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

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”: [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 BA b

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): [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

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.” 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 tAtA tBtB t0t0 AB

7. 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 I Both slits open: 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  SNIM violated LGI hard to construct

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