Why the quantum? — one of John Wheeler’s ‘Really Big Questions’ — motivates my research in quantum theory. Why and how does the world appear classical when at the bottom it follows the strange rules of quantum mechanics? What are the possible ways to understand quantum reality — and how can we experimentally rule out the impossible ones? What are the limits of classical models for the explanation of quantum phenomena? And how can all this be used as a resource for information-processing tasks, such as quantum computation and quantum cryptography?
I have been working on these questions at the interface of the fields of quantum foundations and quantum information since the beginning of my PhD in mid-2004. Below are some current and previous projects.
I am always open for talented and motivated students who are looking for a PhD position. Scholarships are available for excellent candidates. For enquiries and potential projects please email me: email@example.com.
Events, agents and causation in ontological models of quantum theory
Project funded by the Foundational Questions Institute
50 years ago, John Bell proved a theorem that has shaken the foundations of physics, and still causes widespread puzzlement. Bell’s theorem points to an apparent incompatibility between our two best physical theories. According to Bell, “a real synthesis of quantum and relativity theories requires not just technical developments but radical conceptual renewal”. This project starts from the premise that the incompatibility arises from the different roles that concepts of events, agency and causation play in the two theories. Implicit in Bell’s thought was Reichenbach’s principle of common cause (RPCC), which states that if two events are correlated, then either they are causally connected or share a common cause that explains the correlation. Bell’s theorem shows that this principle must be dropped to maintain relativistic causality. But RPCC is widely applicable; simply rejecting it leaves an explanatory vacuum. Some recent work has attempted to propose principles to substitute RPCC, but at the expense of introducing agent-centric notions such as measurement “settings’’ or “outcomes’’. I am interested in the question: are such notions necessary to make sense of causation in a quantum world? And if so, what does that say about the prospect of reconciling quantum theory and relativity?
- Howard M. Wiseman and Eric G. Cavalcanti, “Causarum Investigatio and the Two Bell’s Theorems of John Bell”, In: R. Bertlmann and A. Zeilinger (eds.), Quantum [Un]Speakables II: Half a Century of Bell’s Theorem, The Frontiers Collection, Springer International Publishing, Switzerland (2017).
- Eric G. Cavalcanti, “Bell’s theorem and the measurement problem: reducing two mysteries to one?”, Journal of Physics: Conference Series, 701, 1, 012002 (2016).
- Howard M. Wiseman, Eleanor G. Rieffel and Eric G. Cavalcanti, “Reply to Gillis’s “On the Analysis of Bell’s 1964 Paper by Wiseman, Cavalcanti, and Rieffel”, International Journal of Quantum Foundations, 2 (4), 137-148 (2016).
- Eric G. Cavalcanti and Raymond Lal, “On modifications of Reichenbach’s principle of common cause in light of Bell’s theorem”, Journal of Physics A: Mathematical and Theoretical Physics 47, Special Issue: ’50 years of Bell’s theorem’, 424018 (2014).
Quantum causal models and applications
That our classical notions of causality need revision has been clear since Bell’s 1964 theorem, but surprisingly only very recently we are starting to understand how this revision can be done. This is the program of quantum causal models. In a paper published in the commemorative issue for 50 years of Bell’s theorem in 2014 ( above), Ray Lal and I proposed to break down Reichenbach’s principle into two: a principle of common cause proper, and another principle stating that to explain correlations the common cause must factorise the probabilities. We suggested that it is possible to keep the first without the second, in a way to accommodate quantum correlations, and this proposal has influenced several authors to develop what we now call quantum causal models.
Quantum causal models are an attempt to generalise the classical theory of causal models, such as formulated by Pearl. This theory has wide applicability in fields from medicine to artificial intelligence — wherever we need to reason from limited information about the consequences of our actions (or the actions of our algorithms) in the world. A natural question is then: what can we do differently if the world really obeys quantum rather than classical causality? The answer to this question could have important implications, for example, in the emerging field of quantum machine learning.
Foundations and experimental tests of contextuality
Nonlocality and contextuality are at the root of conceptual puzzles in quantum mechanics, and are key resources for quantum advantage in information-processing tasks. Bell nonlocality is best understood as the incompatibility between quantum correlations and the classical theory of causality, applied to relativistic causal structure. Contextuality, on the other hand, is on a more controversial foundation. In a recent work , I provide a common conceptual ground between nonlocality and contextuality as violations of classical causality, showing that all causal models that allow for violations of Bell or Kochen-Specker-contextuality inequalities violate the principle of “no-fine-tuning”. Thus the quantum violation of classical causality goes beyond the case of space-like separated systems, and manifests already in scenarios involving single systems.
Beyond this result, I’m interested in finding out whether the same holds in quantum causal models (intuitively not), and whether we can use this distinction to shed light on the power of nonlocality and contextuality as resources for quantum information. Other open questions include whether the result applies for arbitrary numbers of parties or measurement choices, and whether we can relax the principle of no-fine-tuning to allow for experimental tests.
- E.G. Cavalcanti, “Quantum nonlocality and contextuality as fine-tuning”, arXiv:1705.05961
- Xiang Zhan, Eric G. Cavalcanti, Jian Li, Zhihao Bian, Yongsheng Zhang, Howard M. Wiseman And Peng Xue, “Experimental generalized contextuality with single-photon qubits”, Optica 4 (8), 966 (2017).
Past or Ongoing Projects
The following is a non-exhaustive list of projects I’ve worked on in the past, and some questions that continue to interest me to various degrees over the years.
Reality of the quantum state
The framework of ontological models attempts to map out the landscape of models of quantum mechanics in terms of the states of reality they posit (ontic states), their properties, and their observable consequences. In a ground-breaking work developed with colleagues at the University of Oxford ,published in Physical Review Letters in 2014, we proved a no-go result providing strong evidence against the class of psi-epistemic ontological models — wherein the quantum state represents a state of information about an underlying objective reality. An experimental test with collaborators at the University of Queensland, published in Nature Physics in 2015 , led to a Nature News Feature and widespread media coverage, including in The New York Times, New Scientist, and numerous others. My popular article for The Conversation attracted more than 50,000 readers and was republished by 8 internet media outlets.
- Jonathan Barrett, Eric G. Cavalcanti, Raymond Lal and Owen J. E. Maroney, “No psi-epistemic model can fully explain the indistinguishability of quantum states”, Physical Review Letters 112, 250403 (2014).
- M. Ringbauer, B. Duffus, C. Branciard, E. G. Cavalcanti, A. G. White and A. Fedrizzi, “Measurements on the reality of the wavefunction”, Nature Physics 11, 249 (2015).
During my PhD I developed, with co-authors in , the first experimental criteria for the Einstein-Podolsky-Rosen paradox that uses discrete variables, subsequently co-authoring a highly-cited Reviews of Modern Physics  on the EPR paradox. This led to my work, together with Howard Wiseman and Margaret Reid, on the general theory of steering inequalities . This work allowed for experimental tests of EPR-steering, and sparked what remains a highly active field today. One of the applications of steering, for one-sided device-independent quantum key distribution, was developed by myself and co-authors in a highly cited paper, and many of my subsequent publications between 2011 and 2016 were on the topic of steering. My leadership in the field was recognised by an invitation to be a Lead Guest Editor for a Special Issue of the Journal of the Optical Society of America B on the 80 years of steering and the EPR paradox, published in 2015.
- E. G. Cavalcanti, P.D. Drummond H.A. Bachor and M.D. Reid, “Spin entanglement, decoherence and Bohm’s EPR paradox”, Optics Express 17, 18693-18702 (2009).
- M. D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen and G. Leuchs, “The Einstein-Podolsky-Rosen paradox: from concepts to applications”, Reviews of Modern Physics 81, 1727–1751 (2009).
- E. G. Cavalcanti, S.J. Jones, H.M. Wiseman and M.D. Reid, “Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox”, Physical Review A 80, 032112 (2009).
- C.Branciard, E.G. Cavalcanti, S. Walborn, V. Scarani and H.M. Wiseman, “One-sided device-independent quantum key distribution: Security, feasibility, and the connection with steering”, Physical Review A 85, 010301(R) (2012).
- A.J. Bennet, D.A. Evans, D.J. Saunders, C. Branciard, E.G. Cavalcanti, H.M.Wiseman and G.J. Pryde, “Arbitrarily Loss-Tolerant Einstein-Podolsky-Rosen Steering Allowing a Demonstration over 1 km of Optical Fiber with No Detection Loophole”, Physical Review X 2, 031003 (2012).
- D.A. Evans, E. G. Cavalcanti and H. M. Wiseman, “Loss-tolerant tests of Einstein-Podolsky-Rosen steering”, Physical Review A 88, 022106 (2013).
- E.G. Cavalcanti, M. J. Hall and H. M. Wiseman, “Entanglement verification and steering when Alice and Bob cannot be trusted”, Physical Review A 87, 032306 (2013).
- James Schneeloch, Curtis J. Broadbent, Stephen P. Walborn, Eric G. Cavalcanti and John C. Howell, “Einstein-Podolsky-Rosen steering inequalities from entropic uncertainty relations”, Physical Review A 87, 062103 (2013).
- Eric G. Cavalcanti, Christopher J. Foster, Maria Fuwa and Howard M. Wiseman, “Analog of the Clauser-Horne-Shimony-Holt inequality for steering”, Journal of the Optical Society of America B 32 (4), A74 (2015).
- Parth Girdhar and Eric G. Cavalcanti, “All two qubit states that are steerable via CHSH-type correlations are Bell-nonlocal”, Physical Review A 94, 032317 (2016).
Bell inequalities and unpredictability
Bell inequalities can be derived from ontological assumptions of locality and determinism, or it can be derived as show in this work, from the operational assumptions of signal locality and predictabilty. It’s an important difference: there are ontological models of quantum theory that satisfy either of the ontological assumptions above, so we can’t affirm that either is false. But no model violates signal locality as it’s a feature of the observations themselves. So we can conclude with confidence that the world has irreducible unpredictability — even if we can’t say anything about whether it is really indeterministic at the bottom. This is the basic idea behind the field of device-independent quantum randomness certification, which this work predates.
- E. G. Cavalcanti and H. M. Wiseman, “Bell Nonlocality, Signal Locality and Unpredictability (or What Bohr Could Have Told Einstein at Solvay Had He Known About Bell Experiments)”, Foundations of Physics 42, 1329–1338 (2012).
Quantum correlations, causality and decision theory
What makes some decisions better than others? One answer is that one should take the action that is more likely to cause good outcomes. This seemingly sensible advice is encoded in what is called “causal decision theory”. However, quantum correlations provide a challenge to that theory, as I’ve shown in a paper published in the British Journal for the Philosophy of Science in 2010.
- E. G. Cavalcanti, “Causation, decision theory and Bell’s theorem: a quantum analogue of the Newcomb problem”, The British Journal for the Philosophy of Science, 61, 569-597 (2010).
Continuous-variables Bell inequalities
My first contribution to the field of quantum nonlocality was motivated by the potential of the high detection efficiencies achievable with homodyne detection for providing a loophole-free test. With this goal in mind, I developed the first class of Bell-type inequalities applicable to continuous variables. This work opened up a new research direction and led to publications, including two Physical Review Letters in 2007 and 2009.
- E.G. Cavalcanti, C.J. Foster, P.D. Drummond and M.D. Reid, “Bell inequalities for continuous-variable correlations”, Physical Review Letters 99, 210405-210408 (2007).
- Q. Y He, E.G. Cavalcanti, P.D. Drummond and M.D. Reid, “Testing for Multipartite Quantum Nonlocality Using Functional Bell Inequalities”, Physical Review Letters 103, 180402 (2009).
- Q.Y He, E.G. Cavalcanti, M.D. Reid and P.D. Drummond, “Bell inequalities for continuous-variable measurements”, Physical Review A 81, 062106 (2010).
- E. G. Cavalcanti, Q.Y He, M.D. Reid and H.M. Wiseman, “Unified criteria for multipartite quantum nonlocality”, Physical Review A 84, 032115 (2011).
My first PhD project I developed experimental criteria for macroscopic quantum superpositions, defining a notion of “macroscopic” and how to certify it experimentally. This work was published in Physical Review Letters in 2006 and subsequent publications, and generated several experimental tests in quantum optics.
- E. G. Cavalcanti and M.D. Reid, “Signatures for generalized macroscopic superpositions”, Physical Review Letters 97, 170405-170408 (2006).
- E. G. Cavalcanti and M.D. Reid, “Criteria for generalized macroscopic and mesoscopic quantum coherence”, Physical Review A 77, 062108 (2008).
- E.G. Cavalcanti and M.D. Reid, “Uncertainty relations for the realization of macroscopic quantum superpositions and EPR paradoxes”, Journal of Modern Optics 54, 2373-2380 (2007).
- M.D. Reid and E.G. Cavalcanti, “Macroscopic quantum Schrodinger and Einstein-Podolsky-Rosen paradoxes”, Journal of Modern Optics 52, 2245-2252 (2005).