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**University of Waterloo**

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I am working on operational approaches to Quantum Theory, General Relativity, and Quantum Gravity. Specifically I have developed an operational framework in which Quantum Theory and General Relativity can be formulated. Ultimately, I hope to formulate Quantum Gravity in this framework.

In 2001 I developed an operational probabilistic approach that provided the basis for a set of "reasonable axioms" from which the usual rules of Quantum Theory can be derived. In 2010 I further developed this framework as a diagrammatic calculus, the duotensor formalism, for general circuits. In 2011 I used this framework to provide a reformulation of Quantum Theory - the operator tensor formulation and, also, provided a new set of reasonable axioms from which Quantum Theory can be reconstructed.

The operator tensor reformulation motivated taking a look at the issue of composition in physics. Typically, when we study a physical object, we regard it as being built out of small objects joined together in a particular way. In 2013 I wrote a paper providing a more general theory for the use of composition in physics. Such ideas of composition may play a role across different fields in physics.

Most recently (2016), I have shown how to use ideas of composition to provide an operational reformulation of General Relativity. This requires, first of all, making an assertion as to what the directly observable quantities are. For this I nominate a set of scalar fields and consider point coincidences in their values. This provides an operational space (or op-space). We can consider regions of op-space and how to glue together solutions corresponding to such regions. This leads to a diagrammatic calculus of the same nature as that used in the operator tensor formulation of Quantum Theory. This operational reformulation of General Relativity naturally suggests approaches to solving the problem of Quantum Gravity.

- 1997-2002 Royal Society University Research Fellow, University of Oxford
- 1996-1997 Postdoctoral position at La Sapienza University, Rome, Italy.
- 1994-1996 Lecturer in Mathematical Sciences Department, University of Durham, UK
- 1993-1994 Royal Society postdoctoral fellow at the University of Innsbruck, Austria
- 1992-1993 Lecturer in Mathematical Physics, Maynooth College, The National University of Ireland.

- Hardy, L. Quantum theory with bold operator tensors. Phil. Trans. R. Soc. A, 373(2047), 20140239. (2015)
- Hardy, L. Bell's theorem with retarded settings. To be published in Quantum [Un]Speakables II: 50 Years of Bell's Theorem, edited by Anton Zeilinger and Reinhold Bertlmann.
- On the theory of composition in physics , in Computation, Logic, Games, and Quantum Foundations. The Many Facets of Samson Abramsky. Lecture Notes in Computer Science Volume 7860, 2013, pp 83-106
- Hardy, L The operator tensor formulation of quantum theory, Phil. Trans. R. Soc. A 28 vol. 370 no. 1971 pages 3385-3417 (special issue in honour of Alan Turing) (2012) also at arXiv: 1201.4390.
- Abramsky, S., and Hardy, L. Logical Bell inequalities, Phys. Rev. A 85, 062114 (2012) [11 pages] also at arXiv: 1203.1352
- Genkina, D., Chiribella, G., and Hardy, L. Optimal Probabilistic Simulation of Quantum Channels from the Future to the Past, Phys. Rev. A 85, 022330 (2012) also in arXiv: 1112.1469
- Hardy, L., and Wootters, W. K., Limited holism and real vector space quantum theory, Volume 42, Number 3 (2012), 454-473.
- Towards Quantum Gravity: A Framework for Probabilistic Theories with Non-Fixed Causal Structure}, J. Phys. A 40, 3081 (2007), gr-qc/0608043.
- Hardy, L; Kent, A; {\sl Cheat sensitive quantum bit commitment}, Phys. Rev. Lett. 92, 157901 (2004).
- Hardy, L; {\sl Quantum ontological excess baggage}, Stud. Hist. Phil. Sci. B 35 267 (2004)
- Jonathan Barrett (Universite Libre de Bruxelles), Lucien Hardy (Perimeter Institute), Adrian Kent (Centre for Quantum Computation, DAMTP, University of Cambridge), No Signalling and Quantum Key Distribution, Phys. Rev. Lett. 95, 010503 (2005), arxiv:quant-ph/405101
- Galvao, E; Hardy, L; Substituting a qubit for an arbitrarily large number of classical bits, Phys. Rev. Lett. 90, 087902 (2003)
- Walgate, J; Hardy, L; Nonlocality, asymmetry, and distinguishing bipar- tite states, Phys. Rev. Lett. 89 147901 (2002).
- Walgate, J; Short, AJ; Hardy, L; Vedral,V. Local Distinguishability of Multipartite Orthogonal Quantum States Authors, Phys. Rev. Lett. 85, 4972 (2000).
- Hardy, L; Song, DD. Entanglement swapping chains for general pure states, Phys. Rev. A 62, 052315 (2000).
- Kwiat, PG; Hardy, L. The mystery of the quantum cakes, Amer. J. Phys. 68, 33 (2000).
- Boschi, D; Branca, S; De Martini, F; Hardy, L; Popescu, S. Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels, Phys. Rev. Lett. 80, 1121 (1998).
- Blasi, B; Hardy, L. Realism and time symmetry in quantum mechanics, Phys. Lett. A 207, 3 (1995).
- Hardy, L. Nonlocality of a single-photon revisited, Phys. Rev. Lett. 73, 2279 (1994).
- Hardy, L. Nonlocality for 2 particles without inequalities for almost-all entangled states, Phys. Rev. Lett. 71, 1665 (1993).
- Hardy, L. On the existence of empty waves in quantum-theory - reply, Phys. Lett. A 175, 259 (1993).
- Hardy, L. On the existence of empty waves in quantum-theory, Phys. Lett. A 167, 11 (1992).
- Hardy, L. Quantum-mechanics, local realistic theories, and lorentz- in- variant realistic theories, Phys. Rev. Lett. 68, 2981 (1992).
- Hardy, L. Can classical wave theory explain the photon anticorrelation e(R)ect on a beam splitter, Europhys. Lett. 15, 591 (1991).
- Operational General Relativity: Possibilistic, Probabilistic, and Quantum, Lucien Hardy, arXiv: 1608.06940
- Reformulating and reconstructing quantum theory, arXiv: 1104.2066
- A formalism-local framework for general probabilistic theories including quantum theory, Lucien Hardy, arXiv: 1005.5164
- Why Physics Needs Quantum Foundations, Lucien Hardy and Robert Spekkens arXiv: 1003.5008
- Foliable Operational Structures for General Probabilistic Theories, arXiv: 0912.4740
- Entropy for theories with indefinite causal structure, Sonia Markes and Lucien Hardy, arXiv: 0910.1323
- Probability Theories with Dynamic Causal Structure: A New Framework for Quantum Gravity, Lucien Hardy, arxiv:gr-qc/509120
- Quantum Theory from five reasonable axioms, Lucien Hardy, arXiv: quant-ph/0101012
- Disentangling nonlocality and teleportation, Lucien Hardy, arXiv: quant-ph/9906123
- Quantum gravity computers: On the theory of computation with indefinite causal structure}, quant-ph/0701019, for proceedings of "Quantum Reality, Relativistic Causality, and Closing the Epistemic Circle: An International Conference in Honour of Abner Shimony" (2007).
- Hardy, L; Quantum gravity computers: On the theory of computation with inde?nite causal structure, quant-ph/0701019, for proceedings of "Quantum Reality, Relativistic Causality, and Closing the Epistemic Circle: An International Conference in Honour of Abner Shimony" (2007).
- Reconstructing quantum theory in "Quantum Theory: Informational Foundations and Foils" edited by Guilio Chiribella and Robert Spekkens (2016)
- Formalism Locality in Quantum Theory and Quantum Gravity, (also at arXiv: 0804.0054), To appear in "Philosophy of Quantum Information and Entanglement" Eds A. Bokulich and G. Jaeger (CUP).
- Why is nature described by quantum theory? in Science and Ultimate Reality, eds. John Barrow, Paul Davies, and Charles Harper, (Cambridge, 2004).

- Operational Road to Quantum Gravity, at Information-Theoretic Interpretations of Quantum Mechanics: 2016 Annual Philosophy of Physics Conference, University of Western Ontario, London.
- Probabilistic General Relativity with Agency in an Operational Framework, at Quantum Probability and Logic 2015, Oxford (invited speaker).
- Steps on route to Probabilistic General Relativity with Agency (PAGeR), at Materials Department, University of Oxford.
- Duotensors, operator tensors, and quantum theory, at the workshop "New geometric concepts in the foundations of quantum physics" held at Chicheley Hall, England.
- Operationalism, probabilities, agency, and composition on the road to quantum gravity, at the QMAC(Quantum Mathematics and Computation) symposium for the opening of the Clay Building in Oxford.
- On the theory of composition in physics, Computer science department
- The operator tensor formulation of quantum theory, Materials department, Oxford
- On the theory of composition in physics, Physics department, Imperial College
- On the theory of composition in physics, Askloster at Oxford (workshop)
- operational approach to quantum theory, Quantum Foundations Workshop at Bellairs, Barbados
- The operator tensor formulation of quantum theory, Q+ hangout.
- Reformulating quantum theory, Department of Computer Science, Oxford
- Reformulating quantum theory, Materials Department, Oxford
- Quantum Theory from reasonable postulates, at New frontiers in quantum foundations, CUPI 2011, Clemson, South Carolina.
- Why we should consider situating the de Broglie-Bohm model in the context of a much more general framework for hidden variable theories, 21st-Century directions in de Broglie-Bohm theory and beyond, The Towler Institute, Vallico Sotto, Tuscany, Italy.
- Operational Computing with Quantum Stuff, Imperial College
- Operational Computing with Quantum Stuff, Developments in Computational Models 2010, Causality, Computation and Physics, FLoC workshop, Edinburgh.
- A formalism-local framework for general probabilistic theories including quantum theory, seminar at ComLab, University of Oxford
- Operational computing with quantum stuff, at Information Theory, Quantum Mechanics, and Security, Bellairs, Barbados
- Computing with quantum stuff, at Conference on quantum information and quantum control III, Toronto
- Natural postulates for quantum theory, at On the nature of the laws of physics, Beyond Center, Arizona
- Natural postulates for quantum theory, at Workshop on informatic phenomena, New Orleans
- An operational approach to Quantum Gravity}, University of Oxford, Computer Science Dept.
- The Causaloid Framework: A tentative framework for Quantum Gravity, at The UK Foundations Conference, Leeds March 2007.
- The causaloid approach to quantum theory and quantum gravity, at Logic, Physics and Quantum Information Theory, Bellairs, Barbados.
- Quantum foundations and quantum gravity}, at PIAF workshop in quantum foundations, Sydney.
- An Operational Framework for a Theory of Quantum Gravity, at Deep Beauty, Princeton
- A foil for quantum gravity, at Foils workshop, Cambridge
- The Causaloid Framework: A tentative framework for Quantum Gravity, at Loops 07, Morellia Mexico.
- Time symmetry and quantum gravity, at Weak values and weak measurements, Arizona.
- The Causaloid Framework: A tentative framework for Quantum Gravity at Philosophical and formal foundations of quantum physics, Les Treilles.
- Quantum theory from reasonable postulates}, University of Birmingham, Physics Dept.
- Beyond quantum theory: Information and entanglement in general probabilistic frameworks, at Foundations of quantum information and entanglement, Boston.
- Probability theories with non-fixed causal structure: a new framework for quantum gravity}, University of Cambridge
- From quantum foundations to quantum gravity, at APS March meeting, Focus session: Foundations of Quantum Theory, Baltimore.
- Generalized Probability theories and how to go beyond Quantum Theory}, Wayne State University, Detroit.
- Generalized probability theories with dynamic causal structure: a new approach to quantum gravity, at Being Baysian in a quantum world, Konstanz.
- Why quantum theory?, at Endophysics, time, quantum and the subjective, Bielefeld.
- Probabilistic theories with dynamical causal structure, at - On the present status of quantum mechanics, Losinj, Croatia.
- The what and the why of quantum theory}, Philosophy dept, Dalhousie University, Halifax.
- Composite systems in quantum theory and beyond, at the 13th UK Meeting on the Foundations of Physics, York UK.
- Cheat sensitive quantum bit commitment, at Special Week on Quantum Cryptography, Newton Institute, Cambridge.
- Are the laws of quantum theory a consequence of the human condition?, at Subtle Technologies, Toronto.
- Quantum theory as an example of a probability theory with special focus on composite systems}, at - New Directions in the Foundations of Physics, Washington.
- Cheat sensitive bit commitment}, at CIAR Quantum Information Processing Program Meeting, Banff, Alberta.
- Quantum theory from reasonable axioms}, Philosophy Dept, University of Western Ontario.
- Quantum theory from reasonable axioms, at Quantum foundations in the light of quantum information, Montreal
- PIRSA:16060076, Operational General Relativity, 2016-06-24, Concepts and Paradoxes in a Quantum Universe
- PIRSA:16010069, PSI 2015/2016 Foundations of Quantum Mechanics - Lecture 15, 2016-01-22, PSI 2015/2016 Foundations of Quantum Mechanics
- PIRSA:16010068, PSI 2015/2016 Foundations of Quantum Mechanics - Lecture 14, 2016-01-21, PSI 2015/2016 Foundations of Quantum Mechanics
- PIRSA:16010067, PSI 2015/2016 Foundations of Quantum Mechanics - Lecture 13, 2016-01-20, PSI 2015/2016 Foundations of Quantum Mechanics
- PIRSA:16010066, PSI 2015/2016 Foundations of Quantum Mechanics - Lecture 12, 2016-01-19, PSI 2015/2016 Foundations of Quantum Mechanics
- PIRSA:16010065, PSI 2015/2016 Foundations of Quantum Mechanics - Lecture 11, 2016-01-18, PSI 2015/2016 Foundations of Quantum Mechanics
- PIRSA:16010064, PSI 2015/2016 Foundations of Quantum Mechanics - Lecture 10, 2016-01-15, PSI 2015/2016 Foundations of Quantum Mechanics
- PIRSA:16010063, PSI 2015/2016 Foundations of Quantum Mechanics - Lecture 9, 2016-01-14, PSI 2015/2016 Foundations of Quantum Mechanics
- PIRSA:16010062, PSI 2015/2016 Foundations of Quantum Mechanics - Lecture 8, 2016-01-13, PSI 2015/2016 Foundations of Quantum Mechanics
- PIRSA:16010061, PSI 2015/2016 Foundations of Quantum Mechanics - Lecture 7, 2016-01-12, PSI 2015/2016 Foundations of Quantum Mechanics
- PIRSA:16010059, PSI 2015/2016 Foundations of Quantum Mechanics - Lecture 6, 2016-01-11, PSI 2015/2016 Foundations of Quantum Mechanics
- PIRSA:16010058, PSI 2015/2016 Foundations of Quantum Mechanics - Lecture 5, 2016-01-08, PSI 2015/2016 Foundations of Quantum Mechanics
- PIRSA:16010057, PSI 2015/2016 Foundations of Quantum Mechanics - Lecture 4, 2016-01-07, PSI 2015/2016 Foundations of Quantum Mechanics
- PIRSA:16010056, PSI 2015/2016 Foundations of Quantum Mechanics - Lecture 3, 2016-01-06, PSI 2015/2016 Foundations of Quantum Mechanics
- PIRSA:16010055, PSI 2015/2016 Foundations of Quantum Mechanics - Lecture 2, 2016-01-05, PSI 2015/2016 Foundations of Quantum Mechanics
- PIRSA:16010054, PSI 2015/2016 Foundations of Quantum Mechanics - Lecture 1, 2016-01-04, PSI 2015/2016 Foundations of Quantum Mechanics
- PIRSA:15110104, Operational approach to Quantum Gravity, 2015-11-26, PI Day - November, 2015
- PIRSA:15060037, General Probability theories: from classical to quantum, 2015-06-24, Quantum Foundations Workshop
- PIRSA:15050080, Bringing General Relativity into the Operational Probabilistic Framework, 2015-05-12, Information Theoretic Foundations for Physics
- PIRSA:15030092, Probabilistic General Relativity with Agency'', 2015-03-05, Quantum Gravity
- PIRSA:15010056, Foundations of Quantum Mechanics-15, 2015-01-23, Foundations of Quantum Mechanics
- PIRSA:15010055, Foundations of Quantum Mechanics-14, 2015-01-21, Foundations of Quantum Mechanics
- PIRSA:15010054, Foundations of Quantum Mechanics-13, 2015-01-20, Foundations of Quantum Mechanics
- PIRSA:15010053, Foundations of Quantum Mechanics-12, 2015-01-19, Foundations of Quantum Mechanics
- PIRSA:15010052, Foundations of Quantum Mechanics-11, 2015-01-19, Foundations of Quantum Mechanics
- PIRSA:15010049, Foundations of Quantum Mechanics-10, 2015-01-16, Foundations of Quantum Mechanics
- PIRSA:15010048, Foundations of Quantum Mechanics-9, 2015-01-15, Foundations of Quantum Mechanics
- PIRSA:15010047, Foundations of Quantum Mechanics-8, 2015-01-14, Foundations of Quantum Mechanics
- PIRSA:15010046, Foundations of Quantum Mechanics-7, 2015-01-13, Foundations of Quantum Mechanics
- PIRSA:15010045, Foundations of Quantum Mechanics-6, 2015-01-12, Foundations of Quantum Mechanics
- PIRSA:15010042, Foundations of Quantum Mechanics-5, 2015-01-09, Foundations of Quantum Mechanics
- PIRSA:15010041, Foundations of Quantum Mechanics-4, 2015-01-08, Foundations of Quantum Mechanics
- PIRSA:15010040, Foundations of Quantum Mechanics-3, 2015-01-07, Foundations of Quantum Mechanics
- PIRSA:15010039, Foundations of Quantum Mechanics-2, 2015-01-06, Foundations of Quantum Mechanics
- PIRSA:15010038, Foundations of Quantum Mechanics-1, 2015-01-05, Foundations of Quantum Mechanics
- PIRSA:14010064, 13/14 PSI - Foundations of Quantum Mechanics - Lecture 15, 2014-01-24, 13/14 PSI - Foundations of Quantum Mechanics
- PIRSA:14010063, 13/14 PSI - Foundations of Quantum Mechanics - Lecture 14, 2014-01-23, 13/14 PSI - Foundations of Quantum Mechanics
- PIRSA:14010062, 13/14 PSI - Foundations of Quantum Mechanics - Lecture 13, 2014-01-22, 13/14 PSI - Foundations of Quantum Mechanics
- PIRSA:14010061, 13/14 PSI - Foundations of Quantum Mechanics - Lecture 12, 2014-01-21, 13/14 PSI - Foundations of Quantum Mechanics
- PIRSA:14010057, 13/14 PSI - Foundations of Quantum Mechanics - Lecture 10, 2014-01-20, 13/14 PSI - Foundations of Quantum Mechanics
- PIRSA:14010060, 13/14 PSI - Foundations of Quantum Mechanics - Lecture 11, 2014-01-20, 13/14 PSI - Foundations of Quantum Mechanics
- PIRSA:14010056, 13/14 PSI - Foundations of Quantum Mechanics - Lecture 9, 2014-01-17, 13/14 PSI - Foundations of Quantum Mechanics
- PIRSA:14010055, 13/14 PSI - Foundations of Quantum Mechanics - Lecture 8, 2014-01-16, 13/14 PSI - Foundations of Quantum Mechanics
- PIRSA:14010054, 13/14 PSI - Foundations of Quantum Mechanics - Lecture 7, 2014-01-15, 13/14 PSI - Foundations of Quantum Mechanics
- PIRSA:14010053, 13/14 PSI - Foundations of Quantum Mechanics - Lecture 6, 2014-01-14, 13/14 PSI - Foundations of Quantum Mechanics
- PIRSA:14010049, 13/14 PSI - Foundations of Quantum Mechanics - Lecture 4, 2014-01-13, 13/14 PSI - Foundations of Quantum Mechanics
- PIRSA:14010050, 13/14 PSI - Foundations of Quantum Mechanics - Lecture 5, 2014-01-13, 13/14 PSI - Foundations of Quantum Mechanics
- PIRSA:14010048, 13/14 PSI - Foundations of Quantum Mechanics - Lecture 3, 2014-01-10, 13/14 PSI - Foundations of Quantum Mechanics
- PIRSA:14010047, 13/14 PSI - Foundations of Quantum Mechanics - Lecture 2, 2014-01-09, 13/14 PSI - Foundations of Quantum Mechanics
- PIRSA:14010046, 13/14 PSI - Foundations of Quantum Mechanics - Lecture 1, 2014-01-08, 13/14 PSI - Foundations of Quantum Mechanics
- PIRSA:13050081, Generalizations of Quantum Theory, 2013-05-30, The Quantum Landscape 2013
- PIRSA:13040121, The theory of composition in physics, 2013-04-16, Quantum Foundations
- PIRSA:12040121, OAPT - Lucien Hardy, 2012-04-27, Quantum Foundations
- PIRSA:11090015, Quantum Theory - Lecture 7, 2011-09-20, 11/12 PSI - Quantum Theory
- PIRSA:11090014, Quantum Theory - Lecture 6, 2011-09-19, 11/12 PSI - Quantum Theory
- PIRSA:11090118, Research Presentation - Quantum Foundations, 2011-09-15, Quantum Foundations
- PIRSA:11090054, Researcher Presentation: Lucien Hardy, 2011-09-02, 11/12 PSI - Researcher Presentations
- PIRSA:11050069, Part 2: Reformulating and reconstructing quantum theory, 2011-05-18, Quantum Foundations
- PIRSA:11050051, Part 1: Reformulating and reconstructing quantum theory, 2011-05-09, Conceptual Foundations and Foils for Quantum Information Processing - 2011
- PIRSA:11040118, Reconstructing quantum theory from reasonable postulates., 2011-04-19, Quantum Gravity Foundations
- PIRSA:11010042, Foundations of Quantum Mechanics - Lecture 5, 2011-01-07, 10/11 PSI - Foundations of Quantum Mechanics (Review)
- PIRSA:10120034, Turning pictures into calculations: the duotensor framework , 2010-12-07, Quantum Foundations
- PIRSA:09100195, Meet a Scientist - Prof. Lucien Hardy, 2009-10-05, Meet a Scientist
- PIRSA:09080011, Operational structures and Natural Postulates for Quantum Theory, 2009-08-14, Reconstructing Quantum Theory - 2009
- PIRSA:09080024, Quantum Physics, 2009-08-05, EinsteinPlus 2009
- PIRSA:09060015, Operational structures as a foundation for probabilistic theories, 2009-06-02, Categories, Quanta, Concepts (CQC) - 2009
- PIRSA:07060042, Operationalism and Quantum Gravity, 2007-06-05, Operational Quantum Physics and the Quantum-Classical Contrast - 2007
- PIRSA:06070045, Causality in quantum theory and beyond: towards a theory of quantum gravity, 2006-07-19, Quantum Reality, Relativistic Causality, and Closing the Epistemic Circle - 2006
- PIRSA:06070036, Quantum Reality, Relativistic Causality, and Closing the Epistemic Circle - Welcome, 2006-07-18, Quantum Reality, Relativistic Causality, and Closing the Epistemic Circle - 2006
- PIRSA:06060026, Quantum Information Theory 1, 2006-06-09, Theory Canada 2 - 2006
- PIRSA:05080041, Evolving Laws: Chapter 26 - Data correlation in physical theories by Lucien Hardy - Pieces of data on pieces of paper..., 2005-08-16, Theory Canada 2 - 2006
- PIRSA:05080026, Evolving Laws: Chapter 11 - Summary of main contemporary issues in physics and cosmology., 2005-08-16, Theory Canada 2 - 2006
- PIRSA:05080021, Evolving Laws: Chapter 6 - Lucien Hardy's opening statement, 2005-08-16, Theory Canada 2 - 2006
- PIRSA:05070113, Generalised Probability Theories as a setting for Quantum Theory and other theories., 2005-07-21, Quantum Information, Computation and Logic: Exploring New Connections - 2005
- PIRSA:05030118, Interpretation of Quantum Theory: Lecture 21, 2005-03-22, Interpretation of Quantum Theory - 2005
- PIRSA:02120005, Five reasonable axioms for quantum mechanics, 2002-12-11, Interpretation of Quantum Theory - 2005
- PIRSA:01110002, What is the difference between classical and quantum and why is quantum better? , 2001-11-21, Interpretation of Quantum Theory - 2005

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