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Quantum entanglement and
macroscopic quantum superpositions
Quantum Information Symposium
Institute of Science and Technology (IST) Austria
7 March 2013
Johannes Kofler
Max Planck Institute of Quantum Optics (MPQ)Garching / Munich, Germany
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
• 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
Classical world view:
Bell’s inequality
Realism
*J. S. Bell, Phys. 1, 195 (1964); J. F. Clauser et al., PRL 23, 880 (1969)
a1,a2
B = ±1A = ±1
b1,b2
A1 (B1+B2) + A2 (B1–B2) = ±2
Local realism: A = A(a,,b,B)
B = B(b,,a,A)
outcomes
settings
variables
S := A1B1 + A1B2 + A2B1 – A2B2 2 Bell’s inequality*
Quantum mechanics:
SQM = 22 2.83
First experimental violation: 1972
Since then: tests with photons, atoms, superconducting qubits, …
using entangled quantum states, e.g.
Locality
|AB = (|HVAB + |VHAB) / 2
Alice Bob
Quantum entanglement
Entangled state:
|AB = (|HVAB + |VHAB) / 2
Picture: http://en.wikipedia.org/wiki/File:SPDC_figure.png
Loopholes
Why important?
- Quantum foundations- Security of entanglement-based quantum cryptography
Three main loopholes:
• Locality loopholehidden communication between the partiesclosing: hard for atoms, achieved for photons (19821,19982)
• Freedom of choicesettings are correlated with hidden variables closing: hard for atoms, achieved for photons (20103)
• Fair samplingmeasured ensemble is not representativeclosing: 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 M. A. Rowe et al., Nature 409, 791 (2001)5 M. Giustina et al., Nature in print (2013)
Loopholes:
maintain local realism despite Sexp > 2
E()
Locality: Alice’s measurement event A is space-like separated from Bob‘s measurement event B and his setting choice b (and vice versa)
T. Scheidl, R. Ursin, J. K., T. Herbst, L. Ratschbacher, X. Ma, S. Ramelow, T. Jennewein, A. Zeilinger, PNAS 107, 10908 (2010)
Ensuring locality & freedom of choice
B,b
E,A
a
Tenerife
La Palma
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)
E()
Ensuring fair sampling
Two main ingredients:
• Superconducting transition edge sensors
• Eberhard inequality*
- undetected (“u”) events in derivation
- required detection efficiency 66.7%
0)()(),(),(),(),( 1122122111 Bo
Aooooooooo SSCCCCJ
From Topics in Applied Physics 99, 63-150 (2005)
*P. H. Eberhard, PRA 47, 747 (1993)
+1–1 Source
+1–1
Local realism
First fair sampling of photons
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)
0)()(),(),(),(),( 1122122111 Bo
Aooooooooo SSCCCCJ
Detection efficiency 75%Violation by 70 standard deviations
Local realism
Quantum violation of local realism with fair sampling
Photon: only system for which all loop-holes are closed; not yet simultaneously
Large distances
* M. Žukowski et al., PRL 71, 4287 (1993)
Bell-state measurement (BSM): Entanglement swapping
How to distribute entanglement over large distances?- qu. cryptography between Vienna and Paris- distributed quantum computation
Two answers:
- glass fibers & quantum repeaters- no fibers: free space
Quantum repeaters use 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
X. Ma, S. Zotter, J. K., R. Ursin, T. Jennewein, Č. Brukner, A. Zeilinger, Nature Phys. 8, 479 (2012)
Temporal order does not matter in qu. mechanics
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
Picture: http://www.blacklightpower.com/theory/DoubleSlit.shtml
Particles Waves Quanta
Superposition:
| = |left + |right
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 test
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 test
can/will give experimental answercommunity still split
Practical relevance
qu. computation, qu. cryptography
Practical relevance
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)
A. J. Leggett and A. Garg, PRL 54, 857 (1985)
• Quantum mechanics:
t1 t2 t3 t4t0
Q Q Q Q ±1
S := A1B1 + A1B2 + A2B1 – A2B2 2
K := Q1Q2 + Q2Q3 + Q3Q4 – Q1Q4 2
Bell:
KQM = 22 2.83
locality
non-invasiveness=
=
time
½
Rotating spin ½ particle (eg. electron)
Rotating classical spin vector (eg. gyroscope)
K > 2: violation of Leggett-Garg inequality
K 2: no violation, classical time evolution
classical limit
Precession around an axis(via magnetic field or external force)
Measurments along different axis
Quantum vs. classical
22
classical limit
Sharp measurement of spin z-component
Violation of Leggett-Garg inequality for arbitrarily large spins j
Classical physics of a rotating classical spin vector
J. K. and Č. Brukner, PRL 99, 180403 (2007)
Spin j
1 3 5 7 ...
2 4 6 8 ...Q = +1
Q = –1
–j +j –j +j
Coarse-grained measurement or decoherence
Sharp vs. coarse-grained measurements
macroscopically distinct states
Sharp measurements
Coarse-grained measurements or decoherence
Superposition vs. mixture
To see quantumness: need to resolve j1/2 levels & protect system from environment
J. K. and Č. Brukner, PRL 101, 090403 (2008)
Oscillating Schrödinger cat“non-classical” rotation in Hilbert space
Rotation in real space“classical”
N sequential steps per t1 single computation step per tall N rotations can be done simultaneously
Non-classical evolutions are complex
J. K. and Č. Brukner, PRL 101, 090403 (2008)
N elemen-tary spins ½
time time
“+” “+”
t t t t
Relation quantum-classical
Macroscopic candidates
Heavy molecules1
(position)
Nanomechanics4
(position, momentum)
Superconducting devices2
(current)
Atomic gases3
(spin)
1 S. Gerlich et al., Nature Comm. 2, 263 (2011) 3 B. Julsgaard et al., Nature 413, 400 (2001)2 M. W. Johnson et al., Nature 473, 194 (2011) 4 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.”*
• 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?
tA tBt0
A B
* J. K. and Č. Brukner, arXiv:1207.3666, to be published (2013)
Candidates for quantum biology
Photosynthesis:Light harvesting in the FMO complex
M. Sarovar et al., Nature Phys. 6, 462 (2010)
Avian compass
electronic excitation (by sunlight) in antenna is transferred to reaction center
evidence for efficiency increase due to quantum coherent transport
radical pair mechanism proposed
reaction products depend on earth magnetic field
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
Anton Zeilinger
Maximilan Ebner
Marissa Giustina
Thomas Herbst
Thomas Jennewein
Michael Keller
Mateusz Kotyrba
Xiao-song Ma
Caslav Brukner
Alexandra Mech
Sven Ramelow
Thomas Scheidl
Mandip Singh
Rupert Ursin
Bernhard Wittmann
Stefan Zotter
Ignacio Cirac