np-hardness and undecidability
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V. Anantharam, A. Gohari, S. Kamath, and C. Nair · 2014
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