1. Indefinite causal order in quantum mechanics Faculty of Physics, University of Vienna & Institute for Quantum Optics and Quantum Information, Vienna Mateus Araujo, Cyril Branciard, Fabio Costa, Adrian Feix, Christina Giarmatzi, Ognyan Oreshkov, Magdalena Zych The 11th “Vienna Central European Seminar on Particle Physics and Quantum Field Theory” Časlav Brukner

2. Possible causal influences

3. Question: Can one have situations in which the causal order is not fixed, but rather is subject to quantum indefiniteness?

4. Dynamical causal structure of general relativity Superposition principle of quantum mechanics + Question: Can one have situations in which the causal order is not fixed, but rather is subject to quantum indefiniteness?

5. Dynamical causal structure of general relativity Superposition principle of quantum mechanics + Question: Can one have situations in which the causal order is not fixed, but rather is subject to quantum indefiniteness?

6. Dynamical causal structure of general relativity Superposition principle of quantum mechanics + Question: Can one have situations in which the causal order is not fixed, but rather is subject to quantum indefiniteness?

7. Outline  “Causal inequalities“ Device-independent approach to causality  Framework for quantum mechanics with no assumed global causal structure: Device-dependent approach to causality Causally non-separable processes  Quantum computation with indefinite order of gates Computational task that cannot be accomplished on a computer with fixed order of gates  Physical realization of causally non-separable processes Linear optical schemes & via superposition of large masses

8. “Correlation does not imply causation”

9. The notion of “causation” Necessity of interventions, or free variables, statistically independent of “the rest of the experiment” One-directional signalling Cause Effect

10. The notion of “causation” Necessity of interventions, or free variables, statistically independent of “the rest of the experiment” One-directional signalling

11. Definite causal order No-signalling One-directional signalling Space-like separated Time-like separated Alice before Bob

12. Causal inequalities (Device-independent approach to causality) Causal correlations: either A signals to B or B signals to A, or no-signalling or a convex combination of these situations.  System enters each laboratory only once.  The laboratories are shielded and interact with “the outside world” only through the system entering and exiting it. Assumptions:

13. Causal inequalities (Device-independent approach to causality) Causal correlations: either A signals to B or B signals to A, or no-signalling or a convex combination of these situations. No-signalling One-directional signalling: Alice to Bob

14. The simplest causal inequality Causal correlations satisfy causal inequalities, which are facets of the causal polytope 1 bit input, 1 bit output 1 bit input, 1 bit output Guess Your Neighbour’s Input (GYNI) game: C. Branciard, M. Araújo, A. Feix, F. Costa, Č. B., to appear in New J. Phys. (2015)

15. “Non-causal correlations” (violating causal inequalities) Interpretation: Both A signals to B and B signals to A, although the system enters only once the laboratory and the laboratories are shielded. Two-directional signalling

16. Past space-like surface Future space-like surface Output Hilbert space Input Hilbert space Local quantum laboratory (Device-dependent approach to causality)

17. Past space-like surface Future space-like surface Output Hilbert space Input Hilbert space Local quantum laboratory (Device-dependent approach to causality) Transformations = completely positive (CP) trace-nonincreasing maps

18. c b Many local quantum laboratories Process matrix: O. Oreshkov, F. Costa, Č.B., Nature Communication 3: 1092 (2012) Probabilities: Quantum mechanics locally valid. (no globar causal order fixed)

19. c b Conditions on W Normalization: O. Oreshkov, F. Costa, Č.B., Nature Communication 3: 1092 (2012) Positivity: Quantum mechanics locally valid. (no global causal order fixed)

20. Forbidden processes Single Loops Double Loops O. Oreshkov, F. Costa, Č.B., Nature Communication 3: 1092 (2012) No “grandfather paradox”

21. Admissible processes Channels from Alice to Bob Time-like separated States Space-like separated O. Oreshkov, F. Costa, Č.B., Nature Communication 3: 1092 (2012)

22. There are causally non-separable processes Causally separable processes A signals to B, or no signaling Most general processes compatible with definite causal structure (convex mixtures of ordered processes): B signals to A, or no signaling Ordered processes:

23. Alice Bob Channel from Alice to Bob Alice Bob Channel from Bob to Alice Quantum switch – quantum control of causal order Path degree of freedom (quantum control) Internal degree of freedom

24. Quantum switch – quantum control of causal order Alice Bob Cleve Quantum switch is a causally nonseparable process

25. Quantum switch – quantum control of causal order Alice Bob Cleve Quantum switch is a causally nonseparable process However, the switch cannot violate a „causal inequality“

26. „Superposition of unitarities“ Alice Bob Cleve

27. Computational advantages 1 C. Branciard, M. Araújo, A. Feix, F. Costa, and C.B., arXiv:1508.01704 (2015) 2 T. Colnaghi, G. M. D’Ariano, S. Facchini, and P. Perinotti, Phys. Lett. A 376, 2940-2943 (2012) 3 G. Chiribella, Phys. Rev. A 86, 040301(R) (2012) 4 M. Araujo, F. Costa, and C.B., Phys. Rev. Lett. 113, 250402 (2015) 5 A. Feix, M. Araujo, and C.B. Phys. Rev. A 92, 052326 (2015)

28. Experimental Demonstration L. M. Procopio et. al, Nature Communication 6, 7913 (2015).

29. Order of events determined by their position in space-time A B

30. General relativity: space-time is dynamical

31. Dynamics of the clock described in: Proper times of clocks a & b General relativity: space-time is dynamical M. Zych, F. Costa, I. Pikovski, Č. B., Nature Communication 2 :505 (2011) I. Pikovski, M. Zych, F. Costa, Č. B., Nature Physics 11, 668 (2015)

32. M. Zych, F. Costa, I. Pikovski, Č. B., Nature Communication 2 :505 (2011) I. Pikovski, M. Zych, F. Costa, Č. B., Nature Physics 11, 668 (2015) Dynamics of the clock described in: Proper times of clocks a & b General relativity: space-time is dynamical

33. Quantum control of temporal order Gravitational quantum switch

34. Summary and Outlook  Global causal order need not be a necessary element of quantum theory.  There exist physical processes that are causally nonseparable.  Causally nonseparable processes is a new resource for quantum information processing  The framework also includes processes with no (known) physical interpretation  Does a theory of quantum gravity provide a physical interpretation to such processes?

35. Thank you! quantumfoundations.org

36. B A R r rBrB Potential r Force-free time dilation

37. Relative degrees of freedom Clock in a superposition Fixed backgroud Local clock Superposition of backgrouds =

38. running clock in a superposition QM+GR: interference cannot be observed since the which- path information is stored in the clock time Clock in a superposition GR: time shown by the clock depends on the path taken QM: either path or interference

39. Visibility modulation Difference in proper time Orthogonalization time M. Zych, F. Costa, I. Pikovski, Č. B., Nature Communication 2 :505 (2011) I. Pikovski, M. Zych, F. Costa, Č. B., Nature Physics 11, 668 (2015)