A comparison between Bell's local realismand Leggett-Garg's macrorealism

Group Workshop

Friedrichshafen, Germany, Sept 13th 2012

Johannes Kofler

With photons, electrons, neutrons, molecules etc.

With cats?

|cat left + |cat right ?

When and how do physical systems stop to behave quantum mechanically and begin to behave classically (“measurement problem”)?

Macroscopic superpositions

6910 AMU

Quantum mechanics says:

“yes”(if you manage to defy decoherence)

Are macroscopic superpositions possible?

Local realism vs. macrorealism

Quantum mechanics says:

“yes”(use entanglement)

Are non-local correlations possible?

Local realism (e.g. classical physics) says

“no”(only classical correlations)

Bell inequality

has given experimental answer in favor of quantum mechanics

Macrorealism (e.g. classical physics, objective collapse models) says

“no”(only classical temporal correlations)

Leggett-Garg inequality

will give experimental answer

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 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):

a

B = ±1A = ±1

b

No-signaling

• Causality demands the no-signaling (NS) condition: “Bob’s outcome statistics 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 ±1

Dichotomic quantity:

Temporal correlationst = 0

t

t1 t2 t3 t4

Violation “macrorealism” per se and/or

“non-invasive measurability” fail/es

Derivation of the Leggett-Garg inequality

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.”

• All macrorealistic theories fulfill NSIT but not the opposite (e.g. fully mixed initial state and suitable Hamiltonian):

• 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

tA tBt0

A B

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]

• However: step from stage 2 to 3 is straightforward via violation of NSIT

[5] A. J. Leggett, J. Phys.: Cond. Mat. 14, R415 (2002)

Ideal negative measurements

Taking only those results where no interaction with the object took place

How to enforce non-invasiveness?

Locality vs. non-invasiveness

Space-like separation

Special relativity guarantees impossibility of physical influence

How to enforce locality?

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

? ?

–1 +1

–1 +1

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

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

NSIT is violated due to interference terms

LGI impossible to construct

I Both slits open:

t

x

Comparison

arXiv:1207.3666v1

Appendix 1: Delayed-choice entanglement swapping

Nature Phys. 8, 479 (2012)

Bell-state measurement (BSM): Entanglement swapping

Mach-Zehnder interferometer and QRNG as tunable beam splitter

Separable-state measurement (SSM): No entanglement swapping

- A later measurement on photons 2 & 3 decides whether photons 1 & 4 were in a separable or an entangled state

- Entanglement-separability duality

Appendix 2: Proposal for a BEC-EPR experiment

Phys. Rev. A, in print (2012)

Momentum-entangled He4 particle pairs are produced by laser kicks and subsequent collision

Double-double slit: two-particle interference (conditional interference fringes):

A. Perrin et al., PRL 99, 150405 (2007)

Appendix 3: Quantum teleportation over 143 km

Nature, in print (2012)

Towards a world-wide “quantum internet”

Future vision: quantum links with satellites