Thesis On the device-independent approach to quantum physics : advances in quantum nonlocality and multipartite entanglement detection BANCAL, Jean-Daniel Abstract La physique quantique a participé au développement de nombreux domaines, qu'il s'agisse de l'informatique en permettant de traiter l'information électroniquement à l'aide de transistors, des communications, rendues possibles à grande échelle par la lumière laser guidée dans des fibre optique, ou bien de la médecine par les méthodes d'imagerie par résonnance magnétique nucléaire. Qui eut cru que l'hypothèse quantique formulée par Max Planck à l'aube du 20ème siècle aurait, de fil en aiguille, de telles répercussions? Malgré cela, la physique quantique reste encore passablement mystérieuse. L'un de ses aspects les plus intriguants étant sans doute son charactère nonlocal, c'est-à-dire sa capacité à violer des inégalités de Bell à l'aide de systèmes isolés les uns des autres. Reference BANCAL, Jean-Daniel. On the device-independent approach to quantum physics : advances in quantum nonlocality and multipartite entanglement detection. Thèse de doctorat : Univ. Genève, 2012, no. Sc. 4419 URN : urn:nbn:ch:unige-217102 DOI : 10.13097/archive-ouverte/unige:21710 Available at: http://archive-ouverte.unige.ch/unige:21710 Disclaimer: layout of this document may differ from the published version. 1 / 1 UNIVERSITE´ DE GENEVE` FACULTE´ DES SCIENCES Groupe de Physique Appliqu´ee - Optique Prof. N. Gisin ON THE DEVICE-INDEPENDENT APPROACH TO QUANTUM PHYSICS ADVANCES IN QUANTUM NONLOCALITY AND MULTIPARTITE ENTANGLEMENT DETECTION THESE` pr´esent´ee`ala Facult´edes Sciences de l'Universit´ede Gen`eve pour obtenir le grade de Docteur `esSciences, mention Physique par Jean-Daniel Bancal de Meyrin (GE) Th`eseN◦ 4419 GENEVE` Atelier d'impression ReproMail 2012 R´esum´e La physique quantique a particip´eau d´eveloppement de nombreux domaines, qu'il s'agisse de l'informatique en permettant de traiter l'information ´electroniquement `al'aide de transistors, des communications, rendues possibles `agrande ´echelle par la lumi`ere laser guid´eedans des fibre optique, ou bien de la m´edecine par les m´eth- odes d'imagerie par r´esonnance magn´etique nucl´eaire. Qui eut cru que l'hypoth`ese quantique formul´eepar Max Planck `al'aube du 20`eme si`ecle aurait, de fil en aiguille, de telles r´epercussions? Malgr´ecela, la physique quantique reste encore passablement myst´erieuse. L'un de ses aspects les plus intriguants ´etant sans doute son charact`ere nonlocal, c'est- `a-dire sa capacit´e`avioler des in´egalit´esde Bell `al'aide de syst`emes isol´esles uns des autres. Une telle violation sugg`ere en effet que ces syst`emes sont causalement reli´es,ce qui semble contredire le fait qu'ils soient mutuellement s´epar´es. La mani`ere directe avec laquelle la nonlocalit´equantique appara^ıt dans des r´esultats exp´erimentaux lui permet d'^etre test´eeen faisant appel `aun minimum d'hypoth`eses. En particulier, aucune erreur de calibration sur des appareils de mesure individuels ne peut remettre en cause le r´esultat d'une telle exp´erience. Cette robustesse face aux erreurs d'impl´ementation, qui sont inh´erentes `atoute manipulation exp´erimentale, ouvre la voie vers de nouvelles approches exp´erimen- tales. En effet elle montre qu'il est possible de r´epondre `acertaines questions en faisant appel `avirtuellement aucune hypoth`ese du moment que les syst`emes mesur´es sont suffisamment s´epar´esles uns des autres. A quelles questions peut-on r´epondre de cette fa¸con-l`a? A quoi peut servir la violation d'une in´egalit´ede Bell en g´en´eral? Mais aussi, comment la nature s'y prend-elle pour violer une in´egalit´ede Bell? Et quelles sont les limites de la nonlocalit´equantique? Voici quelques-unes des questions abord´ees par cette th`ese. iii Contents Introduction 1 1 Bell tests in bipartite scenarios 5 1.1 No-signalling and local causality . .5 1.1.1 Local correlations . .5 1.1.2 No-signalling correlations . .7 1.1.3 Geometrical representation . .7 1.1.4 Experimental loopholes . .8 1.2 Bell test between an atom and an optical mode . .9 1.2.1 Creating atom-photon entanglement . .9 1.2.2 CHSH violation . 10 1.2.3 Space-like separation . 11 1.2.4 Conclusion . 11 1.3 Bell test with multiple pairs . 12 1.3.1 Two sources . 12 1.3.2 Noise model . 13 1.3.3 Bell violation . 14 1.4 Experimental violation of Bell inequalities with a commercial source of entanglement . 14 1.4.1 Experimental setup . 14 1.4.2 Test of several Bell inequalities . 15 1.4.3 Chained Bell inequality . 15 1.4.4 Conclusion . 17 2 Nonlocality with three and more parties 19 2.1 Defining genuine multipartite nonlocality . 19 2.2 Multipartite Bell-like inequalities . 21 2.2.1 A general structure for (n; m; k) scenarios . 21 2.2.2 Recursion relation . 22 2.3 Nonlocality from local marginals . 24 2.3.1 An inequality . 25 2.3.2 Conclusion . 25 2.4 Tripartite nonlocal boxes . 26 2.4.1 The tripartite nosignalling polytope . 26 2.4.2 Conclusion . 26 2.5 A tight limit on quantum nonlocality . 26 2.5.1 Can you guess your neighbour's input (GYNI)? . 26 2.5.2 Outlook . 27 2.6 Simulating projective measurements on the GHZ state . 28 v CONTENTS 2.6.1 Nonlocal resources . 28 2.6.2 Simulation . 28 2.6.3 Conclusion . 29 3 Device-independent entanglement detection 31 3.1 Imperfect measurements . 31 3.1.1 Effects of systematic errors on tomography . 32 3.1.2 Effects of systematic errors on entanglement witnesses . 32 3.2 Witnesses insensitive to systematic errors? . 33 3.2.1 Device-independent witnesses for genuine tripartite entanglement . 34 3.2.2 A witness for genuine multipartite entanglement . 34 3.3 Experimental demonstration . 35 3.3.1 Experimental setup and procedure . 35 3.3.2 Addressing errors . 36 3.3.3 Experimental results . 37 3.4 Conclusion . 37 4 Quantum information put into practice 39 4.1 Memoryless attack on the 6-state QKD protocol . 39 4.1.1 The 6-state protocol . 39 4.1.2 Secret key rate . 40 4.1.3 Discussion . 41 4.2 Private database queries . 42 4.2.1 Sketch of the protocol . 42 4.2.2 Discussion . 43 5 Finite-speed hidden influences 45 5.1 Finite-speed propagation and v-causal theories . 45 5.1.1 v-causal models and experimental limitations . 46 5.1.2 Influences without communication? . 47 5.2 The hidden influence polytope . 47 5.2.1 Quantum violation and faster-than-light communication . 49 5.3 Experimental perspectives . 50 5.4 Conclusion . 51 Conclusion and outlook 53 Acknowledgements 55 Bibliography 57 A Polytopes 63 A.1 Definition and terminology . 63 A.2 Some operations on polytopes . 64 A.2.1 Projection . 64 A.2.2 Slice . 66 A.2.3 Another tasks : finding facets lying under an inequality . 66 B Memoryless attack on the 6-state protocol { proof 67 Papers 71 vi Introduction From its beginning in the 1920's quantum physics has challenged our understanding of the world. Particles that could be conceived previously as points turned out to be provided with a wave evolving in time according to a law of motion. This conceptual change allowed for previously unsuspected phenomenons to be observed, like for instance the interference of a molecule with itself demonstrated several times experimentally (e.g. with C60 molecules in [1]). If the quantum theory is recognized for its extraordinary predictive power, the picture of the world that it suggests is not the subject of a common agreement. For instance, the question of whether the wavefunction , a fundamental ingredient of the theory, should j i be understood as a proper physical object, i.e. a physical property of every quantum system, or rather as a tool from the theory which is only useful to predict the evolution of physically relevant objects, is still an active subject of research [2, 3, 4, 5]. One could argue that questions about the possible interpretation of the elements of the quantum theory are of secondary importance, provided that predictions match exper- imental results. But that would be putting aside the possibility for such considerations to reveal fundamental properties of nature. For instance, the quantum measurement pro- cess is commonly understood as an instantaneous change of the wavefunction throughout all space. If this process is indeed instantaneous, and if the wavefunction is a physical object, then measurement of a quantum system is a strongly nonlocal phenomenon, and one should expect physical quantities to be the subject of such instantaneous change at a distance. On the other hand, if the wavefunction can be understood as a tool of the the- ory, without a concrete physical counterpart, then the nonlocal character of this process might just be an artifact of the theory, without direct incidence on physically relevant quantities. Since a proper understanding of the elements of the quantum theory seems difficult to reach without invoking arguable choices of additional assumptions, and since only properties of nature that can have a measurable impact are worth discussing anyway, we ask what properties of quantum physics can be detected directly from experimental data, without relying on more assumptions than the ones needed in order to make sense out of these data. In this way, we hope to be able to explore properties of quantum physics more directly. Moreover, we can expect to be able to check these properties on nature directly, because we follow an approach which fundamentally relies on experimental results.