Correlations between spacelike separated measurements on entangled quantum systems are stronger than any classical correlations and are at the heart of numerous quantum technologies. In practice, however, spacelike separation is often not guaranteed and we typically face situations where measurements have an underlying time order. Here we aim to provide a fair comparison of classical and quantum models of temporal correlations on a single particle, as well as timelike-separated correlations on multiple particles. We use a causal modeling approach to show, in theory and experiment, that quantum correlations outperform their classical counterpart when allowed equal, but limited communication resources. This provides a clearer picture of the role of quantum correlations in timelike separated scenarios, which play an important role in foundational and practical aspects of quantum information processing.
 J. S. Bell, On the Einstein–Podolsky–Rosen paradox, Physics 1, 195 (1964).
 M. Markiewicz, P. Kurzyński, J. Thompson, S.-Y. Lee, A. Soeda, T. Paterek, and D. Kaszlikowski, Unified approach to contextuality, nonlocality, and temporal correlations, Phys. Rev. A 89, 042109 (2014).
 C. Budroni, T. Moroder, M. Kleinmann, and O. Gühne, Bounding Temporal Quantum Correlations, Phys. Rev. Lett. 111, 020403 (2013).
 T. Fritz, Quantum correlations in the temporal Clauser–Horne–Shimony–Holt (CHSH) scenario, New J. Phys. 12, 083055 (2010).
 A. Fedrizzi, M. P. Almeida, M. A. Broome, A. G. White, and M. Barbieri, Hardy's Paradox and Violation of a State-Independent Bell Inequality in Time, Phys. Rev. Lett. 106, 200402 (2011).
 M. Pawłowski, J. Kofler, T. Paterek, M. Seevinck, and Č. Brukner, Non-local setting and outcome information for violation of Bell's inequality, New J. Phys. 12, 083051 (2010).
 R. Chaves, J. B. Brask, and N. Brunner, Device-Independent Tests of Entropy, Phys. Rev. Lett. 115, 110501 (2015a).
 R. Gallego, N. Brunner, C. Hadley, and A. Acín, Device-Independent Tests of Classical and Quantum Dimensions, Phys. Rev. Lett. 105, 230501 (2010).
 S. Brierley, A. Kosowski, M. Markiewicz, T. Paterek, and A. Przysiȩżna, Nonclassicality of Temporal Correlations, Phys. Rev. Lett. 115, 120404 (2015).
 R. Chaves, R. Kueng, J. B. Brask, and D. Gross, Unifying Framework for Relaxations of the Causal Assumptions in Bell's Theorem, Phys. Rev. Lett. 114, 140403 (2015b).
 C. J. Wood and R. W. Spekkens, The lesson of causal discovery algorithms for quantum correlations: Causal explanations of Bell-inequality violations require fine-tuning, New J. Phys. 17, 033002 (2015).
 J. Pearl, Causality (Cambridge University Press, 2009).
 J. S. Bell, The theory of local beables, Epistem. Lett. 9, 11 (1976).
 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, 1895 (1993).
 C. H. Bennett and S. J. Wiesner, Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states, Phys. Rev. Lett. 69, 2881 (1992).
 R. Gallego, L. E. Würflinger, R. Chaves, A. Acín, and M. Navascués, Nonlocality in sequential correlation scenarios, New J. Phys. 16, 033037 (2014).
 N. Langford, T. Weinhold, R. Prevedel, K. Resch, A. Gilchrist, J. O'Brien, G. Pryde, and A. White, Demonstration of a Simple Entangling Optical Gate and Its Use in Bell-State Analysis, Phys. Rev. Lett. 95, 210504 (2005).
 M. J. W. Hall, Local Deterministic Model of Singlet State Correlations Based on Relaxing Measurement Independence, Phys. Rev. Lett. 105, 250404 (2010).
 R. Chaves, Polynomial Bell Inequalities, Phys. Rev. Lett. 116, 010402 (2016).
 C. M. Lee and R. W. Spekkens, Causal Inference via Algebraic Geometry: Feasibility Tests for Functional Causal Structures with Two Binary Observed Variables, J. Causal Inference 5, 6 (2017).
 C. Emary, N. Lambert, and F. Nori, Leggett–Garg inequalities, Rep. Prog. Phys. 77, 016001 (2014).
 M. Ringbauer, C. J. Wood, K. Modi, A. Gilchrist, A. G. White, and A. Fedrizzi, Characterizing Quantum Dynamics with Initial System-Environment Correlations, Phys. Rev. Lett. 114, 090402 (2015).
 R. Horodecki, P. Horodecki, and M. Horodecki, Violating Bell inequality by mixed spin-12 states: necessary and sufficient condition, Phys. Lett. A 200, 340 (1995).
 G. Carvacho, R. Chaves, and F. Sciarrino, "Perspective on experimental quantum causality", EPL (Europhysics Letters) 125 3, 30001 (2019).
 Martin Ringbauer, Fabio Costa, Michael E. Goggin, Andrew G. White, and Alessandro Fedrizzi, "Multi-time quantum correlations with no spatial analog", npj Quantum Information 4 1, 37 (2018).
 R. V. Nery, M. M. Taddei, R. Chaves, and L. Aolita, "Quantum Steering Beyond Instrumental Causal Networks", Physical Review Letters 120 14, 140408 (2018).
 Philip Taranto, "Memory effects in quantum processes", International Journal of Quantum Information 1941002 (2020).
 Philip Taranto, Simon Milz, Felix A. Pollock, and Kavan Modi, "Structure of quantum stochastic processes with finite Markov order", Physical Review A 99 4, 042108 (2019).
 Rafael Chaves, Gonzalo Carvacho, Iris Agresti, Valerio Di Giulio, Leandro Aolita, Sandro Giacomini, and Fabio Sciarrino, "Quantum violation of an instrumental test", Nature Physics 14 3, 291 (2018).
 Philip Taranto, Felix A. Pollock, Simon Milz, Marco Tomamichel, and Kavan Modi, "Quantum Markov Order", Physical Review Letters 122 14, 140401 (2019).
 Fabio Costa, Martin Ringbauer, Michael E. Goggin, Andrew G. White, and Alessandro Fedrizzi, "Unifying framework for spatial and temporal quantum correlations", Physical Review A 98 1, 012328 (2018).
 Cristhiano Duarte, Samuraí Brito, Barbara Amaral, and Rafael Chaves, "Concentration phenomena in the geometry of Bell correlations", Physical Review A 98 6, 062114 (2018).
 Zhen-Peng Xu and Adán Cabello, "Quantum correlations with a gap between the sequential and spatial cases", Physical Review A 96 1, 012122 (2017).
The above citations are from Crossref's cited-by service (last updated successfully 2020-02-16 12:16:57) and SAO/NASA ADS (last updated successfully 2020-02-16 12:16:58). The list may be incomplete as not all publishers provide suitable and complete citation data.
This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.