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A comparison between Bell's local realism and Leggett-Garg's macrorealism Johannes Kofler Group Workshop Friedrichshafen, Germany, Sept 13th 2012 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”)? Local realism vs. macrorealism Are non-local correlations possible? Are macroscopic superpositions possible? Quantum mechanics says: Quantum mechanics says: “yes” (use entanglement) “yes” (if you manage to defy decoherence) Local realism (e.g. classical physics) says Macrorealism (e.g. classical physics, objective collapse models) says “no” (only classical correlations) “no” (only classical temporal correlations) Bell inequality Leggett-Garg inequality has given experimental answer in favor of quantum mechanics will give experimental answer 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 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”: • Local realism restricts correlations Bell’s inequality (BI): • Quantum mechanics (QM): [1] J. F. Clauser and A. Shimony, Rep. Prog. Phys. 41, 1881 (1978) [2] J. S. Bell, Physics (New York) 1, 195 (1964) A = ±1 B = ±1 a b 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 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): t0 • Macrorealism restricts correlations Leggett-Garg inequality (LGI): t0 • Quantum mechanics (QM): [3] A. J. Leggett and A. Garg, Phys. Rev. Lett. 54, 857 (1985) A B tA tB Q Q Q Q ±1 t1 t2 t3 t4 Derivation of the Leggett-Garg inequality Dichotomic quantity: t=0 Temporal correlations t t1 Violation “macrorealism” per se and/or “non-invasive measurability” fail/es t2 t3 t4 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.” t0 A B tA tB • 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 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) Locality vs. non-invasiveness How to enforce locality? How to enforce non-invasiveness? Space-like separation Ideal negative measurements Special relativity guarantees impossibility of physical influence Taking only those results where no interaction with the object took place ? ? –1 +1 –1 +1 Bohmian mechanics Bohmian mechanics Space-like separation is of no help: non-local influence on hidden variable level Ideal negative measurements are of no help: wavefunction collapse changes subsequent evolution Realistic, non-local Macrorealistic per se, invasive Double slit experiment x = d/2 x t1 t2 t0 t x NSIT is violated due to interference terms LGI impossible to construct I Both slits open: fringes II Block lower slit at x = –d/2: III Block upper slit at x = +d/2: no fringes II,III: ideal negative measurements Picture: N. Bohr, in Quantum Theory and Measurement, eds. J. A. Wheeler and W. H. Zurek, Princeton University Press (1983) Comparison arXiv:1207.3666v1 Appendix 1: Delayed-choice entanglement swapping 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 Nature Phys. 8, 479 (2012) Appendix 2: Proposal for a BEC-EPR experiment Momentum-entangled He4 particle pairs are produced by laser kicks and subsequent collision A. Perrin et al., PRL 99, 150405 (2007) Double-double slit: two-particle interference (conditional interference fringes): Phys. Rev. A, in print (2012) Appendix 3: Quantum teleportation over 143 km Towards a world-wide “quantum internet” Future vision: quantum links with satellites Nature, in print (2012)