A condition for macroscopic realism beyond the Leggett-Garg inequalities

APS March Meeting

Boston, USA, March 1st 2012

Johannes Kofler1 and Časlav Brukner2

1 Max Planck Institute of Quantum Optics (MPQ), Garching/Munich, Germany2 University of Vienna & Institute for Quantum Optics and Quantum Information (IQOQI), Vienna, Austria

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

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 correlationsBell’s inequality (BI):

• Quantum mechanics (QM):

aBA

b

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

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 correlationsLeggett-Garg inequality (LGI):

• Quantum mechanics (QM):

t1 t2 t3 t4

tA tBt0

t0

A B

Q Q Q Q

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

tA tBt0

A B

Double slit experiment

t1

Picture: N. Bohr, in Quantum Theory and Measurement, eds. J. A. Wheeler and W. H. Zurek,Princeton University Press (1983)

t2

I Both slits open:

II Block lower slit at x = –d/2:

III Block upper slit at x = +d/2:

t0

x = d/2 x

fringes

no fringes

II,III: ideal negative measurements

SNIM violated

LGI hard to construct

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)

Summary

SNIM can be violated

technically easier than LGI