To study which are the most general causal structures which are compatible with local quantum mechanics, Oreshkov et al. introduced the notion of a process: a resource shared between some parties that allows for quantum communication between them without a predetermined causal order. These processes can be used to perform several tasks that are impossible in standard quantum mechanics: they allow for the violation of causal inequalities, and provide an advantage for computational and communication complexity. Nonetheless, no process that can be used to violate a causal inequality is known to be physically implementable. There is therefore considerable interest in determining which processes are physical and which are just mathematical artefacts of the framework. Here we make the first step in this direction, by proposing a purification postulate: processes are physical only if they are purifiable. We derive necessary conditions for a process to be purifiable, and show that several known processes do not satisfy them.
Recently, a theoretical class of processes was found that do not respect causality, but nevertheless can not create logical paradoxes such as those where you travel back in time and kill your own grandfather. Whether such “non-causal” processes are physical and can be found in nature is an open question. In our paper we showed that there exists “non-causal” processes that do not generate paradoxes, but nevertheless violate the condition of reversibility. If reversibility is indeed respected in nature, then these processes must be unphysical.
 A. Ashtekar ``Large Quantum Gravity Effects: Unforeseen Limitations of the Classical Theory'' Phys. Rev. Lett. 77, 4864-4867 (1996).
 Ä. Baumelerand S. Wolf ``Perfect signaling among three parties violating predefined causal order'' Information Theory (ISIT), 2014 IEEE International Symposium on 526-530 (2014).
 Ä. Baumeler, A. Feix, and S. Wolf, ``Maximal incompatibility of locally classical behavior and global causal order in multi-party scenarios'' Phys. Rev. A 90, 042106 (2014).
 C. Branciard, M. Araújo, A. Feix, F. Costa, and Č. Brukner, ``The simplest causal inequalities and their violation'' New J. Phys. 18, 013008 (2015).
 Ä. Baumelerand S. Wolf ``The space of logically consistent classical processes without causal order'' New J. Phys. 18, 013036 (2016).
 A. A. Abbott, C. Giarmatzi, F. Costa, and C. Branciard, ``Multipartite Causal Correlations: Polytopes and Inequalities'' Phys. Rev. A 94, 032131 (2016).
 M. Araújo, C. Branciard, F. Costa, A. Feix, C. Giarmatzi, and Č. Brukner, ``Witnessing causal nonseparability'' New J. Phys. 17, 102001 (2015).
 G. Chiribella, G. M. D'Ariano, P. Perinotti, and B. Valiron, ``Quantum computations without definite causal structure'' Phys. Rev. A 88, 022318 (2013).
 G. Chiribella ``Perfect discrimination of no-signalling channels via quantum superposition of causal structures'' Phys. Rev. A 86, 040301 (2012).
 M. Araújo, F. Costa, and Č. Brukner, ``Computational Advantage from Quantum-Controlled Ordering of Gates'' Phys. Rev. Lett. 113, 250402 (2014).
 A. Feix, M. Araújo, and Č. Brukner, ``Quantum superposition of the order of parties as a communication resource'' Phys. Rev. A 92, 052326 (2015).
 P. Allard Guérin, A. Feix, M. Araújo, and Č. Brukner, ``Exponential communication complexity advantage from quantum superposition of the direction of communication'' Phys. Rev. Lett. 117, 100502 (2016).
 L. M. Procopio, A. Moqanaki, M. Araújo, F. Costa, I. A. Calafell, E. G. Dowd, D. R. Hamel, L. A. Rozema, Č. Brukner, and P. Walther, ``Experimental superposition of orders of quantum gates'' Nat. Commun. 6, 7913 (2015).
 G. Rubino, L. A. Rozema, A. Feix, M. Araújo, J. M. Zeuner, L. M. Procopio, Č. Brukner, and P. Walther, ``Experimental verification of an indefinite causal order'' Sci. Adv. 3 (2017).
 G. Brassard, H. Buhrman, N. Linden, A. A. Méthot, A. Tapp, and F. Unger, ``Limit on Nonlocality in Any World in Which Communication Complexity Is Not Trivial'' Phys. Rev. Lett. 96, 250401 (2006).
 N. Linden, S. Popescu, A. J. Short, and A. Winter, ``Quantum Nonlocality and Beyond: Limits from Nonlocal Computation'' Phys. Rev. Lett. 99, 180502 (2007).
 M. Pawłowski, T. Paterek, D. Kaszlikowski, V. Scarani, A. Winter, and M. Żukowski, ``Information causality as a physical principle'' Nature 461, 1101-1104 (2009).
 T. Fritz, A. B. Sainz, R. Augusiak, J. B. Brask, R. Chaves, A. Leverrier, and A. Acín, ``Local orthogonality as a multipartite principle for quantum correlations'' Nat. Commun. 4, 2263 (2013).
 B. Dakićand Č. Brukner ``Deep Beauty: Understanding the Quantum World through Mathematical Innovation'' Cambridge University Press chapter Quantum Theory and Beyond: Is Entanglement Special? (2011).
 H. Barnum, M. P. Müller, and C. Ududec, ``Higher-order interference and single-system postulates characterizing quantum theory'' New J. Phys. 16, 123029 (2014).
 Ä. Baumelerand S. Wolf Private communication (2015).
 G. C. Ghirardi, P. Pearle, and A. Rimini, ``Markov processes in Hilbert space and continuous spontaneous localization of systems of identical particles'' Phys. Rev. A 42, 78-89 (1990).
 A. Bassi, K. Lochan, S. Satin, T. P. Singh, and H. Ulbricht, ``Models of wave-function collapse, underlying theories, and experimental tests'' Rev. Mod. Phys. 85, 471-527 (2013).
 M. Bojowald, D. Cartin, and G. Khanna, ``Lattice refining loop quantum cosmology, anisotropic models, and stability'' Phys. Rev. D 76, 064018 (2007).
 V. Mukhanov ``Physical Foundations of Cosmology'' Cambridge University Press (2005).
 K. Życzkowskiand I. Bengtsson ``Geometry of Quantum States'' Cambridge University Press (2006).
 S. L. Braunstein, G. M. D'Ariano, G. J. Milburn, and M. F. Sacchi, ``Universal Teleportation with a Twist'' Phys. Rev. Lett. 84, 3486-3489 (2000).
 Mateus Araújo, Philippe Allard Guérin, Ämin Baumeler, "Quantum computation with indefinite causal structures", Physical Review A 96 5, 052315 (2017).
 Sally Shrapnel, Fabio Costa, "Causation does not explain contextuality", Quantum 2, 63 (2018).
 Alastair A. Abbott, Julian Wechs, Fabio Costa, Cyril Branciard, "Genuinely multipartite noncausality", Quantum 1, 39 (2017).
 Philippe Allard Guérin, Časlav Brukner, "Observer-dependent locality of quantum events", New Journal of Physics 20 10, 103031 (2018).
 Simon Milz, Felix A Pollock, Thao P Le, Giulio Chiribella, Kavan Modi, "Entanglement, non-Markovianity, and causal non-separability", New Journal of Physics 20 3, 033033 (2018).
(The above data is from Crossref's cited-by service. Unfortunately not all publishers provide suitable and complete citation data so that some citing works or bibliographic details may be missing.)
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.