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A comparison between Bell's local realism
and Leggett-Garg's macrorealism
Johannes Kofler
Group Workshop
Friedrichshafen, Germany, Sept 13th 2012
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”)?
Local realism vs. macrorealism
Are non-local correlations
possible?
Are macroscopic superpositions
possible?
Quantum mechanics says:
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 inequality
Leggett-Garg inequality
has given experimental answer
in favor of quantum mechanics
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”:
• 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)
A = ±1
B = ±1
a
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):
t0
• Macrorealism restricts correlations
Leggett-Garg inequality (LGI):
t0
• Quantum mechanics (QM):
[3] A. J. Leggett and A. Garg, Phys. Rev. Lett. 54, 857 (1985)
A
B
tA
tB
Q
Q
Q Q ±1
t1
t2
t3
t4
Derivation of the Leggett-Garg inequality
Dichotomic quantity:
t=0
Temporal correlations
t
t1
Violation  “macrorealism” per se and/or
“non-invasive measurability” fail/es
t2
t3
t4
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.”
t0
A
B
tA
tB
• 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
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)
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
–1
+1

Bohmian mechanics
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
Double slit experiment
x = d/2
x
t1
t2
t0
t
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)
Comparison
arXiv:1207.3666v1
Appendix 1: Delayed-choice entanglement swapping
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
Nature Phys. 8, 479 (2012)
Appendix 2: Proposal for a BEC-EPR experiment
Momentum-entangled He4 particle
pairs are produced by laser kicks and
subsequent collision
A. Perrin et al., PRL 99,
150405 (2007)
Double-double slit: two-particle interference
(conditional interference fringes):
Phys. Rev. A, in print (2012)
Appendix 3: Quantum teleportation over 143 km
Towards a world-wide “quantum internet”
Future vision: quantum links with satellites
Nature, in print (2012)