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We give an introduction to the theory of multi-partite entanglement.
Can quantum-mechanical description of physical reality be considered complete?
A. Einstein, B. Podolsky, and N. Rosen · 1935
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On the Einstein Podolsky Rosen paradox
J. S. Bell · 1964
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Proposed experiment to test local hidden-variable theories
J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt · 1969
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Bounds for the quantity of information transmitted by a quantum communication channel
A. S. Holevo · 1973
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A fundamental property of quantum-mechanical entropy
E. H. Lieb and M. B. Ruskai · 1973
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Symmetry properties of product states for the system of
R. Alicki, S. Rudnicki, and S. Sadowski · 1988
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Going beyond Bell’s theorem
D. M. Greenberger, M. A. Horne, and A. Zeilinger · 1989
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Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model
R. F. Werner · 1989
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Extreme quantum entanglement in a superposition of macroscopically distinct states
N. D. Mermin · 1990
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Finitely correlated states on quantum spin chains
M. Fannes, B. Nachtergaele, and R. F. Werner · 1992
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Density matrix formulation for quantum renormalization groups
S. R. White · 1992
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Squeezed atomic states and projection noise in spectroscopy
D. J. Wineland, J. J. Bollinger, W. M. Itano, and D. J. Heinzen · 1994
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Mixed-state entanglement and quantum error correction
C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters · 1996
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Optimal frequency measurements with maximally correlated states
J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen · 1996
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Stabilizer codes and quantum error correction
D. Gottesman · 1996
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Entanglement of a pair of quantum bits
I. Hill and W. K. Wootters · 1997
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Improvement of frequency standards with quantum entanglement
S. F. Huelga, C. Macchiavello, T. Pellizzari, A. K. Ekert, M. B. Plenio, and J. I. Cirac · 1997
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Computing local invariants of quantum-bit systems
M. Grassl, M. Rötteler, and T. Beth · 1998
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On multi-particle entanglement
N. Linden and S. Popescu · 1998
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Entanglement of formation of an arbitrary state of two qubits
W. K. Wootters · 1998
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On characterization of entropy function via information inequalities
Z. Zhang and R. W. Yeung · 1998
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Unextendible product bases and bound entanglement
C. H. Bennett, D. P. DiVincenzo, T. Mor, P. W. Shor, J. A. Smolin, and B. M. Terhal · 1999
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Observation of three-photon Greenberger-Horne-Zeilinger entanglement
D. Bouwmeester, J.-W. Pan, D. I. Matthew, H. Weinfurter, and A. Zeilinger · 1999
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How to share a quantum secret
R. Cleve, D. Gottesman, and H.-K. Lo · 1999
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Separability and distillability of multiparticle quantum systems
W. Dür, J. I. Cirac, and R. Tarrach · 1999
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Quantum secret sharing
M. Hillery, V. Bužek, and A. Berthiaume · 1999
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Reversibility of local transformations of multiparticle entanglement
N. Linden, S. Popescu, B. Schumacher, and M. Westmoreland · 1999
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Nonlocal parameters for multiparticle density matrices
N. Linden, S. Popescu, and A. Sudbery · 1999
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Conditions for a class of entanglement transformations
M. A. Nielsen · 1999
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Nonbinary quantum codes
E. M. Rains · 1999
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Quantum codes of minimum distance two
E. M. Rains · 1999
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Exact and asymptotic measures of multipartite pure-state entanglement
C. H. Bennett, S. Popescu, D. Rohrlich, J. A. Smolin, and A. V. Thapliyal · 2000
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Multipartite generalization of the Schmidt decomposition
H. A. Carteret, A. Higuchi, and A. Sudbery · 2000
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Distributed entanglement
V. Coffman, J. Kundu, and W. K. Wootters · 2000
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Classification of multiqubit mixed states: Separability and distillability properties
W. Dür and J. I. Cirac · 2000
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Three qubits can be entangled in two inequivalent ways
W. Dür, G. Vidal, and J. I. Cirac · 2000
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Tripartite entanglement and quantum relative entropy
E. F. Galvao, M. B. Plenio, and S Virmani · 2000
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Quantum information and quantum computation
M. A. Nielsen and I. L. Chuang · 2000
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Experimental test of quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement
J.-W. Pan, D. Bouwmeester, D. L. Matthew, H. Weinfurter, and A. Zeilinger · 2000
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Experimental entanglement of four particles
C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, et al · 2000
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Entanglement monotones
G. Vidal · 2000
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Reversible combination of inequivalent kinds of multipartite entanglement
G. Vidal, W. Dür, and J. I. Cirac · 2000
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Three-qubit pure-state canonical forms
A. Acin, A. Andrianov, E. Jané, and R. Tarrach · 2001
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Classification of mixed three-qubit states
A. Acin, D. Bruß, M. Lewenstein, and A. Sanpera · 2001
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Entanglement in quantum information theory
J. Eisert · 2001
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Schmidt measure as a tool for quantifying multiparticle entanglement
J. Eisert and H.-J. Briegel · 2001
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Estimating the spectrum of a density operator
M. Keyl and R. F. Werner · 2001
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Experimental demonstration of entanglement-enhanced rotation angle estimation using trapped ions
V. Meyer, M. A. Rowe, D. Kielpinski, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland · 2001
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Bounds on relative entropy of entanglement for multi-party systems
M. B. Plenio and V. Vedral · 2001
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A one-way quantum computer
R. Raussendorf and H. J. Briegel · 2001
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Local filtering operations on two qubits
F. Verstraete, J. Dehaene, and B. DeMoor · 2001
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Secure multi-party quantum computing
C. Creapeau, D. Gottesman, and A. Smith · 2002
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Distinguishing separable and entangled states
A. C. Doherty, P. A. Parrilo, and F. M. Spedalieri · 2002
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The uniqueness theorem for entanglement measures
M. J. Donald, M. Horodecki, and O. Rudolph · 2002
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Quantum Correlations in Systems of Indistinguishable Particles
K. Eckert, J. Schliemann, D. Bruß, and M. Lewenstein · 2002
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Detection of entanglement with few local measurements
O. Gühne, P. Hyllus, D. Bruß, A. Ekert, M. Lewenstein, C. Macchiavello, and A. Sanpera · 2002
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Quantum universal variable-length source coding
M. Hayashi and K. Matsumoto · 2002
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Four qubits can be entangled in nine different ways
F. Verstraete, J. Dehaene, B. De Moor, and H. Verschelde · 2002
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On the structure of a reversible entanglement generating set for tripartite states
A. Acin, G. Vidal, and J. I. Cirac · 2003
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A complete set of covariants of the four qubit system
E. Briand, J.-G. Luque, and J.-Y. Thibon · 2003
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Introduction to the basics of entanglement theory in continuous-variable systems
J. Eisert and M. B. Plenio · 2003
Cited alongside, same era.
Mode entanglement and entangling power in bosonic graphs
P. Giorda and P. Zanardi · 2003
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Classical deterministic complexity of Edmonds’ Problem and quantum entanglement
L. Gurvits · 2003
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Fault-tolerant quantum computation by anyons
A. Y. Kitaev · 2003
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Classification of multipartite entangled states by multidimensional determinants
A. Miyake · 2003
Cited alongside, same era.
A quantum information theoretical model for quantum secret sharing schemes
A. C. A. Nascimento, P. Tuyls, A. Winter, H. Imai, and J. Müller-Quade · 2003
Cited alongside, same era.
Entanglement detection
O. Gühne and G. Tóth · 2009
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Quantum entanglement
R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki · 2009
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Entanglement combing
D. Yang and J. Eisert · 2009
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Area laws for the entanglement entropy
J. Eisert, M. Cramer, and M. B. Plenio · 2010
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Multipartite entanglement and frustration
P. Facchi, G. Florio, U. Marzolino, G. Parisi, and S. Pascazio · 2010
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Strong NP-hardness of the quantum separability problem
S. Gharibian · 2010
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All maximally entangled four-qubit states
G. Gour and N. R. Wallach · 2010
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The inequalities of quantum information theory
N. Pippenger · 2003
Cited alongside, same era.
Entangled graphs: Bipartite entanglement in multiqubit systems
M. Plesch and V. Bužek · 2003
Cited alongside, same era.
Logical network implementation for cluster states and graph codes
D. Schlingemann · 2003
Cited alongside, same era.
Quantum Nonlocality in the Presence of Superselection Rules and Data Hiding Protocols
F. Verstraete and J. I. Cirac · 2003
Cited alongside, same era.
Normal forms and entanglement measures for multipartite quantum states
F. Verstraete, J. Dehaene, and B. De Moor · 2003
Cited alongside, same era.
Geometric measure of entanglement and applications to bipartite and multipartite quantum states
T.-C. Wei and P. M. Goldbart · 2003
Cited alongside, same era.
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Local unitary equivalence and entanglement of multipartite pure states
B. Kraus · 2010
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Local unitary equivalence of multipartite pure states
B. Kraus · 2010
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Quantum computational capability of a 2d valence bond solid phase
A. Miyake · 2011
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The density-matrix renormalization group in the age of matrix product states
U. Schollwöck · 2011
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Classifying quantum phases using matrix product states and projected entangled pair states
N. Schuch, D. Perez-Garcia, and J. I. Cirac · 2011
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From classical to quantum Shannon theory
M. M. Wilde · 2011
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Infinitely many constrained inequalities for the von Neumann entropy
J. Cadney, N. Linden, and A. Winter · 2012
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Recoupling coefficients and quantum entropies
M. Christandl, M. B. Şahinoğlu, and M. Walter · 2012
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Measurement-based quantum computation in a 2D phase of matter
A. S. Darmawan, G. K. Brennen, and S. D. Bartlett · 2012
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Multipartite-entanglement monotones and polynomial invariants
C. Eltschka, T. Bastin, A. Osterloh, and J. Siewert · 2012
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Absolute maximal entanglement and quantum secret sharing
W. Helwig, W. Cui, J. I. Latorre, A. Riera, and H.-K. Lo · 2012
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Entanglement and extreme spin squeezing for a fluctuating number of indistinguishable particles
P. Hyllus, L. Pezzé, A. Smerzi, and G. Tóth · 2012
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Tensors: geometry and applications
J. M. Landsberg · 2012
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Incompatible local hidden-variable models of quantum correlations
W. Laskowski, M. Markiewicz, T. Paterek, and M. Wieśniak · 2012
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Detection of symmetry-protected topological phases in one dimension
F. Pollmann and A. M. Turner · 2012
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Critical sets of the total variance can detect all stochastic local operations and classical communication classes of multiparticle entanglement
A. Sawicki, M. Oszmaniec, and M. Kuś · 2012
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Constructing holographic spacetimes using entanglement renormalization
B. Swingle · 2012
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Entanglement renormalization and holography
B. Swingle · 2012
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Gaussian quantum information
C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd · 2012
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A stronger subadditivity relation
A. Winter and K. Li · 2012
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Nonlocal multipartite correlations from local marginal probabilities
L. E. Würflinger, J.-D. Bancal, A. Acín, N. Gisin, and T. Vértesi · 2012
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The maximally entangled set of multipartite quantum states
J. I. de Vicente, C. Spee, and B. Kraus · 2013
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Classification of multipartite entanglement of all finite dimensionality
G. Gour and N. R. Wallach · 2013
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Stabilizer information inequalities from phase space distributions
D. Gross and M. Walter · 2013
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Most tensor problems are NP-hard
L.-H. Lim and C. Hillar · 2013
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The quantum entropy cone of stabiliser states
N. Linden, F. Matúš, M. B. Ruskai, and A. Winter · 2013
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Exact holographic mapping and emergent space-time geometry
X.-L. Qi · 2013
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When is a pure state of three qubits determined by its single-particle reduced density matrices?
A. Sawicki, M. Walter, and M. Kuś · 2013
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Entanglement polytopes: multiparticle entanglement from single-particle information
M. Walter, B. Doran, D. Gross, and M. Christandl · 2013
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Everything you always wanted to know about LOCC (but were afraid to ask)
E. Chitambar, D. Leung, L. Mančinska, M. Ozols, and A. Winter · 2014
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A practical introduction to tensor networks: Matrix product states and projected entangled pair states
R. Orús · 2014
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Topological transitions from multipartite entanglement with tensor networks: a procedure for sharper and faster characterization
R. Orús, T.-C. Wei, O. Buerschaper, and A. García-Saez · 2014
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Convexity of momentum map, Morse index, and quantum entanglement
A. Sawicki, M. Oszmaniec, and M. Kuś · 2014
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Multipartite Quantum States and their Marginals
M. Walter · 2014
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Entanglement and the fermion sign problem in auxiliary field quantum monte carlo simulations
P. Broecker and S. Trebst · 2015
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Quantum conditional mutual information and approximate Markov chains
O. Fawzi and R. Renner · 2015
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From three-photon Greenberger-Horne-Zeilinger states to ballistic universal quantum computation
M. Gimeno-Segovia, P. Shadbolt, D. E. Browne, and T. Rudolph · 2015
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Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence
F. Pastawski, B. Yoshida, D. Harlow, and J. Preskill · 2015
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Asymptotic entanglement transformation between W and GHZ states
P. Vrana and M. Christandl · 2015
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The Clifford group forms a unitary 3-design
Z. Webb · 2015
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Bidirectional holographic codes and sub-ads locality
Z. Yang, P. Hayden, and X.-L. Qi · 2015
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B. Zeng, X. Chen, D.-L. Zhou, and X.-G. Wen · 2015
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The Mathematics of Entanglement
F. G. S. L. Brandao, M. Christandl, A. W. Harrow, and M. Walter · 2016
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H. Buhrman, M. Christandl, and J. Zuiddam · 2016
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Conditional mutual information of bipartite unitaries and scrambling
D. Ding, P. Hayden, and M. Walter · 2016
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Quantum entanglement of identical particles by standard information-theoretic notions
R. L. Franco and G. Compagno · 2016
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Holographic duality from random tensor networks
P. Hayden, Sepehr Nezami, X.-L. Qi, N. Thomas, M. Walter, and Z. Yang · 2016
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Multipartite entanglement in stabilizer tensor networks
S. Nezami and M. Walter · 2016
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Survey on nonlocal games and operator space theory
C. Palazuelos and T. Vidick · 2016
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The maximally entangled set of 4-qubit states
C. Spee, J. I. de Vicente, and B. Kraus · 2016
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Entanglement distillation from Greenberger-Horne-Zeilinger shares
P. Vrana and M. Christandl · 2016
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The Clifford group fails gracefully to be a unitary 4-design
H. Zhu, R. Kueng, M. Grassl, and D. Gross · 2016
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