Semi-device-independent certification of indefinite causal order

Jessica Bavaresco1, Mateus Araújo2, Časlav Brukner1,3, and Marco Túlio Quintino4

1Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria
2Institute for Theoretical Physics, University of Cologne, Zülpicher Strasse 77, 50937 Cologne, Germany
3Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria
4Department of Physics, Graduate School of Science, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033, Japan

When transforming pairs of independent quantum operations according to the fundamental rules of quantum theory, an intriguing phenomenon emerges: some such higher-order operations may act on the input operations in an indefinite causal order. Recently, the formalism of process matrices has been developed to investigate these noncausal properties of higher-order operations. This formalism predicts, in principle, statistics that ensure indefinite causal order even in a device-independent scenario, where the involved operations are not characterised. Nevertheless, all physical implementations of process matrices proposed so far require full characterisation of the involved operations in order to certify such phenomena. Here we consider a semi-device-independent scenario, which does not require all operations to be characterised. We introduce a framework for certifying noncausal properties of process matrices in this intermediate regime and use it to analyse the quantum switch, a well-known higher-order operation, to show that, although it can only lead to causal statistics in a device-independent scenario, it can exhibit noncausal properties in semi-device-independent scenarios. This proves that the quantum switch generates stronger noncausal correlations than it was previously known.

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[1] M. Horodecki, P. Horodecki, and R. Horodecki. Separability of mixed states: necessary and sufficient conditions. Phys. Lett. A 223, 1-8 (1996). [arXiv: quant-ph/​9605038].
https:/​/​doi.org/​10.1016/​S0375-9601(96)00706-2
arXiv:quant-ph/9605038

[2] G. M. D'Ariano, Martina de Laurentis, M. G. A. Paris, A. Porzio, and S. Solimeno. Quantum tomography as a tool for the characterization of optical devices. Journal of Optics B: Quantum and Semiclassical Optics 4, S127 (2002). [arXiv: quant-ph/​0110110].
https:/​/​doi.org/​10.1088/​1464-4266/​4/​3/​366
arXiv:quant-ph/0110110

[3] J. S. Bell. On the Einstein Podolsky Rosen paradox. Physics 1, 195-200 (1964).
https:/​/​doi.org/​10.1103/​PhysicsPhysiqueFizika.1.195

[4] N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and Stephanie Wehner. Bell nonlocality. Rev. Mod. Phys. 86, 419-478 (2014).
https:/​/​doi.org/​10.1103/​RevModPhys.86.419

[5] M. M. Wolf, D. Perez-Garcia, and C. Fernandez. Measurements incompatible in quantum theory cannot be measured jointly in any other no-signaling theory. Phys. Rev. Lett. 103, 230402 (2009). [arXiv: 0905.2998].
https:/​/​doi.org/​10.1103/​PhysRevLett.103.230402
arXiv:0905.2998

[6] D. Mayers and A. Yao. Self testing quantum apparatus. Quantum Information and Computation 4, 273-286 (2004). [arXiv: quant-ph/​0307205].
https:/​/​doi.org/​10.26421/​QIC4.4
arXiv:quant-ph/0307205

[7] C.-E. Bardyn, T. C. H. Liew, S. Massar, M. McKague, and V. Scarani. Device-independent state estimation based on bell's inequalities. Phys. Rev. A 80, 062327 (2009). [arXiv: 0907.2170].
https:/​/​doi.org/​10.1103/​PhysRevA.80.062327
arXiv:0907.2170

[8] A. Aspect, P. Grangier, and G. Roger. Experimental Realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment: A New Violation of Bell's Inequalities. Phys. Rev. Lett. 49, 91-94 (1982).
https:/​/​doi.org/​10.1103/​PhysRevLett.49.91

[9] B. Hensen, et al. Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres. Nature 526, 682-686 (2015). [arXiv: 1508.05949].
https:/​/​doi.org/​10.1038/​nature15759
arXiv:1508.05949

[10] Marissa Giustina, et al. Significant-loophole-free test of Bell's theorem with entangled photons. Phys. Rev. Lett. 115, 250401 (2015). [arXiv: 1511.03190].
https:/​/​doi.org/​10.1103/​PhysRevLett.115.250401
arXiv:1511.03190

[11] L. K. Shalm, et al. Strong loophole-free test of local realism. Phys. Rev. Lett. 115, 250402 (2015). [arXiv: 1511.03189].
https:/​/​doi.org/​10.1103/​PhysRevLett.115.250402
arXiv:1511.03189

[12] A. Acín, N. Brunner, N. Gisin, S. Massar, S. Pironio, and V. Scarani. Device-independent security of quantum cryptography against collective attacks. Phys. Rev. Lett. 98, 230501 (2007). [arXiv: quant-ph/​0702152].
https:/​/​doi.org/​10.1103/​PhysRevLett.98.230501
arXiv:quant-ph/0702152

[13] A. Acín, S. Massar, and S. Pironio. Randomness versus nonlocality and entanglement. Phys. Rev. Lett. 108, 100402 (2012). [arXiv: 1107.2754].
https:/​/​doi.org/​10.1103/​PhysRevLett.108.100402
arXiv:1107.2754

[14] H. M. Wiseman, S. J. Jones, and A. C. Doherty. Steering, entanglement, nonlocality, and the Einstein-Podolsky-Rosen paradox. Phys. Rev. Lett. 98, 140402 (2007). [arXiv: quant-ph/​0612147].
https:/​/​doi.org/​10.1103/​PhysRevLett.98.140402
arXiv:quant-ph/0612147

[15] M. T. Quintino, T. Vértesi, and N. Brunner. Joint Measurability, Einstein-Podolsky-Rosen Steering, and Bell Nonlocality. Phys. Rev. Lett. 113, 160402 (2014). [arXiv: 1406.6976].
https:/​/​doi.org/​10.1103/​PhysRevLett.113.160402
arXiv:1406.6976

[16] R. Uola, T. Moroder, and O. Gühne. Joint measurability of generalized measurements implies classicality. Phys. Rev. Lett. 113, 160403 (2014). [arXiv: 1407.2224].
https:/​/​doi.org/​10.1103/​PhysRevLett.113.160403
arXiv:1407.2224

[17] C. Branciard, E. G. Cavalcanti, S. P. Walborn, V. Scarani, and H. M. Wiseman. One-sided device-independent quantum key distribution: Security, feasibility, and the connection with steering. Phys. Rev. A 85, 010301 (2012). [arXiv: 1109.1435].
https:/​/​doi.org/​10.1103/​PhysRevA.85.010301
arXiv:1109.1435

[18] O. Oreshkov, F. Costa, and Č. Brukner. Quantum correlations with no causal order. Nat. Commun. 3, 1092 (2012). [arXiv: 1105.4464].
https:/​/​doi.org/​10.1038/​ncomms2076
arXiv:1105.4464

[19] G. Chiribella, G. M. D'Ariano, and P. Perinotti. Transforming quantum operations: Quantum supermaps. Europhysics Letters 83, 30004 (2008). [arXiv: 0804.0180].
https:/​/​doi.org/​10.1209/​0295-5075/​83/​30004
arXiv:0804.0180

[20] G. Chiribella, G. M. D'Ariano, and P. Perinotti. Theoretical framework for quantum networks. Phys. Rev. A 80, 022339 (2009). [arXiv: 0904.4483].
https:/​/​doi.org/​10.1103/​PhysRevA.80.022339
arXiv:0904.4483

[21] M. Araújo, A. Feix, M. Navascués, and Č. Brukner. A purification postulate for quantum mechanics with indefinite causal order. Quantum 1, 10 (2017). [arXiv: 1611.08535].
https:/​/​doi.org/​10.22331/​q-2017-04-26-10
arXiv:1611.08535

[22] G. Chiribella. Perfect discrimination of no-signalling channels via quantum superposition of causal structures. Phys. Rev. A 86, 040301 (2012). [arXiv: 1109.5154].
https:/​/​doi.org/​10.1103/​PhysRevA.86.040301
arXiv:1109.5154

[23] A. Feix, M. Araújo, and Č. Brukner. Quantum superposition of the order of parties as a communication resource. Phys. Rev. A 92, 052326 (2015). [arXiv: 1508.07840].
https:/​/​doi.org/​10.1103/​PhysRevA.92.052326
arXiv:1508.07840

[24] P. A. 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). [arXiv: 1605.07372].
https:/​/​doi.org/​10.1103/​PhysRevLett.117.100502
arXiv:1605.07372

[25] M. Araújo, F. Costa, and Č. Brukner. Computational advantage from quantum-controlled ordering of gates. Phys. Rev. Lett. 113, 250402 (2014). [arXiv: 1401.8127].
https:/​/​doi.org/​10.1103/​PhysRevLett.113.250402
arXiv:1401.8127

[26] M. T. Quintino, Q. Dong, A. Soeda A. Shimbo, and Mio Murao. Reversing unknown quantum transformations: A universal protocol for inverting general unitary operations. arXiv e-prints, (2018). [arXiv: 1810.06944].
arXiv:1810.06944

[27] M. Araújo, C. Branciard, F. Costa, A. Feix, Christina Giarmatzi, and Č. Brukner. Witnessing causal nonseparability. New J. Phys. 17, 102001 (2015). [arXiv: 1506.03776].
https:/​/​doi.org/​10.1088/​1367-2630/​17/​10/​102001
arXiv:1506.03776

[28] C. Branciard. Witnesses of causal nonseparability: an introduction and a few case studies. Scientific Reports 6, 26018 (2016). [arXiv: 1603.00043].
https:/​/​doi.org/​10.1038/​srep26018
arXiv:1603.00043

[29] Giulia 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. Science Advances 3, 3 (2017). [arXiv: 1608.01683].
https:/​/​doi.org/​10.1126/​sciadv.1602589
arXiv:1608.01683

[30] K. Goswami, Christina Giarmatzi, M. Kewming, F. Costa, C. Branciard, Jacquiline Romero, and A. G. White. Indefinite causal order in a quantum switch. Phys. Rev. Lett. 121, 090503 (2018). [arXiv: 1803.04302].
https:/​/​doi.org/​10.1103/​PhysRevLett.121.090503
arXiv:1803.04302

[31] L. M. Procopio, A. Moqanaki, M. Araújo, F. Costa, Irati Alonso Calafell, Emma 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). [arXiv: 1412.4006].
https:/​/​doi.org/​10.1038/​ncomms8913
arXiv:1412.4006

[32] Giulia Rubino, L. A. Rozema, F. Massa, M. Araújo, Magdalena Zych, Č. Brukner, and P. Walther. Experimental entanglement of temporal orders. arXiv e-prints, (2017). [arXiv: 1712.06884].
arXiv:1712.06884

[33] K. Goswami, Jacquiline Romero, and A.G. White. Communicating via ignorance. arXiv e-prints, (2018). [arXiv: 1807.07383].
arXiv:1807.07383

[34] C. Branciard, M. Araújo, A. Feix, F. Costa, and Č. Brukner. The simplest causal inequalities and their violation. New J. Phys. 18, 013008 (2016). [arXiv: 1508.01704].
https:/​/​doi.org/​10.1088/​1367-2630/​18/​1/​013008
arXiv:1508.01704

[35] G. Chiribella, G. M. D'Ariano, P. Perinotti, and B. Valiron. Quantum computations without definite causal structure. Phys. Rev. A 88, 022318 (2013). [arXiv: 0912.0195].
https:/​/​doi.org/​10.1103/​PhysRevA.88.022318
arXiv:0912.0195

[36] K. Kraus, A. Böhm, J. D. Dollard, and W. H. Wootters. States, Effects, and Operations: Fundamental Notions of Quantum Theory. Lectures in Mathematical Physics at the University of Texas at Austin. Cambridge University Press (1983).
https:/​/​doi.org/​10.1007/​3-540-12732-1

[37] J. de Pillis. Linear transformations which preserve hermitian and positive semidefinite operators. Pacific Journal of Mathematics 23, 129-137 (1967).
https:/​/​doi.org/​10.2140/​pjm.1967.23.129

[38] A. Jamiołkowski. Linear transformations which preserve trace and positive semidefiniteness of operators. Reports on Mathematical Physics 3, 275-278 (1972).
https:/​/​doi.org/​10.1016/​0034-4877(72)90011-0

[39] M.-D. Choi. Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285-290 (1975).
https:/​/​doi.org/​10.1016/​0024-3795(75)90075-0

[40] F. Riesz. Sur une espèce de géométrie analytique des systèmes de fonctions sommables. C. R. Acad. Sci. Paris 144, 1409-1411 (1907).

[41] E. Prugovečki. Information-theoretical aspects of quantum measurement. International Journal of Theoretical Physics 16, 321-331 (1977).
https:/​/​doi.org/​10.1007/​BF01807146

[42] C. M. Caves, C. A. Fuchs, and R. Schack. Unknown quantum states: The quantum de finetti representation. Journal of Mathematical Physics 43, 4537-4559 (2002). [arXiv: quant-ph/​0104088].
https:/​/​doi.org/​10.1063/​1.1494475
arXiv:quant-ph/0104088

[43] Costantino Budroni, et al. (in preparation).

[44] L. A. Khalfin and B. S. Tsirelson. Quantum and quasi-classical analogs of Bell inequalities. Symposium on the Foundations of Modern Physics, 441-460 (1985).

[45] P. Rastall. Locality, Bell's theorem, and quantum mechanics. Foundations of Physics 15, 963-972 (1985).
https:/​/​doi.org/​10.1007/​BF00739036

[46] S. Popescu and D. Rohrlich. Quantum nonlocality as an axiom. Foundations of Physics 24, 379-385 (1994).
https:/​/​doi.org/​10.1007/​BF02058098

[47] O. Oreshkov and Christina Giarmatzi. Causal and causally separable processes. New J. Phys. 18, 093020 (2016). [arXiv: 1506.05449].
https:/​/​doi.org/​10.1088/​1367-2630/​18/​9/​093020
arXiv:1506.05449

[48] A. Feix, M. Araújo, and Č. Brukner. Causally nonseparable processes admitting a causal model. New J. Phys. 18, 083040 (2016). [arXiv: 1604.03391].
https:/​/​doi.org/​10.1088/​1367-2630/​18/​8/​083040
arXiv:1604.03391

[49] M. F. Pusey. Negativity and steering: A stronger Peres conjecture. Phys. Rev. A 88, 032313 (2013). [arXiv: 1305.1767].
https:/​/​doi.org/​10.1103/​PhysRevA.88.032313
arXiv:1305.1767

[50] E. Schrödinger. Discussion of probability relations between separated systems. Proceedings of the Cambridge Philosophical Society 31, 555 (1935).
https:/​/​doi.org/​10.1017/​S0305004100013554

[51] N. Gisin. Stochastic quantum dynamics and relativity. Helvetica Physica Acta 62, 363-371 (1989).

[52] L. P. Hughston, R. Jozsa, and W. K. Wootters. A complete classification of quantum ensembles having a given density matrix. Phys. Lett. A 183, 14-18 (1993).
https:/​/​doi.org/​10.1016/​0375-9601(93)90880-9

[53] https:/​/​github.com/​jessicabavaresco/​sdi-causality.
https:/​/​github.com/​jessicabavaresco/​SDI-causality

[54] J. Wechs, A. A. Abbott, and C. Branciard. On the definition and characterisation of multipartite causal (non)separability. New J. Phys. 21, 013027 (2019). [arXiv: 1807.10557].
https:/​/​doi.org/​10.1088/​1367-2630/​aaf352
arXiv:1807.10557

[55] A. A. Abbott, J. Wechs, F. Costa, and C. Branciard. Genuinely multipartite noncausality. Quantum 1, 39 (2017). [arXiv: 1708.07663].
https:/​/​doi.org/​10.22331/​q-2017-12-14-39
arXiv:1708.07663

Cited by

[1] Nikola Paunkovic and Marko Vojinovic, "Causal orders, quantum circuits and spacetime: distinguishing between definite and superposed causal orders", arXiv:1905.09682.

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