Bell and Leggett-Garg inequalities in tests of local and macroscopic realism

Transcription

1 Max Planck Institute of Quantum Optics (MPQ) Garching / Munich, Germany Bell and Leggett-Garg inequalities in tests of local and macroscopic realism Johannes Kofler University of Valencia, Spain 25 June 2013

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 Classical world view: 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

4 Bell s inequality Realism Locality Alice Bob Local realism: A = A(a,λ,b,B) outcomes A = ±1 B = ±1 B = B(b,λ,a,A) settings a 1,a 2 b 1,b 2 A 1 (B 1 +B 2 ) + A 2 (B 1 B 2 ) = ±2 λ 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 = using entangled quantum states, e.g. Φ AB = ( HV AB + VH AB ) / 2 First experimental violation: 1972 Since then: tests with photons, atoms, superconducting qubits, *J. S. Bell, Phys. 1, 195 (1964); J. F. Clauser et al., PRL 23, 880 (1969)

5 Quantum entanglement Entangled state: Φ AB = ( AB + AB ) / 2 = ( AB + AB ) / 2 Alice basis: result / : / : / : / : / : / : / : / : locally: random Bob basis: result / : / : / : / : / : / : / : / : globally: perfect correlations A 2 B 2 A B 1 1 Top picture:

6 Entanglement and knowledge 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) Erwin Schrödinger

7 Loopholes Loopholes: maintain local realism despite S exp > 2 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, ) Freedom of choice settings are correlated with hidden variables closing: hard for atoms, achieved for photons ( ) Fair sampling measured ensemble is not representative closing: achieved for atoms ( ) and photons ( ) E λ 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, (2010) 4 M. A. Rowe et al., Nature 409, 791 (2001) 5 M. Giustina et al., Nature 497, 227 (2013)

8 Ensuring locality & freedom of choice S exp = 2.37 ± 0.02 Tenerife b,b La Palma E,A E λ a La Palma Tenerife Locality: A is space-like sep. from b and B B is space-like sep. from a and A p(a,b a,b,λ) = p(a a,λ) p(b b,λ) Freedom of choice: a and b are random a and b are space-like sep. from E λ p(a,b λ) = p(a,b) T. Scheidl, R. Ursin, J. K., T. Herbst, L. Ratschbacher, X. Ma, S. Ramelow, T. Jennewein, A. Zeilinger, PNAS 107, (2010)

9 Ensuring fair sampling Problem: detection efficiency could depend on settings η A = η A (α), η B = η B (β) Solution: Superconducting transition edge sensors very good detectors Eberhard inequality* - undetected ( u ) events in derivation - required detection efficiency η only 2/ Source +1 1 From Topics in Applied Physics 99, (2005) local realism J A B = C α, β ) C ( α, β ) C ( α, β ) + C ( α, β ) + S ( α ) + S ( β ) oo ( 1 1 oo 1 2 oo 2 1 oo 2 2 o 1 o 1 0 * P. H. Eberhard, PRA 47, 747 (1993)

10 First fair sampling of photons J A B = C α, β ) C ( α, β ) C ( α, β ) + C ( α, β ) + S ( α ) + S ( β ) oo ( 1 1 oo 1 2 oo 2 1 oo 2 2 o 1 o 1 0 local realism quantum violation of local realism with fair sampling Detection efficiency 75% Violation by 70 standard deviations Photon: only system for which all loopholes are closed (not yet simultaneously) 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)

11 Large distances 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* Bell-state measurement (BSM): Entanglement swapping * M. Žukowski et al., PRL 71, 4287 (1993)

12 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 Temporal order does not matter in qu. mechanics X. Ma, S. Zotter, J. K., R. Ursin, T. Jennewein, Č. Brukner, A. Zeilinger, Nature Phys. 8, 479 (2012)

13 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)

14 The next step ISS (350 to 400 km altitude)

15 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

16 The double slit experiment Particles Waves Quanta Superposition: ψ = left + right Picture:

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

18 Local realism vs. macrorealism Are non-local correlations possible? Quantum mechanics says yes (use entanglement) Local realism (e.g. classical physics) says no (only classical correlations) Bell test has given experimental answer in favor of quantum mechanics Practical relevance qu. computation, qu. cryptography Are macroscopic superpositions possible? Quantum mechanics says yes (if you manage to defy decoherence) 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 witnessing temporal qu. coherence

19 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) Bell: Quantum mechanics: K := Q 1 Q 2 + Q 2 Q 3 + Q 3 Q 4 Q 1 Q 4 2 = non-invasiveness S := A 1 B 1 + A 1 B 2 + A 2 B 1 A 2 B 2 2 = locality t 0 Q Q Q Q ±1 t 1 t 2 t 3 t 4 time K QM = A. J. Leggett and A. Garg, PRL 54, 857 (1985)

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

21 Sharp vs. coarse-grained measurements Spin j Sharp measurement of spin z-component Coarse-grained measurement or decoherence Q = 1 j +j j +j Q = +1 macroscopically distinct states classical limit 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, (2007)

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

23 Non-classical evolutions are complex Rotation in real space classical Oscillating Schrödinger cat non-classical rotation in Hilbert space N elementary spins ½ + + time t t t t time 1 single computation step per t all N rotations can be done simultaneously N sequential steps per t J. K. and Č. Brukner, PRL 101, (2008)

24 Relation quantum-classical

25 Macroscopic candidates Heavy molecules 1 (position) Superconducting devices 2 (current) Atomic gases 3 (spin) Nanomechanics 4 (position, momentum) 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)

26 Alternative to Leggett-Garg inequality No-signaling in time (NSIT): A measurement does not change the outcome statistics of a later measurement. * t 0 A B t A t B 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? * J. K. and Č. Brukner, PRA 87, (2013)

27 Candidates for quantum biology Photosynthesis: Light harvesting in the FMO complex 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 M. Sarovar et al., Nature Phys. 6, 462 (2010) N. Lambert et al., Nature Phys. 9, 10 (2013)

28 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

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

30 Appendix

31 Einstein vs. Bohr Albert Einstein ( ) Niels Bohr ( ) What is nature? What can be said about nature?

32 Interpretations Copenhagen interpretation Bohmian mechanics Many-worlds interpretation quantum 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 quantum 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 all possibilities are realized parallel worlds

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

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