Necessary and sufficient conditions for macroscopic realism from

Introduction ? • ? How does our macroscopic & classical world arise out of

Macroscopic superpositions With photons, electrons, neutrons, molecules etc. With cats? |cat left + |cat

Candidates 1 2 Heavy molecules 1 (position) Superconducting devices 2 (current) Atomic gases 3

Macrorealism • Macrorealism per se: 1 given a set of macroscopically distinct states, a

Local realism vs. macrorealism Are non-classical correlations possible? Are macroscopic superpositions possible? Quantum mechanics

Locality vs. non-invasiveness How to enforce locality? How to enforce non-invasiveness? Space-like separation Ideal

Sharp vs. coarse-grained measurements Macroscopic spin j Sharp measurements (resolution of individual quantum levels)

Non-classical evolutions are complex Rotation in real space “classical” Oscillating Schrödinger cat “non-classical” rotation

The quantum-to-classical transition decoherence or J. K. and Č. Brukner, PRL 99, 180403 (2007)

Alternative to LGI No-signaling (NS): “A measurement on one side does not change the

Double slit experiment t 0 x = d/2 x t 1 t 2 t

Mach-Zehnder interferometer LGI NSIT violated in specific parameter regimes violated up to measure 0

Necessary conditions for MR Variety of necessary conditions for macrorealism 1 1 L. Clemente

Necessary and sufficient for MR Sufficient 1 for LGI 012 1 O. J. E.

NSIT for quantum measurements proj. Violation requires non-classical resource 1, 2, 3, 4 non-classical

Conclusion & Outlook • Quantum-to-classical transition: • • classical Hamiltonians & coarse-grained measurements No-signaling

Acknowledgments Časlav Brukner Lucas Clemente J. K. and Č. Brukner, PRA 87, 052115 (2013)

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Necessary and sufficient conditions for macroscopic realism from quantum mechanics Johannes Kofler Max Planck Institute of Quantum Optics (MPQ) Garching/Munich, Germany Quantum Theory: from foundations to technologies – QTFT Linnaeus University, Växjö, Sweden 9 June 2015

Introduction ? • ? How does our macroscopic & classical world arise out of quantum mechanics? - Decoherence (within quantum mechanics) - Spontaneous collapse models (altering quantum mechanics) - Complementary to decoherence: coarse-grained measurements • Macroscopic realism: “every object is in a definite macrostate at all times and can be measured non-invasively” Leggett-Garg inequality (LGI) • Quantum mechanics: superpositions of macroscopically distinct states (“Schrödinger cats”) violation of LGI • Alternative to the Leggett-Garg inequalities: “no-signaling in time” (NSIT)

Macroscopic superpositions With photons, electrons, neutrons, molecules etc. With cats? |cat left + |cat right ? Measurement problem Quantum-to-classical transition

Candidates 1 2 Heavy molecules 1 (position) Superconducting devices 2 (current) Atomic gases 3 (spin) Nanomechanics 4 (position, momentum) S. Gerlich et al. , Nature Comm. 2, 263 (2011) M. W. Johnson et al. , Nature 473, 194 (2011) 3 4 B. Julsgaard et al. , Nature 413, 400 (2001) G. Cole et al. , Nature Comm. 2, 231 (2011)

Macrorealism • Macrorealism per se: 1 given a set of macroscopically distinct states, a macroscopic object is at any given time in a definite one of these states • Non-invasive measurability: 1 measurements reveal the state without any effect on the state itself or on the subsequent dynamics • Leggett-Garg inequality (LGI): K : = Q 1 Q 2 + Q 2 Q 3 + Q 3 Q 4 – Q 1 Q 4 2 = t 0 Q Q ± 1 t 2 t 3 t 4 time non-invasiveness Bell: S : = A 1 B 1 + A 2 B 1 + A 1 B 2 – A 2 B 2 2 = A = ± 1 B = ± 1 a b locality • Quantum mechanics: KQM = 2 2 2. 83 Exp. LGI violations for microscopic systems: 1 A. J. Leggett and A. Garg, PRL 54, 857 (1985) J. Dressel et al. , PRL 106, 040402 (2011) M. E. Goggin et al. , PNAS 108, 1256 (2011) A. Fedrizzi et al. , PRL 106, 200402 (2011) G. Waldherr et al. , PRL 107, 090401 (2011) G. C. Knee et al. , Nature Comm. 3, 606 (2012) A. Asadian et al. , PRL 112, 190402 (2013)

Local realism vs. macrorealism Are non-classical correlations possible? Are macroscopic superpositions possible? 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 test Leggett-Garg test has given experimental answer in favor of quantum mechanics can/will give experimental answer, community still split Practical relevance qu. computation, qu. cryptography witnessing temporal qu. coherence

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 ü 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

Sharp vs. coarse-grained measurements Macroscopic spin j Sharp measurements (resolution of individual quantum levels) Decoherence or coarse-grained meas. (smeared phase space observables) To see quantumness: need to resolve j 1/2 levels & protect system from environment J. K. and Č. Brukner, PRL 99, 180403 (2007)

Non-classical evolutions are complex Rotation in real space “classical” Oscillating Schrödinger cat “non-classical” rotation in Hilbert space N elementary spins ½ “+” t t time 1 single computation step per t all N rotations can be done simultaneously J. K. and Č. Brukner, PRL 101, 090403 (2008) t “+” t N sequential steps per t time

The quantum-to-classical transition decoherence or J. K. and Č. Brukner, PRL 99, 180403 (2007) J. K. and Č. Brukner, PRL 101, 090403 (2008)

Alternative to LGI No-signaling (NS): “A measurement on one side does not change the outcome statistics on the other side. ” A B a b No-signaling in time (NSIT): “A measurement does not change the outcome statistics of a later measurement. ” 1 A B t 0 t. A t. B LR BI NS BI necessary for LR tests NS “useless” NSIT LGI not essential for MR tests alternative: NSIT (interference) more physical, simpler, stronger, more robust to noise QM MR LGI QM 1 J. K. and Č. Brukner, PRA 87, 052115 (2013)

Double slit experiment t 0 x = d/2 x t 1 t 2 t x NSIT is violated due to interference terms LGI impossible 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)

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

Necessary conditions for MR Variety of necessary conditions for macrorealism 1 1 L. Clemente and J. K. , PRA 91, 062103 (2015)

Necessary and sufficient for MR Sufficient 1 for LGI 012 1 O. J. E. Maroney and C. G Timpson, ar. Xiv: 1412. 6139 Necessary and sufficient 2 for MR 012 2 L. Clemente and J. K. , PRA 91, 062103 (2015)

NSIT for quantum measurements proj. Violation requires non-classical resource 1, 2, 3, 4 non-classical states / sharp measurements or non-classical Hamiltonians proj. coarse-grained observables “classical” Hamiltonians J. K. and Č. Brukner, PRL 101, 090403 (2008) T. Wang, R. Ghobadi, S. Raeisi, C. Simon, PRA 88, 062114 (2013) 3 H. Jeong, Y. Lim, M. S. Kim, PRL 112, 010402 (2014). 4 P. Sekatski, N. Gisin, N. Sangouard, PRL 113, 090403 (2014) 1 2 L. Clemente and J. K. , PRA 91, 062103 (2015)

Conclusion & Outlook • Quantum-to-classical transition: • • classical Hamiltonians & coarse-grained measurements No-signaling in time (NSIT): - alternative to the Leggett-Garg inequalities (simpler, stronger) - combination of NSIT clauses: necessary and sufficient for macrorealism Open problems: - general trade-off “measurement precision vs. Hamiltonian complexity” - coarse-graining requires notion of “neighborhood” of states

Acknowledgments Časlav Brukner Lucas Clemente J. K. and Č. Brukner, PRA 87, 052115 (2013) L. Clemente and J. K. , PRA 91, 062103 (2015)