Fast Tests for Probing the Causal Structure of Quantum Processes
631
On a more practical side, it is important to extend the analysis from the idealized
scenario where the cause-effect dependencies are induced by reversible processes,
to the more realistic scenario where they are induced by general noisy processes.
Preliminary results in Ref. [19] indicate that quantum advantages may still persist
for sufficiently low noise levels. However, a fully general treatment of noise is still
lacking and will be important for future applications.
Given the success of causal discovery algorithms in classical statistics and
machine learning, it is natural to expect that the development of quantum causal
discovery algorithms may have applications to the burgeoning field of quantum
machine learning [30–32]. This connection is largely unexplored and represents an
exciting direction of future research.
Acknowledgments GC is grateful to R Spekkens, D Schmid, and M T Quintino for stimulating
discussions on the notion of causality for quantum processes. This work is supported by the
National Science Foundation of China through Grant No. 11675136, by Hong Kong Research
Grant Council through Grants No. 17326616 and 17300918, by the Croucher Foundation, and
by the John Templeton Foundation through grant 61466, The Quantum Information Structure of
Spacetime (qiss.fr). The opinions expressed in this publication are those of the authors and do not
necessarily reflect the views of the John Templeton Foundation. Research at the Perimeter Institute
is supported by the Government of Canada through the Department of Innovation, Science and
Economic Development Canada and by the Province of Ontario through the Ministry of Research,
Innovation and Science.
References
1. P. Spirtes, C. Glymour, R. Scheines (eds.) Causation, Prediction, and Search (MIT Press,
Cambridge, 2000)
2. J. Pearl, Causality (Cambridge University Press, Cambridge, 2009)
3. J. Pearl, Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference
(Morgan Kaufmann Publishers Inc., San Francisco, CA, 1988)
4. C.J. Wood, 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(3),
033002 (2015)
5. R. Chaves, G. Carvacho, I. Agresti, V. Di Giulio, L. Aolita, S. Giacomini, F. Sciarrino,
Quantum violation of an instrumental test. Nat. Phys. 14(3), 291–296 (2018)
6. T. Van Himbeeck, J. Bohr Brask, S. Pironio, R. Ramanathan, A.B. Sainz, E. Wolfe, Quantum
violations in the instrumental scenario and their relations to the bell scenario. Quantum 3, 186
(2019)
7. G. Chiribella, G.M. D’Ariano, P. Perinotti, Quantum circuit architecture. Phys. Rev. Lett.
101(6), 060401 (2008)
8. G. Chiribella, G.M. D’Ariano, P. Perinotti, Memory effects in quantum channel discrimination.
Phys. Rev. Lett. 101(18), 180501 (2008)
9. G. Chiribella, G.M. D’Ariano, P. Perinotti, Theoretical framework for quantum networks. Phys.
Rev. A 80(2), 022339 (2009)
10. G. Chiribella, G.M. D’Ariano, P. Perinotti, Probabilistic theories with purification. Phys. Rev.
A 81(6), 062348 (2010)
11. B. Coecke, R.W. Spekkens, Picturing classical and quantum Bayesian inference. Synthese
186(3), 651–696 (2011)
631
On a more practical side, it is important to extend the analysis from the idealized
scenario where the cause-effect dependencies are induced by reversible processes,
to the more realistic scenario where they are induced by general noisy processes.
Preliminary results in Ref. [19] indicate that quantum advantages may still persist
for sufficiently low noise levels. However, a fully general treatment of noise is still
lacking and will be important for future applications.
Given the success of causal discovery algorithms in classical statistics and
machine learning, it is natural to expect that the development of quantum causal
discovery algorithms may have applications to the burgeoning field of quantum
machine learning [30–32]. This connection is largely unexplored and represents an
exciting direction of future research.
Acknowledgments GC is grateful to R Spekkens, D Schmid, and M T Quintino for stimulating
discussions on the notion of causality for quantum processes. This work is supported by the
National Science Foundation of China through Grant No. 11675136, by Hong Kong Research
Grant Council through Grants No. 17326616 and 17300918, by the Croucher Foundation, and
by the John Templeton Foundation through grant 61466, The Quantum Information Structure of
Spacetime (qiss.fr). The opinions expressed in this publication are those of the authors and do not
necessarily reflect the views of the John Templeton Foundation. Research at the Perimeter Institute
is supported by the Government of Canada through the Department of Innovation, Science and
Economic Development Canada and by the Province of Ontario through the Ministry of Research,
Innovation and Science.
References
1. P. Spirtes, C. Glymour, R. Scheines (eds.) Causation, Prediction, and Search (MIT Press,
Cambridge, 2000)
2. J. Pearl, Causality (Cambridge University Press, Cambridge, 2009)
3. J. Pearl, Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference
(Morgan Kaufmann Publishers Inc., San Francisco, CA, 1988)
4. C.J. Wood, 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(3),
033002 (2015)
5. R. Chaves, G. Carvacho, I. Agresti, V. Di Giulio, L. Aolita, S. Giacomini, F. Sciarrino,
Quantum violation of an instrumental test. Nat. Phys. 14(3), 291–296 (2018)
6. T. Van Himbeeck, J. Bohr Brask, S. Pironio, R. Ramanathan, A.B. Sainz, E. Wolfe, Quantum
violations in the instrumental scenario and their relations to the bell scenario. Quantum 3, 186
(2019)
7. G. Chiribella, G.M. D’Ariano, P. Perinotti, Quantum circuit architecture. Phys. Rev. Lett.
101(6), 060401 (2008)
8. G. Chiribella, G.M. D’Ariano, P. Perinotti, Memory effects in quantum channel discrimination.
Phys. Rev. Lett. 101(18), 180501 (2008)
9. G. Chiribella, G.M. D’Ariano, P. Perinotti, Theoretical framework for quantum networks. Phys.
Rev. A 80(2), 022339 (2009)
10. G. Chiribella, G.M. D’Ariano, P. Perinotti, Probabilistic theories with purification. Phys. Rev.
A 81(6), 062348 (2010)
11. B. Coecke, R.W. Spekkens, Picturing classical and quantum Bayesian inference. Synthese
186(3), 651–696 (2011)