1. A comparison between Bell's local realism and Leggett-Garg's macrorealism Group Workshop Friedrichshafen, Germany, Sept 13 th 2012 Johannes Kofler

2. 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

3. 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 inequality 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 inequality will give experimental answer

4. Historical development Bell’s inequality & local realism - well developed research field - important for quantum information technologies - experiments exist (photons, atoms, superconducting qubits, …) Leggett-Garg inequality & macroscopic realism - gained momentum in last years - experiments approach regime of macroscopic quantum superpositions - candidates:superconducting devices, heavy molecules, quantum-optical systems in combination with atomic gases or massive objects - community still divided into two groups This talk - local realism vs. macrorealism - alternative to the Leggett-Garg inequality

5. Local realism Realism is a worldview ”according to which external reality is assumed to exist and have definite properties, whether or not they are observed by someone.” [1] Locality demands that ”if two measurements are made at places remote from one another the [setting of one measurement device] does not influence the result obtained with the other.” [2] Joint assumption local realism (LR) or “local causality”: [1] J. F. Clauser and A. Shimony, Rep. Prog. Phys. 41, 1881 (1978) [2] J. S. Bell, Physics (New York) 1, 195 (1964) Local realism restricts correlations Bell’s inequality (BI): Quantum mechanics (QM): a B = ±1A = ±1 b

6. No-signaling Causality demands the no-signaling (NS) condition: “Bob’s outcome statistics does not depend on space-like separated events on Alice’s side.” All local realistic theories are no-signaling but not the opposite (e.g. Bohmian mechanics, PR boxes): Violation of NS implies violation of LR, but all reasonable theories (including quantum mechanics) fulfill NS  Bell inequalities necessary

7. Macrorealism Macrorealism per se: ” A macroscopic object which has available to it two or more macroscopically distinct states is at any given time in a definite one of those states.” [3] Non-invasive measurability: “It is possible in principle to determine which of these states the system is in without any effect on the state itself or on the subsequent system dynamics.” [3] Joint assumption macrorealism (MR): [3] A. J. Leggett and A. Garg, Phys. Rev. Lett. 54, 857 (1985) Macrorealism restricts correlations Leggett-Garg inequality (LGI): Quantum mechanics (QM): t1t1 t2t2 t3t3 t4t4 tAtA tBtB t0t0 t0t0 AB QQQQ ±1

8. Dichotomic quantity: Temporal correlations t = 0 t t1t1 t2t2 t3t3 t4t4 Violation  “macrorealism” per se and/or “non-invasive measurability” fail/es Derivation of the Leggett-Garg inequality

9. No-signaling in time In analogy to NS: No-signaling in time (NSIT): “A measurement does not change the outcome statistics of a later measurement.” All macrorealistic theories fulfill NSIT but not the opposite (e.g. fully mixed initial state and suitable Hamiltonian): Key difference between NS and NSIT: - NS cannot be violated due to causality  BI necessary - NSIT can be violated according to quantum mechanics  no need for LGI tAtA tBtB t0t0 AB

10. 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.” [5] However: step from stage 2 to 3 is straightforward via violation of NSIT [5] A. J. Leggett, J. Phys.: Cond. Mat. 14, R415 (2002)

11. 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? Bohmian mechanics Space-like separation is of no help: non-local influence on hidden variable level Realistic, non-local Bohmian mechanics Ideal negative measurements are of no help: wavefunction collapse changes subsequent evolution Macrorealistic per se, invasive ?? –1+1 –1+1

12. Double slit experiment t1t1 Picture:N. Bohr, in Quantum Theory and Measurement, eds. J. A. Wheeler and W. H. Zurek, Princeton University Press (1983) t2t2 II Block lower slit at x = –d/2 : III Block upper slit at x = +d/2 : t0t0 x =  d/2 x fringes no fringes II,III : ideal negative measurements  NSIT is violated due to interference terms LGI impossible to construct I Both slits open: t x

13. Comparison arXiv:1207.3666v1

14. Appendix 1: Delayed-choice entanglement swapping Nature Phys. 8, 479 (2012) Bell-state measurement (BSM): Entanglement swapping Mach-Zehnder interferometer and QRNG as tunable beam splitter Separable-state measurement (SSM): No entanglement swapping -A later measurement on photons 2 & 3 decides whether photons 1 & 4 were in a separable or an entangled state -Entanglement-separability duality

15. Appendix 2: Proposal for a BEC-EPR experiment Phys. Rev. A, in print (2012) Momentum-entangled He 4 particle pairs are produced by laser kicks and subsequent collision Double-double slit: two-particle interference (conditional interference fringes): A. Perrin et al., PRL 99, 150405 (2007)

16. Appendix 3: Quantum teleportation over 143 km Nature, in print (2012) Towards a world-wide “quantum internet” Future vision: quantum links with satellites