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A condition for macroscopic realism beyond the Leggett- Garg inequalities

A condition for macroscopic realism beyond the Leggett- Garg inequalities. Johannes Kofler 1 and Č aslav Brukner 2. 1 Max Planck Institute of Quantum Optics (MPQ), Garching /Munich, Germany

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A condition for macroscopic realism beyond the Leggett- Garg inequalities

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  1. A condition for macroscopic realism beyond the Leggett-Garg inequalities Johannes Kofler1 and Časlav Brukner2 1Max Planck Institute of Quantum Optics (MPQ), Garching/Munich, Germany 2University of Vienna & Institute for Quantum Optics and Quantum Information (IQOQI), Vienna, Austria APS March Meeting Boston, USA, March 1st 2012

  2. Introduction • 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

  3. 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”: A B a b • 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)

  4. No-signaling • Causality demands the no-signaling (NS) condition: “Bob’s outcome statistic 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

  5. 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): A B t0 tA tB • Macrorealismrestricts correlations • Leggett-Garg inequality (LGI): Q Q Q Q t0 t1 t2 t3 t4 • Quantum mechanics (QM): [3] A. J. Leggett and A. Garg, Phys. Rev. Lett. 54, 857 (1985)

  6. Statistical non-invasive measurability • In analogy to NS: • Statistical non-invasive measurability (SNIM): “A measurement does not change the outcome statistics of a later measurement.” A B t0 tA tB • All macrorealistic theories fulfill SNIM but not the opposite (e.g. fully mixed initial state and suitable Hamiltonian): • Key difference between NS and SNIM: • - NS cannot be violated due to causality • - SNIM can be violated according to quantum mechanics

  7. Double slit experiment x = d/2 x t1 t0 t2  SNIM violated LGI hard to construct I Both slits open: II Block lower slit at x = –d/2: III Block upper slit at x = +d/2: fringes 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)

  8. 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] • Our conclusion: step from stage 2 to 3 is straightforward via violation of SNIM [5] A. J. Leggett, J. Phys.: Cond. Mat. 14, R415 (2002)

  9. Summary SNIM can be violated technically easier than LGI

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