1. Bell and Leggett-Garg tests of local and macroscopic realism Theory Colloquium Johannes Gutenberg University Mainz, Germany 13 June 2013 Johannes Kofler Max Planck Institute of Quantum Optics (MPQ) Garching / Munich, Germany

2. Outlook Quantum entanglement vs. local realism  Bell’s inequality  Loopholes  Entanglement swapping & teleportation Macroscopic quantum superpositions vs. macrorealism  Leggett-Garg inequality  Quantum-to-classical transition  Witnessing non-classical evolutions in complex systems Conclusion and outlook

3. Local realism Realism:properties of physical objects exist independent of whether or not they are observed by anyone Locality:no physical influence can propagate faster than the speed of light External world Passive observers Classical world view:

4. Bell’s inequality Realism *J. S. Bell, Phys. 1, 195 (1964); J. F. Clauser et al., PRL 23, 880 (1969) a1,a2a1,a2 B = ±1A = ±1 b1,b2b1,b2 A 1 (B 1 +B 2 ) + A 2 (B 1 –B 2 ) = ±2 Local realism:A = A(a,,b,B) B = B(b,,a,A) outcomes settings variables S :=  A 1 B 1  +  A 1 B 2  +  A 2 B 1  –  A 2 B 2   2 Bell’s inequality* Quantum mechanics: S QM = 2  2  2.83 First experimental violation: 1972 Since then: tests with photons, atoms, superconducting qubits, … using entangled quantum states, e.g. Locality |  AB = (|HV  AB + |VH  AB ) /  2 AliceBob

5. Quantum entanglement Entangled state: |  AB = (|   AB + |   AB ) /  2 = (|   AB + |   AB ) /  2 BobAlice locally:random  /  :   /  :   /  :   /  :   /  :   /  :   /  :   /  :   /  :   /  :   /  :   /  :   /  :   /  :   /  :   /  :  globally:perfect correlations basis: result Top picture: http://en.wikipedia.org/wiki/File:SPDC_figure.png A1A1 A2A2 B1B1 B2B2

6. Loopholes Why important? - Quantum foundations - Security of entanglement-based quantum cryptography Three main loopholes: Locality loophole hidden communication between the parties closing: hard for atoms, achieved for photons (1982 1,1998 2 ) Freedom of choice settings are correlated with hidden variables closing: hard for atoms, achieved for photons (2010 3 ) Fair sampling measured ensemble is not representative closing: achieved for atoms (2001 4 ) and photons (2013 5 ) 1 A. Aspect et al., PRL 49, 1804 (1982) 2 G. Weihs et al., PRL 81, 5039 (1998) 3 T. Scheidl et al., PNAS 107, 10908 (2010) 4 M. A. Rowe et al., Nature 409, 791 (2001) 5 M. Giustina et al., Nature 497, 227 (2013) Loopholes: maintain local realism despite S exp > 2 E

7. Locality:A is space-like sep. from b and B B is space-like sep. from a and A T. Scheidl, R. Ursin, J. K., T. Herbst, L. Ratschbacher, X. Ma, S. Ramelow, T. Jennewein, A. Zeilinger, PNAS 107, 10908 (2010) Ensuring locality & freedom of choice b,Bb,B E,AE,A a Tenerife La Palma Freedom of choice:a and b are random a and b are space-like sep. from E E p(a,b| ) = p(a,b) p(A,B|a,b, ) = p(A|a, ) p(B|b, ) La PalmaTenerife S = 2.37

8. Ensuring fair sampling Solution: very good detectors Eberhard inequality* - undetected (“u”) events in derivation - required detection efficiency  only 2/3 From Topics in Applied Physics 99, 63-150 (2005) * P. H. Eberhard, PRA 47, 747 (1993) +1 –1 Source +1 –1 local realism Problem:detection efficiency could depend on settings  A =  A (  ),  B =  B (  ) Superconducting transition edge sensors

9. First fair sampling of photons M. Giustina, A. Mech, S. Ramelow, B. Wittmann, J. K., Jörn Beyer, A. Lita, B. Calkins, T. Gerrits, S. W. Nam, R. Ursin, A. Zeilinger, Nature 497, 227 (2013) Detection efficiency  75% Violation by 70 standard deviations local realism quantum violation of local realism with fair sampling Photon: only system for which all loop- holes are closed (not yet simultaneously)

10. Large distances * M. Žukowski et al., PRL 71, 4287 (1993) Bell-state measurement (BSM): Entanglement swapping How to distribute entanglement over large distances? - qu. cryptography between Vienna and Paris - distributed quantum computation Two answers: - glass fibers & quantum repeaters - no fibers: free space Quantum repeaters use entanglement swapping*

11. Delayed-choice entanglement swapping Later measurement on photons 2 & 3 decides whether 1 & 4 were separable or entangled Naïve class. interpretation would require influences into the past X. Ma, S. Zotter, J. K., R. Ursin, T. Jennewein, Č. Brukner, A. Zeilinger, Nature Phys. 8, 479 (2012) Temporal order does not matter in qu. mechanics

12. Quantum teleportation Towards a world-wide “quantum internet” X. Ma, T. Herbst, T. Scheidl, D. Wang, S. Kropatschek, W. Naylor, A. Mech, B. Wittmann, J. K., E. Anisimova, V. Makarov, T. Jennewein, R. Ursin, A. Zeilinger, Nature 489, 269 (2012)

13. The next step ISS (350 km altitude)

14. Contents Quantum entanglement vs. local realism  Bell’s inequality  Loopholes  Entanglement swapping & teleportation Macroscopic quantum superpositions vs. macrorealism  Leggett-Garg inequality  Quantum-to-classical transition  Witnessing non-classical evolutions in complex systems Conclusion

15. The double slit experiment Picture: http://www.blacklightpower.com/theory/DoubleSlit.shtml ParticlesWavesQuanta Superposition: |   = |left  + |right 

16. With photons, electrons, neutrons, molecules etc. With cats? |cat left  + |cat right  ? When and how do physical systems stop to behave quantum mechanically and begin to behave classically (“measurement problem”)? Macroscopic superpositions 6910 AMU* * S. Gerlich et al., Nature Comm. 2, 263 (2011)

17. Quantum mechanics says “yes” (if you manage to defy decoherence) Are macroscopic superpositions possible? Local realism vs. macrorealism Quantum mechanics says “yes” (use entanglement) Are “non-local” correlations possible? Local realism (e.g. classical physics) says “no” (only classical correlations) Bell test has given experimental answer in favor of quantum mechanics Macrorealism (e.g. classical physics, objective collapse models) says “no” (only classical temporal correlations) Leggett-Garg test can/will give experimental answer, community still split Practical relevance qu. computation, qu. cryptography Practical relevance witnessing temporal qu. coherence

18. Macrorealism Macrorealism per se: given a set of macroscopically distinct states, a macroscopic object is at any given time in a definite one of these states Non-invasive measurability:measurements reveal the state without any effect on the state itself or on the subsequent dynamics Leggett-Garg inequality (LGI) A. J. Leggett and A. Garg, PRL 54, 857 (1985) Quantum mechanics: t1t1 t2t2 t3t3 t4t4 t0t0 QQQQ ±1 S :=  A 1 B 1  +  A 1 B 2  +  A 2 B 1  –  A 2 B 2   2 K :=  Q 1 Q 2  +  Q 2 Q 3  +  Q 3 Q 4  –  Q 1 Q 4   2 Bell: K QM = 2  2  2.83 locality non-invasiveness = = time

19. ½ Rotating spin ½ particle (eg. electron) Rotating classical spin vector (eg. gyroscope) K > 2: violation of Leggett- Garg inequality K  2: no violation, classical time evolution classical limit Precession around an axis (via magnetic field or external force) Measurments along different axis Quantum vs. classical 2222

20. classical limit Sharp measurement of spin z-component Violation of Leggett-Garg inequality for arbitrarily large spins j Classical physics of a rotating classical spin vector J. K. and Č. Brukner, PRL 99, 180403 (2007) Spin j 1 3 5 7... 2 4 6 8... Q = +1 Q = –1 –j–j+j –j–j Coarse-grained measurement or decoherence Sharp vs. coarse-grained measurements macroscopically distinct states

21. Sharp measurements Coarse-grained measurements or decoherence Superposition vs. mixture To see quantumness: need to resolve j 1/2 levels & protect system from environment J. K. and Č. Brukner, PRL 101, 090403 (2008)

22. Oscillating Schrödinger cat “non-classical” rotation in Hilbert space Rotation in real space “classical” N sequential steps per  t1 single computation step per  t all N rotations can be done simultaneously Non-classical evolutions are complex J. K. and Č. Brukner, PRL 101, 090403 (2008) N elemen- tary spins ½ time “+” tt tt tt tt

23. Relation quantum-classical

24. Macroscopic candidates Heavy molecules 1 (position) Nanomechanics 4 (position, momentum) Superconducting devices 2 (current) Atomic gases 3 (spin) 1 S. Gerlich et al., Nature Comm. 2, 263 (2011) 3 B. Julsgaard et al., Nature 413, 400 (2001) 2 M. W. Johnson et al., Nature 473, 194 (2011) 4 G. Cole et al., Nature Comm. 2, 231 (2011)

25. Alternative to Leggett-Garg inequality No-signaling in time (NSIT): “A measurement does not change the outcome statistics of a later measurement.”* MR  NSIT Violation of NSIT witnesses non-classical time evolution Advantages of NSIT compared to LGI: - Only two measurement times (simpler witness) - Violated for broader parameter regime (better witness) LGI and NSIT are tools for witnessing temporal quantum coherence in complex systems (not necessarily having macroscopic superpositions) Does quantum coherence give biological systems an evolutionary advantage? tAtA tBtB t0t0 AB * J. K. and Č. Brukner, PRA 87, 052115 (2013)

26. Candidates for quantum biology Photosynthesis: Light harvesting in the FMO complex M. Sarovar et al., Nature Phys. 6, 462 (2010) Avian compass electronic excitation (by sunlight) in antenna is transferred to reaction center evidence for efficiency increase due to quantum coherent transport radical pair mechanism proposed reaction products depend on earth magnetic field N. Lambert et al., Nature Phys. 9, 10 (2013)

27. Conclusion and outlook Local realism - world view radically different from quantum mechanics - violated experimentally (Bell tests) by qu. entanglement - all loopholes are closed, but not yet simultaneously - loopholes relevant for qu. cryptography - long distance distribution of entanglement Macrorealism - related to the measurement problem (Schrödinger’s cat) - quantum mechanics predicts violation - quantum-to-classical transition - Leggett-Garg inequality (LGI) not yet violated for macroscopic objects; several candidates - no-signaling in time (NSIT) as an alternative - LGI and NSIT: tools for witnessing quantum time evolution in mesoscopic systems including biological organisms

28. Acknowledgments Anton Zeilinger Maximilan Ebner Marissa Giustina Thomas Herbst Thomas Jennewein Michael Keller Mateusz Kotyrba Xiao-song Ma Caslav Brukner Alexandra Mech Sven Ramelow Thomas Scheidl Mandip Singh Rupert Ursin Bernhard Wittmann Stefan Zotter Ignacio Cirac

29. Appendix

30. Entanglement Erwin Schrödinger “Total knowledge of a composite system does not necessarily include maximal knowledge of all its parts, not even when these are fully separated from each other and at the moment are not influencing each other at all.” (1935) What is the difference between the entangled state |  AB = (|   AB + |   AB ) /  2 and the “classical” mixed state probability ½: |   AB probability ½: |   AB which is also locally random and globally perfectly correlated?  = ½ |   AB   | + ½ |   AB   |

31. Einstein vs. Bohr Albert Einstein (1879–1955) Niels Bohr (1885–1962) What is nature? What can be said about nature?

32. Interpretations Copenhagen interpretationquantum state (wave function) only describes probabilities objects do not possess all properties prior to and independent of measurements (violating realism) individual events are irreducibly random Bohmian mechanicsquantum state is a real physical object and leads to an additional “force” particles move deterministically on trajectories position is a hidden variable & there is a non-local influence (violating locality) individual events are only subjectively random Many-worlds interpretationall possibilities are realized parallel worlds

33. Entanglement from Bose-Einstein condensates J. K., M. Singh, M. Ebner, M. Keller, M. Kotyrba, A. Zeilinger, PRA 86, 032115 (2012) First entanglement of massive particles in external degree of freedom (momentum) Picture: A. Perrin et al., PRL 99, 150405 (2007)

34. Ideal negative measurements Taking only those results where no interaction with the object took place How to enforce non-invasiveness? Locality vs. non-invasiveness Space-like separation Special relativity guarantees impossibility of physical influence How to enforce locality? ?? –1+1 –1+1

35. Stages towards violation of MR Quantum interference between macroscopically distinct states (QIMDS) does not necessarily establish the truth of quantum mechanics (QM) Leggett’s three stages of experiments:* “Stage 1. One conducts circumstantial tests to check whether the relevant macroscopic variable appears to be obeying the prescriptions of QM. Stage 2. One looks for direct evidence for QIMDS, in contexts where it does not (necessarily) exclude macrorealism. Stage 3. One conducts an experiment which is explicitly designed so that if the results specified by QM are observed, macrorealism is thereby excluded.” However: step from stage 2 to 3 is straightforward via violation of NSIT * A. J. Leggett, J. Phys.: Cond. Mat. 14, R415 (2002)