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[MTQ1] F. Hirsch, M. T. Quintino, J. Bowles, and N. Brunner, “Genuine Hidden Quantum Nonlocality,”Physical Review Letters111,16(2013) 160402,arXiv:1307.4404 [quant-ph].

[MTQ2] J. Bowles, M. T. Quintino, and N. Brunner, “Certifying the Dimension of Classical and Quantum Systems in a

Prepare-and-Measure Scenario with Independent Devices,”Physical Review Letters112,14(2014)140407,arXiv:1311.1525 [quant-ph]. [MTQ3] J. Bowles, T. Vértesi, M. T. Quintino, and N. Brunner, “One-way

Einstein-Podolsky-Rosen Steering,”Physical Review Letters112,20 (2014)200402,arXiv:1402.3607 [quant-ph].

[MTQ4] M. T. Quintino, T. Vértesi, and N. Brunner, “Joint Measurability, Einstein-Podolsky-Rosen Steering, and Bell Nonlocality,”Phys. Rev.

Lett.113,16(2014)160402,arXiv:1406.6976 [quant-ph].

[MTQ5] J. Bowles, F. Hirsch, M. T. Quintino, and N. Brunner, “Local Hidden Variable Models for Entangled Quantum States Using Finite Shared Randomness,”Physical Review Letters114,12(2015)120401,

arXiv:1412.1416 [quant-ph].

[MTQ6] M. T. Quintino, T. Vértesi, D. Cavalcanti, R. Augusiak, M. Demianowicz, A. Acín, and N. Brunner, “Inequivalence of entanglement, steering, and Bell nonlocality for general

measurements,”Phys. Rev. A92,3(2015)032107,arXiv:1501.03332 [quant-ph].

[MTQ7] J. Bowles, F. Hirsch, M. T. Quintino, and N. Brunner, “Sufficient criterion for guaranteeing that a two-qubit state is unsteerable,”

Phys. Rev. A93,2(2016)022121,arXiv:1510.06721 [quant-ph]. [MTQ8] M. Túlio Quintino, J. Bowles, F. Hirsch, and N. Brunner,

“Incompatible quantum measurements admitting a local hidden variable model,”Phys. Rev. A93, (2016)052115.

http://link.aps.org/doi/10.1103/PhysRevA.93.052115.

78

LIST OF PUBLICATIONS DURING THE PHD 79 [MTQ9] F. Hirsch, M. Túlio Quintino, T. Vértesi, M. F. Pusey, and N. Brunner,

“Algorithmic construction of local hidden variable models for entangled quantum states,”ArXiv e-prints(2015) ,

arXiv:1512.00262 [quant-ph].

[MTQ10] F. Hirsch, M. Túlio Quintino, J. Bowles, T. Vértesi, and N. Brunner,

“Entanglement without hidden nonlocality,”ArXiv e-prints(2016) , arXiv:1606.02215 [quant-ph].

[MTQ11] R. Ramanathan, M. Túlio Quintino, A. Belén Sainz, G. Murta, and R. Augusiak, “On the tightness of correlation inequalities with no quantum violation,”ArXiv e-prints(2016) ,arXiv:1607.05714 [quant-ph].

Bibliography

[1] A. Einstein, B. Podolsky, and N. Rosen, “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?,”Phys. Rev.47, (1935)777–780.

[2] E. Schrödinger, “Probability relations between separated systems,”

Mathematical Proceedings of the Cambridge Philosophical Society32, (1936) 446–452.

http://journals.cambridge.org/article_S0305004100019137.

[3] J. S. Bell, “On the Einstein-Poldolsky-Rosen paradox,”Physics1,3(1964) 195–200.

[4] R. F. Werner, “Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model,”Phys. Rev. A40, (1989)4277–4281. [5] H. M. Wiseman, S. J. Jones, and A. C. Doherty, “Steering, Entanglement,

Nonlocality, and the Einstein-Podolsky-Rosen Paradox,”Phys. Rev. Lett.

98,14(2007)140402,quant-ph/0612147.

[6] W. Heisenberg, “Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen.,”Zeitschrift für Physik33,1(1925) 879–893.http://dx.doi.org/10.1007/BF01328377.

[7] L. A. Khalfin and B. S. Tsirelson, “Quantum and quasi-classical analogs of Bell inequalities,”Symposium on the Foundations of Modern Physics (1985)441–460.

[8] L. A. Khalfin and B. S. Tsirelson, “Quantum/classical correspondence in the light of Bell’s inequalities,”Foundations of physics22,7(1992)879–948. [9] M. M. Wolf, D. Perez-Garcia, and C. Fernandez, “Measurements

Incompatible in Quantum Theory Cannot Be Measured Jointly in Any Other No-Signaling Theory,”Physical Review Letters103,23(2009) 230402.

[10] M. Nielsen and I. Chuang,Quantum Computation and Quantum

Information. Cambridge Series on Information and the Natural Sciences.

Cambridge University Press,2000.

[11] J. Watrous, “Theory of Quantum Information.”

https://cs.uwaterloo.ca/~watrous/LectureNotes.html. 80

BIBLIOGRAPHY 81 [12] N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, “Bell

nonlocality,”Reviews of Modern Physics86, (2014)419–478, arXiv:1303.2849 [quant-ph].

[13] R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki,

“Quantum entanglement,”Reviews of Modern Physics81, (2009)865–942, quant-ph/0702225.

[14] O. Gühne and G. Tóth, “Entanglement detection,”Physics Reports474, (2009)1–75,arXiv:0811.2803 [quant-ph].

[15] R. Augusiak, M. Demianowicz, and A. Acín, “Local hidden–variable models for entangled quantum states,”Journal of Physics A: Mathematical and Theoretical47,42(2014)424002.

http://stacks.iop.org/1751-8121/47/i=42/a=424002.

[16] J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed Experiment to Test Local Hidden-Variable Theories,”Phys. Rev. Lett.23, (1969)880–884.

[17] G. Ziegler,Lectures on polytopes. Graduate texts in mathematics.

Springer-Verlag,1995.

http://books.google.com.br/books?id=xd25TXSSUcgC.

[18] J. B. Fourier, “Solution d’une Question Particulière du Calcul des Inégalités,”Nouveau Bulletin des Sciences par la Socieété Philomathique de Paris(1826)99.

[19] T. Motzkin, “Beitrage zur Theorie der linearen Ungleichungen.,”.

http://worldcat.org/oclc/79382233.

[20] http://www.iwr.uni-heidelberg.de/groups/comopt/software/PORTA. [21] http://www.ifor.math.ethz.ch/~fukuda/cdd_home/index.html. [22] http://www.ifor.math.ethz.ch/~fukuda/polyfaq/polyfaq.html. [23] I. Pitowsky, “Correlation polytopes: Their geometry and complexity,”

Mathematical Programming50,1(1991)395–414. http://dx.doi.org/10.1007/BF01594946.

[24] A. Fine, “Hidden Variables, Joint Probability, and the Bell Inequalities,”

Phys. Rev. Lett.48, (1982)291–295.

[25] P. Rastall, “Locality, Bell’s theorem, and quantum mechanics,”

Foundations of Physics15, (1985)963–972.

[26] B. S. Tsirelson, “Some results and problems on quantum Bell-type inequalities,”Hadronic Journal Supplement8,4(1993)329–345. [27] D. Rohrlich and S. Popescu, “Nonlocality as an axiom for quantum

theory,”eprint arXiv:quant-ph/9508009(1995) ,quant-ph/9508009.

BIBLIOGRAPHY 82 [28] A. Acín, N. Brunner, N. Gisin, S. Massar, S. Pironio, and V. Scarani,

“Device-Independent Security of Quantum Cryptography against Collective Attacks,”Physical Review Letters98,23(2007)230501, quant-ph/0702152.

[29] S. Pironio, A. Acín, S. Massar, A. B. de La Giroday, D. N. Matsukevich, P. Maunz, S. Olmschenk, D. Hayes, L. Luo, T. A. Manning, and

C. Monroe, “Random numbers certified by Bell’s theorem,”Nature464, (2010)1021–1024,arXiv:0911.3427 [quant-ph].

[30] A. Aspect, J. Dalibard, and G. Roger, “Experimental Test of Bell’s Inequalities Using Time- Varying Analyzers,”Phys. Rev. Lett.49, (1982) 1804–1807.http://link.aps.org/doi/10.1103/PhysRevLett.49.1804. [31] G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger,

“Violation of Bell’s Inequality under Strict Einstein Locality Conditions,”

Phys. Rev. Lett.81, (1998)5039–5043.

http://link.aps.org/doi/10.1103/PhysRevLett.81.5039. [32] M. A. Rowe, D. Kielpinski, V. Meyer, C. A. Sackett, W. M. Itano,

C. Monroe, and D. J. Wineland, “Experimental violation of a Bell’s inequality with efficient detection,”Nature409, (2001)791–794. [33] D. N. Matsukevich, P. Maunz, D. L. Moehring, S. Olmschenk, and

C. Monroe, “Bell Inequality Violation with Two Remote Atomic Qubits,”

Physical Review Letters100,15(2008)150404,arXiv:0801.2184 [quant-ph].

[34] B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3km,”Nature526, (2015)682–686,arXiv:1508.05949 [quant-ph]. [35] L. K. Shalm, E. Meyer-Scott, B. G. Christensen, P. Bierhorst, M. A. Wayne,

M. J. Stevens, T. Gerrits, S. Glancy, D. R. Hamel, M. S. Allman, K. J.

Coakley, S. D. Dyer, C. Hodge, A. E. Lita, V. B. Verma, C. Lambrocco, E. Tortorici, A. L. Migdall, Y. Zhang, D. R. Kumor, W. H. Farr, F. Marsili, M. D. Shaw, J. A. Stern, C. Abellán, W. Amaya, V. Pruneri, T. Jennewein, M. W. Mitchell, P. G. Kwiat, J. C. Bienfang, R. P. Mirin, E. Knill, and S. W.

Nam, “Strong Loophole-Free Test of Local Realism,”Physical Review Letters115,25(2015)250402,arXiv:1511.03189 [quant-ph].

[36] M. Giustina, M. A. M. Versteegh, S. Wengerowsky, J. Handsteiner, A. Hochrainer, K. Phelan, F. Steinlechner, J. Kofler, J.-Å. Larsson, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, J. Beyer, T. Gerrits, A. E. Lita, L. K. Shalm, S. W. Nam, T. Scheidl, R. Ursin, B. Wittmann, and A. Zeilinger, “Significant-Loophole-Free Test of Bell’s Theorem with Entangled Photons,”Physical Review Letters115,25(2015)250401, arXiv:1511.03190 [quant-ph].

BIBLIOGRAPHY 83 [37] E. G. Cavalcanti, S. J. Jones, H. M. Wiseman, and M. D. Reid,

“Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox,”Phys. Rev. A80,3(2009)032112,arXiv:0907.1109 [quant-ph].

[38] https://en.wikipedia.org/wiki/Hyperplane_separation_theorem. [39] M. F. Pusey, “Negativity and steering: A stronger Peres conjecture,”

Phys. Rev. A88,3(2013)032313.

[40] P. Skrzypczyk, M. Navascués, and D. Cavalcanti, “Quantifying

Einstein-Podolsky-Rosen Steering,”Physical Review Letters112,18(2014) 180404,arXiv:1311.4590 [quant-ph].

[41] N. Gisin, “Bell’s inequality holds for all non-product states,”Physics Letters A154,5–6(1991)201–202.

[42] J. Barrett, “Nonsequential positive-operator-valued measurements on entangled mixed states do not always violate a Bell inequality,”Phys.

Rev. A65,4(2002)042302.

[43] A. Acín, N. Gisin, and B. Toner, “Grothendieck’s constant and local models for noisy entangled quantum states,”Phys. Rev. A73,6(2006) 062105,quant-ph/0606138.

[44] M. Horodecki, P. Horodecki, and R. Horodecki, “General teleportation channel, singlet fraction, and quasidistillation,”Phys. Rev. A60, (1999) 1888–1898,arXiv:quant-ph/9807091.

[45] M. L. Almeida, S. Pironio, J. Barrett, G. Tóth, and A. Acín, “Noise Robustness of the Nonlocality of Entangled Quantum States,”Phys. Rev.

Lett.99,4(2007)040403.

[46] S. Jevtic, M. J. W. Hall, M. R. Anderson, M. Zwierz, and H. M. Wiseman,

“Einstein-Podolsky-Rosen steering and the steering ellipsoid,”Journal of the Optical Society of America B Optical Physics32,27(2015) A40,

arXiv:1411.1517 [quant-ph].

[47] H. Chau Nguyen and T. Vu, “Necessary and sufficient condition for steerability of two-qubit states by the geometry of steering outcomes,”

ArXiv e-prints(2016) ,arXiv:1604.03815 [quant-ph]. [48] D. J. Saunders, S. J. Jones, H. M. Wiseman, and G. J. Pryde,

“Experimental EPR-steering using Bell-local states,”Nature Physics6, (2010)845–849,arXiv:0909.0805 [quant-ph].

[49] T. Vértesi and E. Bene, “Two-qubit Bell inequality for which positive operator-valued measurements are relevant,”Phys. Rev. A82,6(2010) 062115,arXiv:1007.2578 [quant-ph].

[50] S. L. W. Midgley, A. J. Ferris, and M. K. Olsen, “Asymmetric Gaussian steering: When Alice and Bob disagree,”Phys. Rev. A81,2(2010)022101, arXiv:0906.4851 [quant-ph].

BIBLIOGRAPHY 84 [51] V. Händchen, T. Eberle, S. Steinlechner, A. Samblowski, T. Franz, R. F.

Werner, and R. Schnabel, “Observation of one-way

Einstein-Podolsky-Rosen steering,”Nature Photonics6, (2012)598–601, arXiv:1206.4446 [quant-ph].

[52] R. Werner, “Steering, or maybe why Einstein did not go all the way to Bell’s argument,”Journal of Physics A: Mathematical and Theoretical47,42 (2014)424008.

[53] G. Mauro D’Ariano, P. Lo Presti, and P. Perinotti, “Classical randomness in quantum measurements,”Journal of Physics A Mathematical General38, (2005)5979–5991.

[54] R. Gallego and L. Aolita, “Resource Theory of Steering,”Physical Review X5,4(2015)041008,arXiv:1409.5804 [quant-ph].

[55] A. Peres, “Separability Criterion for Density Matrices,”Physical Review Letters77, (1996)1413–1415,quant-ph/9604005.

[56] M. Horodecki, P. Horodecki, and R. Horodecki, “Separability of mixed states: necessary and sufficient conditions,”Physics Letters A223, (1996) 1–8,quant-ph/9605038.

[57] A. Acín, R. Augusiak, D. Cavalcanti, C. Hadley, J. K. Korbicz, M. Lewenstein, L. Masanes, and M. Piani, “Unified Framework for Correlations in Terms of Local Quantum Observables,”Physical Review Letters104,14(2010)140404,arXiv:0911.3606 [quant-ph].

[58] H. Barnum, S. Beigi, S. Boixo, M. B. Elliott, and S. Wehner, “Local Quantum Measurement and No-Signaling Imply Quantum Correlations,”

Physical Review Letters104,14(2010)140401,arXiv:0910.3952 [quant-ph].

[59] D. Cariello, “An Elementary Description of the Positive Maps with Positive Inverse,”CNMAC12.

www.sbmac.org.br/eventos/cnmac/xxxiv_cnmac/pdf/541.pdf. [60] M. M. Wolf,Quantum Channels and Operations.2012.

http://www.m5.ma.tum.de/foswiki/pub/M5/Allgemeines/

MichaelWolf/QChannelLecture.pdf.

[61] C. H. Bennett, D. P. Divincenzo, and J. A. Smolin, “Capacities of

Quantum Erasure Channels,”Physical Review Letters78, (1997)3217–3220, quant-ph/9701015.

[62] P. Skrzypczyk and D. Cavalcanti, “Loss-tolerant

Einstein-Podolsky-Rosen steering for arbitrary-dimensional states: Joint measurability and unbounded violations under losses,”Phys. Rev. A92, 2(2015)022354,arXiv:1502.04926 [quant-ph].

BIBLIOGRAPHY 85 [63] R. Horodecki, P. Horodecki, and M. Horodecki, “Violating Bell inequality

by mixed spin-12states: necessary and sufficient condition,”Physics Letters A200,5(1995)340–344.http:

//www.sciencedirect.com/science/article/pii/037596019500214N. [64] S. Wollmann, N. Walk, A. J. Bennet, H. M. Wiseman, and G. J. Pryde,

“Observation of Genuine One-Way Einstein-Podolsky-Rosen Steering,”

Physical Review Letters116,16(2016)160403,arXiv:1511.01231 [quant-ph].

[65] J. Bavaresco,When Bob cannot trust Alice A semi-device independent tale of quantum steering. PhD thesis, Master Thesis,2016,2016.

[66] C. Branciard, E. G. Cavalcanti, S. P. Walborn, V. Scarani, and H. M.

Wiseman, “One-sided device-independent quantum key distribution:

Security, feasibility, and the connection with steering,”Phys. Rev. A85,1 (2012)010301,arXiv:1109.1435 [quant-ph].

[67] V. Varadarajan,Geometry of Quantum Theory. Springer,1985. [68] P. Busch, P. Lahti, and P. Mittelstaedt,The Quantum Theory of

Measurement. No. v.2in Environmental Engineering. Springer,1996. [69] W. Son, E. Andersson, S. M. Barnett, and M. S. Kim, “Joint

measurements and Bell inequalities,”Phys. Rev. A72,5(2005)052116. [70] E. Andersson, S. M. Barnett, and A. Aspect, “Joint measurements of spin,

operational locality, and uncertainty,”Phys. Rev. A72,4(2005)042104. [71] K. Kraus, A. Böhm, J. Dollard, and W. Wootters,States, effects, and

operations: fundamental notions of quantum theory : lectures in mathematical physics at the University of Texas at Austin. Lecture notes in physics.

Springer-Verlag,1983.

https://books.google.ch/books?id=fRBBAQAAIAAJ.

[72] T. Heinosaari, D. Reitzner, and P. Stano, “Notes on Joint Measurability of Quantum Observables,”Foundations of Physics38, (2008)1133–1147. [73] R. Uola, T. Moroder, and O. Gühne, “Joint Measurability of Generalized

Measurements Implies Classicality,”Phys. Rev. Lett.113,16(2014) 160403,arXiv:1407.2224 [quant-ph].

[74] S. T. Ali, C. Carmeli, T. Heinosaari, and A. Toigo, “Commutative POVMs and Fuzzy Observables,”Foundations of Physics39, (2009)593–612, arXiv:0903.0523 [quant-ph].

[75] T. Heinosaari and M. M. Wolf, “Nondisturbing quantum measurements,”

Journal of Mathematical Physics51,9(2010)092201–092201, arXiv:1005.5659 [quant-ph].

[76] D. Reeb, D. Reitzner, and M. M. Wolf, “Coexistence does not imply joint measurability,”Journal of Physics A Mathematical General46, (2013) 462002,arXiv:1307.6986 [quant-ph].

BIBLIOGRAPHY 86 [77] V. Heinosaari and M. Ziman,The Mathematical Language of Quantum

Theory. Cambridge University Press,2012.

http://www.cambridge.org/us/academic/subjects/physics/

quantum-physics-quantum-information-and-quantum-computation/

mathematical-language-quantum-theory-uncertainty-entanglement?

format=HB.

[78] P. Busch, “Unsharp reality and joint measurements for spin observables,”

Phys. Rev. D33, (1986)2253–2261.

http://link.aps.org/doi/10.1103/PhysRevD.33.2253.

[79] S. Yu, N. Liu, L. Li, and C. H. Oh, “Joint measurement of two unsharp observables of a qubit,”ArXiv e-prints(2008) ,arXiv:0805.1538 [quant-ph].

[80] R. Uola, C. Budroni, O. Gühne, and J.-P. Pellonpää, “One-to-One Mapping between Steering and Joint Measurability Problems,”Physical Review Letters115,23(2015)230402,arXiv:1507.08633 [quant-ph]. [81] D. Cavalcanti, P. Skrzypczyk, G. H. Aguilar, R. V. Nery, P. H. S. Ribeiro,

and S. P. Walborn, “Detection of entanglement in asymmetric quantum networks and multipartite quantum steering,”Nature Communications6, (2015)7941,arXiv:1412.7730 [quant-ph].

[82] Y.-C. Liang, R. W. Spekkens, and H. M. Wiseman, “Specker’s parable of the overprotective seer: A road to contextuality, nonlocality and

complementarity,”Phys. Rep.506, (2011)1–39,arXiv:1010.1273 [quant-ph].

[83] D. Rosset and J.-D. Bancal, “FAACETS.” http://www.faacets.com/. [84] T. Vértesi and K. F. Pál, “Bounding the dimension of bipartite quantum

systems,”Physical Review A79,4(2009)042106,arXiv:0812.1572 [quant-ph].

[85] J. Krivine, “Constantes de Grothendieck et fonctions de type positif sur les sphères,”Advances in Mathematics31,1(1979)16–30.http:

//www.sciencedirect.com/science/article/pii/0001870879900173. [86] M. Navascués and D. Pérez-García, “Quantum Steering and Spacelike

Separation,”Physical Review Letters109,16(2012)160405.

[87] N. Gisin, “Stochastic Quantum Dynamics and Relativity,”Helvetica Physica Acta62,4(1989)363–371.

[88] L. P. Hughston, R. Jozsa, and W. K. Wootters, “A complete classification of quantum ensembles having a given density matrix,”Physics Letters A 183,1(1993)14–18.

[89] D. Collins and N. Gisin, “A relevant two qubit Bell inequality

inequivalent to the CHSH inequality,”Journal of Physics A Mathematical General37, (2004)1775–1787.

BIBLIOGRAPHY 87 [90] C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K.

Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,”Phys. Rev. Lett.70, (1993)1895–1899. http://link.aps.org/doi/10.1103/PhysRevLett.70.1895.

[91] A. Peres, “Collective tests for quantum nonlocality,”Phys. Rev. A54, (1996)2685–2689.

[92] Y.-C. Liang and A. C. Doherty, “Better Bell-inequality violation by collective measurements,”Physical Review A73,5(2006)052116, quant-ph/0604045.

[93] M. Navascués and T. Vértesi, “Activation of Nonlocal Quantum Resources,”Physical Review Letters106,6(2011)060403,

arXiv:1010.5191 [quant-ph].

[94] M. Junge, C. Palazuelos, D. Pérez-García, I. Villanueva, and M. M. Wolf,

“Unbounded Violations of Bipartite Bell Inequalities via Operator Space Theory,”Communications in Mathematical Physics300, (2010)715–739, arXiv:0910.4228 [quant-ph].

[95] C. Palazuelos, “Superactivation of Quantum Nonlocality,”Physical Review Letters109,19(2012)190401.

[96] D. Cavalcanti, A. Acín, N. Brunner, and T. Vértesi, “All quantum states useful for teleportation are nonlocal resources,”Phys. Rev. A87,4(2013) 042104,arXiv:1207.5485 [quant-ph].

[97] S. A. Khot and N. K. Vishnoi, “The Unique Games Conjecture,

Integrality Gap for Cut Problems and Embeddability of Negative Type Metrics into`_1,”ArXiv e-prints(2013) ,arXiv:1305.4581 [cs.CC]. [98] H. Buhrman, O. Regev, G. Scarpa, and R. de Wolf, “Near-Optimal and

Explicit Bell Inequality Violations,”Proceedings of IEEE Complexity(2011) , arXiv:1012.5043 [quant-ph].

[99] M. Horodecki and P. Horodecki, “Reduction criterion of separability and limits for a class of protocols of entanglement distillation,”eprint arXiv:quant-ph/9708015(1997) ,quant-ph/9708015.

[100] A. Müller-Hermes, D. Reeb, and M. M. Wolf, “Positivity of linear maps under tensor powers,”Journal of Mathematical Physics57,1(2016)015202, arXiv:1502.05630 [quant-ph].

[101] C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels,”Physical Review Letters76, (1996) 722–725,quant-ph/9511027.

[102] M. Horodecki, P. Horodecki, and R. Horodecki, “Mixed-State Entanglement and Distillation: Is there a “Bound” Entanglement in Nature?,”Physical Review Letters80, (1998)5239–5242,

quant-ph/9801069.

BIBLIOGRAPHY 88 [103] T. Moroder, O. Gittsovich, M. Huber, and O. Gühne, “Steering Bound

Entangled States: A Counterexample to the Stronger Peres Conjecture,”

Phys. Rev. Lett.113,5(2014)050404,arXiv:1405.0262 [quant-ph]. [104] T. Vértesi and N. Brunner, “Disproving the Peres conjecture by showing

Bell nonlocality from bound entanglement,”Nature Communications5, (2014)5297,arXiv:1405.4502 [quant-ph].

[105] C. H. Bennett, D. P. Divincenzo, J. A. Smolin, and W. K. Wootters,

“Mixed-state entanglement and quantum error correction,”Physical Review A54, (1996)3824–3851,quant-ph/9604024.

[106] I. Devetak and A. Winter, “Distillation of secret key and entanglement from quantum states,”Proceedings of the Royal Society of London Series A 461, (2005)207–235,quant-ph/0306078.

[107] J. von Neumann,Mathematische Grundlagen der Quantenmechanik. “Die”

Grundlehren der mathematischen Wissenschaften / “Die” Grundlehren der mathematischen Wissenschaften. Springer,1996.

https://books.google.de/books?id=HFHjkEjJyKIC.

Appendix A

Papers published in the course of