University of Gdańsk, Poland ‘No-signaling in time’ as an alternative to the Leggett-Garg inequalities Johannes Kofler University of Gdańsk, Poland Sept 17th 2013

With photons, electrons, neutrons, molecules etc. 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”)?

Superconducting devices2 Candidates for macro-superpositions Heavy molecules1 (position) Superconducting devices2 (current) Atomic gases3 (spin) Nanomechanics4 (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)

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 talk1 - local realism vs. macrorealism - alternative to the Leggett-Garg inequality 1 J. K. and Č. Brukner, PRA 87, 052115 (2013)

Local realism vs. macrorealism Are non-classical correlations possible? Are macroscopic superpositions possible? Quantum mechanics says “yes” (use entanglement) Quantum mechanics says “yes” (if you manage to defy decoherence) Local realism (e.g. classical physics) says “no” (only classical correlations) Macrorealism (e.g. classical physics, objective collapse models) says “no” (only classical temporal correlations) Bell test has given experimental answer in favor of quantum mechanics Leggett-Garg test can/will give experimental answer, community still split Practical relevance qu. computation, qu. cryptography Practical relevance witnessing temporal qu. coherence

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 = ±1 B = ±1 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)

No-signaling Causality demands the no-signaling (NS) condition: “Bob’s outcome statistics do not depend on space-like separated events on Alice’s side.” All local realistic theories are no-signaling but not the opposite (e.g. quantum mechanics, PR boxes): Violation of NS implies violation of LR, but all reasonable theories (including QM) 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.”1 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.”1 Joint assumption: Macrorealism (MR): A B t0 tA tB Macrorealism restricts temporal correlations Leggett-Garg inequality (LGI): Q Q Q Q ±1 t0 t1 t2 t3 t4 Quantum mechanics (QM): 1 A. J. Leggett and A. Garg, Phys. Rev. Lett. 54, 857 (1985)

Derivation of the Leggett-Garg inequality Dichotomic quantity: Qi = 1 Temporal correlations Q Q Q Q ±1 t0 t1 t2 t3 t4 Q1Q2 + Q2Q3 + Q3Q4 – Q1Q4 = 2 LGI: K := Q1Q2 + Q2Q3 + Q3Q4 – Q1Q4  2 KQM = 22 = non-invasiveness S := A1B1 + A2B1 + A2B2 – A1B2  2 BI: SQM = 22 = locality LGI violation  “macrorealism per se” and/or “non-invasive measurability” fail/es Up to now: 1-to-1 correspondence between LR (BI) and MR (LGI)

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.” A B t0 tA tB All macrorealistic theories fulfill NSIT but not the opposite: 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 (the 1-to-1 correspondence breaks) J. K. and Č. Brukner, PRA 87, 052115 (2013)

Violation of no-signaling in time NSIT demands “classical probability paths”: ! A B B t0 tA tB t0 tB Violation of NSIT due to quantum mechanical interference terms Advantages of NSIT compared to LGI: - Only two measurement times (“simpler witness”) - Usually violated for broader parameter regimes (“better witness”) J. K. and Č. Brukner, PRA 87, 052115 (2013)

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:1 “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.” Step from stage 2 to 3: logically important but straightforward via violation of NSIT just need to show that QIMDS vanishes when prior measurement is made 1 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 Special relativity guarantees impossibility of physical influence Ideal negative measurements Taking only those results where no interaction with the object took place –1 +1 ? ? –1 +1 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

Double slit experiment x = d/2 x t t0 t1 t2 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)

violated in specific parameter regimes Mach-Zehnder interferometer LGI NSIT violated in specific parameter regimes violated up to measure 0 J. K. and Č. Brukner, PRA 87, 052115 (2013)

or no-signaling in time The quantum-to-classical transition decoherence or or no-signaling in time LGI and NSIT: tools for witnessing temporal quantum coherence in complex systems J. K. and Č. Brukner, PRL 99, 180403 (2007) J. K. and Č. Brukner, PRL 101, 090403 (2008)

Conclusion LR MR BI NS LGI NSIT QM QM BI necessary for LR tests NS “useless” LGI not essential for MR tests alternative: NSIT