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Max Planck Institute of Quantum Optics (MPQ)
Garching / Munich, Germany
Quantum entanglement and
macroscopic quantum superpositions
Johannes Kofler
Quantum Information Symposium
Institute of Science and Technology (IST) Austria
7 March 2013
Outlook
•
•
•
Quantum entanglement vs. local realism

Bell’s inequality

Loopholes

Entanglement swapping & teleportation
Macroscopic quantum superpositions vs. macrorealism

Leggett-Garg inequality

Quantum-to-classical transition

Witnessing non-classical evolutions in complex systems
Conclusion and outlook
Local realism
Classical world view:
• Realism: properties of physical objects exist independent of whether or not
they are observed by anyone
• Locality: no physical influence can propagate faster than the speed of light
External world
Passive observers
Bell’s inequality
Realism Locality
Local realism: A = A(a,,b,B)
B = B(b,,a,A)
outcomes
settings
Alice
Bob
A = ±1
B = ±1
a1,a2
b1,b2
A1 (B1+B2) + A2 (B1–B2) = ±2
S := A1B1 + A1B2 + A2B1 – A2B2  2
 variables
Bell’s inequality*
Quantum mechanics:
SQM = 22  2.83
using entangled quantum states, e.g.
|AB = (|HVAB + |VHAB) / 2
First experimental violation: 1972
Since then: tests with photons, atoms, superconducting qubits, …
*J. S. Bell, Phys. 1, 195 (1964); J. F. Clauser et al., PRL 23, 880 (1969)
Quantum entanglement
Entangled state:
|AB = (|HVAB + |VHAB) / 2
Picture: http://en.wikipedia.org/wiki/File:SPDC_figure.png
Loopholes
Loopholes:
Why important?
maintain local realism
despite Sexp > 2
- Quantum foundations
- Security of entanglement-based quantum cryptography
Three main loopholes:
• Locality loophole
hidden communication between the parties
closing: hard for atoms, achieved for photons (19821,19982)
• Freedom of choice
settings are correlated with hidden variables
closing: hard for atoms, achieved for photons (20103)
• Fair sampling
measured ensemble is not representative
E()
closing: achieved for atoms (20014) and photons (20135)
1
A. Aspect et al., PRL 49, 1804 (1982)
2 G. Weihs et al., PRL 81, 5039 (1998)
3 T. Scheidl et al., PNAS 107, 10908 (2010)
4
5
M. A. Rowe et al., Nature 409, 791 (2001)
M. Giustina et al., Nature in print (2013)
Ensuring locality & freedom of choice
Tenerife
B,b
La Palma
E,A
E()
a
Locality: Alice’s measurement event A is space-like separated from Bob‘s
measurement event B and his setting choice b (and vice versa)
Freedom of choice: Setting choices (a and b) are random and space-like
separated from the entangled pair emission event E(): p(a,b|) = p(a,b)
T. Scheidl, R. Ursin, J. K., T. Herbst, L. Ratschbacher, X. Ma, S. Ramelow,
T. Jennewein, A. Zeilinger, PNAS 107, 10908 (2010)
Ensuring fair sampling
Two main ingredients:
• Superconducting transition edge sensors
• Eberhard inequality*
- undetected (“u”) events in derivation
- required detection efficiency  66.7%
From Topics in Applied
Physics 99, 63-150 (2005)
+1
–1
Source
+1
–1
Local realism
J   Coo (1 , 1 )  Coo (1 ,  2 )  Coo ( 2 , 1 )  Coo ( 2 ,  2 )  SoA (1 )  SoB ( 1 )  0
*P. H. Eberhard, PRA 47, 747 (1993)
First fair sampling of photons
J   Coo (1 , 1 )  Coo (1 ,  2 )  Coo ( 2 , 1 )  Coo ( 2 ,  2 )  SoA (1 )  SoB ( 1 )  0
Local realism
Quantum violation
of local realism with
fair sampling
Detection efficiency  75%
Violation by 70 standard deviations
Photon: only system for which all loopholes are closed; not yet simultaneously
M. Giustina, A. Mech, S. Ramelow, B. Wittmann, J. K., Jörn Beyer, A. Lita, B. Calkins, T. Gerrits,
S. W. Nam, R. Ursin, A. Zeilinger, Nature in print (2013)
Large distances
How to distribute entanglement over large
distances?
Two answers:
- qu. cryptography between Vienna and Paris
- distributed quantum computation
- glass fibers & quantum repeaters
- no fibers: free space
Quantum repeaters use
entanglement swapping*
* M. Žukowski et al., PRL 71, 4287 (1993)
Bell-state measurement (BSM):
Entanglement swapping
Delayed-choice entanglement swapping
Later measurement on photons
2 & 3 decides whether 1 & 4
were separable or entangled
Naïve class. interpretation would
require influences into the past
Temporal order does not matter
in qu. mechanics
X. Ma, S. Zotter, J. K., R. Ursin, T. Jennewein, Č. Brukner, A. Zeilinger, Nature Phys. 8, 479 (2012)
Quantum teleportation
Towards a world-wide “quantum internet”
X. Ma, T. Herbst, T. Scheidl, D. Wang, S. Kropatschek, W. Naylor, A. Mech, B. Wittmann, J. K.,
E. Anisimova, V. Makarov, T. Jennewein, R. Ursin, A. Zeilinger, Nature 489, 269 (2012)
Contents
•
Quantum entanglement vs. local realism
 Bell’s inequality
 Loopholes
 Entanglement swapping & teleportation
•
Macroscopic quantum superpositions vs. macrorealism
 Leggett-Garg inequality
 Quantum-to-classical transition
 Witnessing non-classical evolutions in complex systems
•
Conclusion
The double slit experiment
Particles
Waves
Quanta
Superposition:
|  = |left + |right
Picture: http://www.blacklightpower.com/theory/DoubleSlit.shtml
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 test
Leggett-Garg test
has given experimental answer
in favor of quantum mechanics
can/will give experimental answer
community still split
Practical relevance
Practical relevance
qu. computation, qu. cryptography
witnessing temporal qu. coherence
Macrorealism
• Macrorealism per se:
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: measurements reveal the state without any effect
on the state itself or on the subsequent dynamics
• Leggett-Garg inequality (LGI)
K := Q1Q2 + Q2Q3 + Q3Q4 – Q1Q4  2
=
non-invasiveness
Bell:
S := A1B1 + A1B2 + A2B1 – A2B2  2
=
locality
• Quantum mechanics:
KQM = 22  2.83
A. J. Leggett and A. Garg, PRL 54, 857 (1985)
t0
Q
Q
Q Q ±1
t1
t2
t3
t4 time
Quantum vs. classical
Rotating spin ½ particle
(eg. electron)
½
Rotating classical spin
vector (eg. gyroscope)
Precession around an axis
(via magnetic field or external force)
Measurments along different axis
K > 2: violation of LeggettGarg inequality
K  2: no violation, classical
time evolution
22
classical limit
Sharp vs. coarse-grained measurements
Spin j
Coarse-grained measurement
or decoherence
Sharp measurement
of spin z-component
1 3 5 7 ... Q = –1
–j
+j
2 4 6 8 ... Q = +1
–j
+j
macroscopically distinct states
classical limit
Violation of Leggett-Garg inequality
for arbitrarily large spins j
J. K. and Č. Brukner, PRL 99, 180403 (2007)
Classical physics of a rotating
classical spin vector
Superposition vs. mixture
Sharp
measurements
Coarse-grained
measurements
or decoherence
To see quantumness: need to resolve j1/2 levels & protect system from environment
J. K. and Č. Brukner, PRL 101, 090403 (2008)
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
Relation quantum-classical
Macroscopic candidates
1
Heavy molecules1
Superconducting devices2
(position)
(current)
Atomic gases3
Nanomechanics4
(spin)
(position, momentum)
S. Gerlich et al., Nature Comm. 2, 263 (2011)
2 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)
Alternative to Leggett-Garg inequality
• No-signaling in time (NSIT): “A measurement does not change the outcome
statistics of a later measurement.”*
t0
A
B
tA
tB
• MR  NSIT
Violation of NSIT witnesses non-classical time evolution
• Advantages of NSIT compared to LGI:
- Only two measurement times (simpler witness)
- Violated for broader parameter regime (better witness)
• LGI and NSIT are tools for witnessing temporal quantum coherence in complex
systems (not necessarily having macroscopic superpositions)
• Does quantum coherence give biological systems an evolutionary advantage?
* J. K. and Č. Brukner, arXiv:1207.3666, to be published (2013)
Candidates for quantum biology
Photosynthesis:
Light harvesting in the FMO complex
Avian compass
electronic excitation (by sunlight) in antenna is
transferred to reaction center
radical pair mechanism
proposed
evidence for efficiency increase due to
quantum coherent transport
reaction products depend on
earth magnetic field
M. Sarovar et al., Nature Phys. 6, 462 (2010)
N. Lambert et al., Nature Phys. 9, 10 (2013)
Conclusion and outlook
•
Local realism
- world view radically different from quantum mechanics
- violated experimentally (Bell tests) by qu. entanglement
- all loopholes are closed, but not yet simultaneously
- loopholes relevant for qu. cryptography
- long distance distribution of entanglement
•
Macrorealism
- related to the measurement problem (Schrödinger’s cat)
- quantum mechanics predicts violation
- quantum-to-classical transition
- Leggett-Garg inequality (LGI) not yet violated for
macroscopic objects; several candidates
- no-signaling in time (NSIT) as an alternative
- LGI and NSIT: tools for witnessing quantum time evolution
in mesoscopic systems including biological organisms
Acknowledgments
Caslav Brukner
Ignacio Cirac
Anton Zeilinger
Maximilan Ebner
Alexandra Mech
Marissa Giustina
Sven Ramelow
Thomas Herbst
Thomas Scheidl
Thomas Jennewein
Mandip Singh
Michael Keller
Rupert Ursin
Mateusz Kotyrba
Bernhard Wittmann
Xiao-song Ma
Stefan Zotter