From Einstein's questions to Quantum bits:
a new quantum era?
Alain Aspect – Institut d’Optique – Palaiseau
http://www.lcf.institutoptique.fr/Alain-Aspect-homepage
ASIAA/CCMS/IAMS/LeCosPA/NTU- Physics Joint Colloquium,
Taipei , September 16 2014
From the Einstein-Bohr debate to Quantum Information:
a new quantum revolution?
1. Quantum information: how did it emerge?
2. From the Einstein-Bohr debate to
Bell's inequalities tests: entanglement 3. A new quantum revolution? Quantum
cryptography, quantum computing, simulating
http://www.lcf.institutoptique.fr/Alain-Aspect-homepage
From the Einstein-Bohr debate to Quantum Information:
a new quantum revolution?
1. Quantum information: how did it emerge?
2. From the Einstein-Bohr debate to
Bell's inequalities tests: entanglement 3. A new quantum revolution? Quantum
cryptography, quantum computing, simulating
4
Quantum information
a flourishing field
Quantum information how did it emerge?
Entanglement is different!
6
Quantum information how did it emerge?
Entanglement is more!
From the Einstein-Bohr debate to Quantum Information:
a new quantum revolution?
1. Quantum information: how did it emerge?
2. From the Einstein-Bohr debate to
Bell's inequalities tests: entanglement 3. A new quantum revolution? Quantum
cryptography, quantum computing, simulating
8
Einstein and quantum physics
A founding contribution (1905)
Light is made of quanta, later named
photons, which have well defined energy and momentum. Nobel 1922.
A fruitful objection (1935): entanglement
Einstein, Podolsky, Rosen (EPR): The quantum formalism allows one to envisage amazing situations (pairs of entangled particles):
the formalism must be completed.
Objection underestimated for a long time (except Bohr’s answer, 1935) until Bell’s theorem (1964) and the acknowledgement of its importance (1970-82).
Entanglement at the core of quantum information (198x-20??)
Is it possible (necessary) to explain the probabilistic character of quantum predictions by invoking a
supplementary underlying level of description (supplementary parameters, hidden variables) ?
A positive answer was the conclusion of the Einstein-
Podolsky-Rosen reasoning (1935). Bohr strongly opposed this conclusion.
Bell’s theorem (1964) has allowed us to settle the debate.
The EPR question
10
The EPR GedankenExperiment with photons correlated in polarization
S
ν2 +1
+1 +1 -1
ν1 +1
-1 +1
I II
a b x
y z
Measurement of the polarization of ν1 along orientation a and and of polarization of ν2 along orientation b : results +1 or –1
Ø Probabilities to find +1 ou –1 for ν1 (measured along a) and +1 or –1 for ν2 (measured along b).
Single probabiliti ( ) ,
e ( ) ( )
s
, ( )
P P
P P
+ −
+ −
a a
b b
( , )
Joint probabilities , ( , ) ( , ) , ( , )
P P
P P
++ +−
−+ −−
a b a b
a b a b
The EPR GedankenExperiment with photons correlated in polarization
S
ν2 +1
+1 +1 -1
ν1 +1
-1 +1
I II
a b x
y z
For the entangled EPR state… Ψ( , )ν ν1 2 = 12
{
x x, + y y,}
Quantum mechanics predicts
results separately random … P+( )a = P−( )a = 12 ; ( )P+ b = P−( )b = 12
but
strongly correlated:
(0) (0) 1
2 (0) (0) 0
P P
P P
++
=
−−=
= =
2
2
( , ) ( , ) 1cos ( , ) 2
( , ) ( , ) 1sin ( , ) 2
P P
P P
++ −−
+− −+
= =
= =
a b a b a b
a b a b a b
12
Coefficient of correlation of polarization (EPR state)
S
ν2 +1
+1 +1 -1
ν1 +1
-1 +1
I II
a b x
y z
MQ
( , ) cos2( , ) E a b = a b
MQ
1
⇒ E =
E = P++ + P−− − P+− − P−+ = P(résultats id°) − P(résultats ≠ ) Quantitative expression of the correlations between results of measurements in I et II: coefficient:
1 2 0 P P
P P
++ −−
+− −+
= =
= =
QM predicts, for parallel polarizers (a,b) = 0
More generally, for an arbitrary angle (a,b) between polarizers
Total correlation
{ }
1 2
( , ) 1 , ,
2 x x y y ν ν
Ψ = +
How to “understand” the EPR correlations predicted by quantum mechanics?
S
ν2 +1
+1 +1 -1
ν1 +1
-1 +1
I II
a b x
y z
{ }
1 2
( , ) 1 , ,
2 x x y y ν ν
Ψ = +
MQ
( , ) cos2( , ) E a b = a b
Can we derive an image from the QM calculation?
14
How to “understand” the EPR correlations predicted by quantum mechanics?
The direct calculation ( , ) , ( , )1 2 2 1cos ( , )2 P++ a b = + + Ψa b ν ν = 2 a b
Can we derive an image from the QM calculation?
is done in an abstract space, where the two particles are described globally: impossible to extract an image in real space where the two photons are separated.
Related to the non factorability of the entangled state:
{ }
1 2 1 2
( , ) 1 , , ( ) ( )
2 x x y y
ν ν φ ν χ ν
Ψ = + ≠ ⋅
One cannot identify properties attached to each photon separately
“Quantum phenomena do not occur in a Hilbert space, they occur in a laboratory” (A. Peres) ⇒ An image in real space?
A real space image of the EPR correlations derived from a quantum calculation
2 step calculation (standard QM) 1) Measure on ν1 by I (along a)
2) Measure on ν2 by II (along b = a )
Just after the measure, “collapse of the state vector”: projection onto the
eigenspace associated to the result
The measurement on ν1 seems to influence instantaneously at a distance
ν2 +1
+1+1
−1
ν1 +1
−1
+1 I a b II
S ν2 +1
+1+1
−1
ν2 +1+1
+1+1
−1
ν1 +1
−1
+1 I a b II
S
b = a
• If one has found +1 for ν1 then the state of ν2 is and the measurement along b = a yields +1;
+a
• If one has found -1 for ν1 then the state of ν2 is and the measurement along b = a yields -1;
−a
{ }
1 2 2
( , )ν ν 1 x x, y y,
Ψ = + = 12{+ + + − −a, a a, a }
⇒ result +1 or
⇒ result -1
+a
−a
+ +a, a
− −a, a or
Easily generalized to b ≠ a (Malus law)
16
A classical image for the correlations at a distance (suggested by the EPR reasoning)
x
y z
• The two photons of the same pair bear from their very emission an identical property (λ) , that will determine the results of polarization measurements.
• The property λ differs from one pair to another.
Image simple and convincing (analogue of identical chromosomes for twin brothers), but……amounts to completing quantum formalism:
λ = supplementary parameter, “hidden variable”.
S
ν2 +1
+1+1−1
ν1 +1
−1 +1
I II
a λ λ λ b
S
ν2 +1
+1+1−1
ν1 +1
−1 +1
I II
a b
S
ν2 +1
+1+1−1
ν2 +1+1
+1+1−1
ν1 +1
−1 +1
I II
a λ λ λ b
Bohr disagreed: QM description is complete, you cannot add anything to it
a
a
exemple ou λ λ
= +
= −
A debate for many decades
Intense debate between Bohr and Einstein…
… without much attention from a majority of physicists
• Quantum mechanics accumulates success:
• Understanding nature: structure and properties of matter, light, and their interaction (atoms, molecules, absorption, spontaneous emission, solid properties, superconductivity, superfluidity, elementary particles …)
• New concepts leading to revolutionary inventions: transistor (later: laser, integrated circuits…)
• No disagreement on the validity of quantum predictions, only on its interpretation.
18
1964: Bell’s formalism
Consider local supplementary parameters theories (in the spirit of Einstein’s ideas on EPR correlations):
ν2 +1
+1+1
−1
ν1 +1
−1
+1 I a b II
S ν2 +1
+1+1
−1
ν2 +1+1
+1+1
−1
ν1 +1
−1
+1 I a b II
S
• The supplementary parameter λ determines the results of
measurements at I and II
( , ) 1 or 1
A λ a = + − at polarizer I ( , ) 1 or 1
B λ b = + − at polarizer II
• The supplementary parameter λ is randomly distributed among pairs
( ) 0 and
λ
( )λ
d 1ρ
≥∫ ρ λ
=at source S
λ λ
• The two photons of a same pair have a common property λ (sup.
param.) determined at the joint emission
( , ) d ( ) ( , ) ( , )
E a b = ∫ λ ρ λ A λ a B λ b
1964: Bell’s formalism to explain correlations
ν2 +1
+1+1
−1
ν1 +1
−1
+1 I a b II
S ν2 +1
+1+1
−1
ν2 +1+1
+1+1
−1
ν1 +1
−1
+1 I a b II
S
An example
• Common polarisation λ , randomly distributed among pairs
{ }
( , ) sign cos 2( ) A λ a = θa −λ
{ }
( , ) sign cos 2( ) B λ b = θb −λ
( ) 1/ 2 ρ λ = π
-90 -45 0 45 90
-1,0 -0,5 0,0 0,5 1,0
( , )a b
( , ) E a b
Not bad, but no exact agreement
• Result (±1) depends on the angle between λ and polarizer orientation (a or b)
Resulting correlation
λ λ
Is there a better model, agreeing with QM predictions at all orientations?
Quantum predictions
Bell’s theorem gives the answer
20
Bell’s theorem
Quantum predictions
-90 -45 0 45 90
-1,0 -0,5 0,0 0,5 1,0
( , )a b ( , )
E a b
No local hidden variable theory (in the spirit of Einstein’s ideas) can reproduce quantum
mechanical predictions for EPR correlations at all the orientations of polarizers.
No!
Impossible to cancel the difference everywhere
LHVT
Impossible to have quantum predictions exactly reproduced at all orientations, by any
model à la Einstein
Bell’s inequalities are violated by certain quantum predictions
Any local hidden variables theory ⇒ Bell’s inequalities 2 S 2 avec S E( , ) E( , )ʹ′ E( ʹ′, ) E( , )ʹ′ ʹ′
− ≤ ≤ = a b − a b + a b + a b
Quantum mechanics
QM
2 2 2.828 .. . 2
S = = >
a b
a’
b’
( , ) ( , ) ( , )
8 ʹ′ ʹ′ π
= = =
a b b a a b
CONFLICT ! The possibility to complete quantum mechanics according to Einstein ideas is no longer a matter of taste (of interpretation). It has turned into an experimental question.
For orientations
MQ( , ) cos2( , )
E a b = a b
CHSH inequ. (Clauser, Horne, Shimony, Holt, 1969)
22
Conditions for a conflict
(⇒ hypotheses for Bell’s inequalities)
Supplementary parameters λ carried along by each particle.
Explanation of correlations « à la Einstein » attributing individual properties to each separated particle: local realist world view.
Bell’s locality condition
• The result of the measurement on ν1 by I does not depend on the orientation b of distant polarizer II (and conv.)
• The distribution of supplementary parameters over the pairs does not depend on the orientations a and b.
( , ) A λ a
ρ λ( )
λ λ
Bell’s locality condition
…in an experiment with variable polarizers (orientations modified faster than the propagation time L / c of light between polarizers) Bell’s locality condition becomes a consequence of Einstein’s
relativistic causality (no faster than light influence) cf. Bohm & Aharonov, Physical Review, 1957
can be stated as a reasonable hypothesis, but…
( , , ) ( , , ) ( , , )
A λ a b B λ a b ρ λ a b
ν2 +1
+1 +1 -1
ν1 +1
-1
+1 I a b II
S
L
Conflict between quantum mechanics and Einstein’s
world view (local realism based on relativity).
24
From epistemology debates to experimental tests
Bell’s theorem demonstrates a quantitative incompatibility between the local realist world view (à la Einstein) –which is constrained by Bell’s inequalities, and quantum predictions for pairs of entangled particles –which violate Bell’s inequalities.
An experimental test is possible.
When Bell’s paper was written (1964), there was no experimental result available to be tested against Bell’s inequalities:
• Bell’s inequalities apply to all correlations that can be described within classical physics (mechanics, electrodynamics).
• B I apply to most of the situations which are described within quantum physics (except EPR correlations)
One must find a situation where the test is possible:
CHSH proposal (1969)
Three generations of experiments
Pioneers (1972-76): Berkeley, Harvard, Texas A&M
• First results contradictory (Clauser = QM; Pipkin ≠ QM)
• Clear trend in favour of Quantum mechanics (Clauser, Fry)
• Experiments significantly different from the ideal scheme Institut d’optique experiments (1975-82)
• A source of entangled photons of unprecedented efficiency
• Schemes closer and closer to the ideal GedankenExperiment
• Test of quantum non locality (relativistic separation) Third generation experiments (1988-): Maryland, Rochester,
Malvern, Genève, Innsbruck, Los Alamos, Boulder, Urbana Champaign, Vienna, Delft…
• New sources of entangled pairs
• Closure of the last loopholes
• Entanglement at very large distance
26
Orsay’s source of pairs of entangled photons (1981)
J = 0
551 nm
ν
1ν
2423 nm
Kr ion laser dye laser
J = 0
τr= 5 ns
Two photon selective excitation
Polarizers at 6 m from the source:
violation of Bell’s inequalities, entanglement survives “large” distance
J 100 coincidences per second 1% precision for 100 s counting
J = 1
m =0
-1 +1
0
{ }
{ }
1 2
1 2
, ,
, ,
x x y y σ σ+ − + σ σ− +
= +
Pile of plates polarizer
(10 plates at Brewster angle)
Experiment with 2-channel polarizers
(AA, P. Grangier, G. Roger, 1982)Direct measurement of the polarization correlation coefficient:
simultaneous measurement of the 4 coincidence rates
( , ) ( , ) ( , ) ( , )
( , )
( , ) ( , ) ( , ) ( , )
N N N N
E N N N N
a b a b a b a b
a b a b a b a b a b
++ +− −+ −−
++ +− −+ −−
− − +
= + + +
S
ν2
+1
ν1
+1
a b
PM PM
PM
−1
PM
( , ) , ( , ) ( , ) , ( , )
N N
N N
++ +−
−+ −−
a b a b
a b a b
−1
28
Experiment with 2-channel polarizers
(AA, P. Grangier, G. Roger, 1982)exp( ) 2.697 0.01 For θ = ( , ) ( , ) ( , ) 22.5a b = b aʹ′ = a bʹ′ = ° S θ = ± 5 Violation of Bell’s inequalities S ≤ 2 by more than 40 σ
Bell’s limits
Measured value
± 2 standard dev.
Quantum mechanical prediction (including
imperfections of real experiment)
Excellent agreement with quantum predictions SMQ = 2.70
Experiment with variable
polarizers
AA, J. Dalibard, G. Roger, PRL 1982S ν2 ν1
a b
PM PM
( , ) , ( , ) ( , ) , ( , )
N N
N N
ʹ′
ʹ′ ʹ′ ʹ′
a b a b
a b a b
b’
C2 a’
C1
Impose locality as a consequence of relativistic causality: change of polarizer orientations faster than the time of propagation of light between the two polarizers (40 nanoseconds for L = 12 m)
L Not realist with massive polarizer
• either towards pol. in orient. a
Equivalent to a single polarizer switching between a and a’
Switch C1
redirects light
• or towards pol.
in orient. a’
J Possible with optical switch
30
Experiment with variable polarizers:
results AA, J. Dalibard, G. Roger, PRL 1982
S ν2 ν1
a b
PM PM
( , ) , ( , ) ( , ) , ( , )
N N
N N
ʹ′
ʹ′ ʹ′ ʹ′
a b a b
a b a b
b’
C2 a’
C1
Acousto optical switch: change every 10 ns. Faster than propagation of light between polarizers (40 ns) and even than time of flight of
photons between the source S and each switch (20 ns).
Difficult experiment:
reduced signal;
data taking for several hours;
switching not fully random Convincing result: Bell’s inequalities violated by 6 standard
deviations. Each measurement space-like separated from setting of distant polarizer: Einstein’s causality enforced
Third generation experiments
Geneva experiment (1998):
• Optical fibers of the commercial telecom network
• Measurements separated by 30 km Agreement with QM.
Innsbruck experiment (1998):
variable polarizers with orientation chosen by a random generator
during the propagation of photons (several hundreds meters).
Entangled photon pairs by parametric down conversion, well defined directions: injected into optical fibers.
Entanglement at a very large distance
32
Bell’s inequalities have been violated in almost ideal experiments
• Sources of entangled photons more and more efficient
• Relativistic separation of measurements with variable polarizers (Orsay 1982,
Innsbruck 1998); closure of locality loophole
Results in agreement with quantum mechanics in
experiments closer and closer to the GedankenExperiment:
Einstein’s local realism is untenable
J = 0
551 nm
ν1
ν2
423 nm Kr ion laser
dye laser
J = 0
τr= 5 ns
• Experiment with trapped ions (Boulder 2000):
closure of the “sensitivity loophole” (recent experiments with photons in Vienna, Urbana Champaign).
The failure of local realism
Einstein had considered (in order to reject it by reductio ad
absurdum) the consequences of the failure of the EPR reasoning:
[If quantum mechanics could not be completed, one would have to]
• either drop the need of the independence of the physical realities present in different parts of space
• or accept that the measurement of S
1changes (instantaneously) the real situation of S
2Quantum non locality – Quantum holism
The properties of a pair of entangled particles are more than the addition of the individual properties of the constituents of the
pairs (even space like separated). Entanglement = global property.
From the Einstein-Bohr debate to Quantum Information:
a new quantum revolution?
1. Quantum information: how did it emerge?
2. From the Einstein-Bohr debate to
Bell's inequalities tests: entanglement 3. A new quantum revolution? Quantum
cryptography, quantum computing, simulating
http://www.lcf.institutoptique.fr/Alain-Aspect-homepage
It took a long time for entanglement to be recognized as a revolutionary concept
In this chapter we shall tackle immediately the basic element of the mysterious behavior in its most strange form. We choose to examine a phenomenon which is impossible, absolutely impossible, to explain in any classical way, and which has in it the heart of quantum mechanics. In reality it contains the only mystery.
Wave particle duality for a single particle: the only mystery (1960)
This point was never accepted by Einstein… It became known as the Einstein-Podolsky-Rosen paradox. But when the situation is described
36
It took a long time for entanglement to be recognized as a revolutionary concept
we always have had (secret, secret, close the doors!) we always have had a great deal of difficulty in
understanding the world view that quantum mechanics represents.
At least I do
I've entertained myself always by squeezing the difficulty of quantum mechanics into a smaller and smaller place, so as to get more and more worried about this particular item.
It seems to be almost ridiculous that
you can squeeze it to a numerical question that one thing is bigger than another. But
there you are-it is bigger than any logical argument can produce
1982
a second mystery, and then…
Entanglement: a resource for quantum information
Hardware based on different physical principles allows emergence of new concepts in information processing and transport:
• Quantum computing (R. Feynman 1982, D. Deutsch 1985 )
• Quantum cryptography (Bennett Brassard 84, Ekert 1991)
• Quantum teleportation (BB&al., 1993; Innsbruck, Roma 1997)
• Quantum simulation (Feynman 1982, Hänsch and col. 2002) The understanding of the extraordinary properties of entanglement has triggered a new research field: quantum information
Entanglement is at the root of
most of the schemes for quantum information
Entanglement: a resource for quantum information
Hardware based on different physical principles allows emergence of new concepts in information science, realized experimentally with ions, photons, atoms, Josephson junctions, RF circuits:
• Quantum computing (R. Feynman 1982, D. Deutsch 1985;…
Boulder, Innsbruck, Paris, Roma, Palaiseau, Munich, Saclay, Yale, Santa Barbara, Zurich, Lausanne, Berne … )
• Quantum cryptography (Bennett Brassard 84, Ekert 1991;…
Geneva, Singapore, Palaiseau, …)
• Quantum teleportation (BB&al., 1993; Roma, Innsbruck 1997)
• Quantum simulation (Feynman, Cirac and Zoller;… Munich, Innsbruck, Zurich, Lausanne, Palaiseau, Paris, Roma … )
The understanding of the extraordinary properties of entanglement and its generalization to more than two particles (GHZ) has
triggered a new research field: quantum information
Mathematically proven safe cryptography:
sharing two identical copies of a secret key
The goal: distribute to two partners (Alice et Bob) two identical secret keys (a random sequence of 1 and 0), with absolute certainty that no spy (Eve) has been able to get a copy of the key.
Using that key, Alice and Bob can exchange (publicly) a coded message with a mathematically proven safety (Shannon theorem) (provided the message is not longer than the key)
Alice Bob
Eve
110100101 110100101
Quantum optics provides means of safe key distribution
40
Quantum Key Distribution with entangled photons (Ekert)
There is nothing to spy on the entangled flying photons: the key is created at the moment of the measurement.
If Eve chooses a particular direction of analysis, makes a measurement, and reemits a photon according to her result, his maneuver leaves a trace that can be detected by doing a Bell’s inequalities test.
Alice and Bob select their analysis directions a et b randomly among 2, make measurements, then send publicly the list of all selected directions
Cases of a et b identical : identical results ⇒ 2 identical keys
ν2
ν1
+1
+1+1
−1 +1
II
b +1
+1+1
−1 +1
II b I
−1
+1 a
−1
+1 a
S
Alice Bob
ν1
Entangled pairs
Eve
QKD at large distance, from space, on the agenda
Quantum computing
A quantum computer could operate new types of algorithms able to make calculations exponentially faster than classical computers.
Example: Shor’s algorithm for factorization of numbers: the RSA encryption method would no longer be safe.
Fundamentally different hardware:
fundamentally different software.
What would be a quantum computer?
An ensemble of interconnected quantum gates, processing strings of entangled quantum bits (qubit: 2 level system)
Entanglement ⇒ massive parallelism
The Hilbert space to describe N entangled qubits has dimension 2N !
42
Quantum computing???
A quantum computer could operate new types of algorithms able to make calculations exponentially faster than classical computers.
Example: Shor’s algorithm for factorization of numbers: the RSA encryption method would no longer be safe.
What would be a quantum computer?
An ensemble of entangled quantum bits (qubit: 2 level system)
Entanglement ⇒ massive information 2N
A dramatic problem: decoherence: hard to increase the number of entangled qubits
Nobody knows if such a quantum computer will ever work:
• Needed: 105 = 100 000 entangled qubits
• Record: 14 entangled qubits (R. Blatt) Would be a kind of Schrödinger cat
Quantum simulation
Goal: understand a system of many entangled particles, absolutely impossible to describe, least to study, on a classical computer (Feynman 1982)
Example: electrons in solids (certain materials still not understood, e.g. high TC supraconductors)
Quantum simulation: mimick the system to study with other quantum particles "easy" to manipulate, observe, with parameters "easy" to modify
Example: ultracold atoms in synthetic potentials created with laser beams
• Can change density, potential parameters
• Many observation tools: position or velocity distributions, correlations…
44
Quantum simulator of the Anderson transition in a disordered potential
Atoms suspended, released in the disordered potential created with lasers. Absorption images
Similar experiments in Florence
(Inguscio's group)
Direct observation of a localized component, with an exponential profile (localized wave function)
A new quantum revolution?
Entanglement
• A revolutionary concept, as guessed by Einstein and Bohr, strikingly demonstrated by Bell, put to use by Feynman et al.
• Drastically different from concepts underlying the first quantum revolution (wave particle duality).
Individual quantum objects
• experimental control
• theoretical description
(quantum Monte-Carlo) échantillon Objectif de microscope x 100, ON=1.4 Miroir
dichroïque
“scanner”
piezo. x,y,z
Laser d’excitation
Examples: electrons, atoms, ions, single photons, photons
Two concepts at the root of a new quantum era
What was the first quantum revolution?
A revolutionary concept: Wave particle duality
• Understanding the structure of matter, its properties, its interaction with light
• Electrical, mechanical properties
• Understanding “exotic properties”
• Superfluidity, supraconductivity, Bose Einstein Condensate Revolutionary applications
• Inventing new devices
• Laser, transistor, integrated circuits
• Information and
communication society
(8 Juillet 1960, New York Times) (8 Juillet 1960, New York Times)
As revolutionary as the invention of heat engine (change society)
Not only conceptual, also technological
Towards a new technological revolution?
Will the new conceptual revolution (entanglement + individual quantum systems) give birth to a new technological revolution?
The most likely roadmap (as usual): from proofs of principle with well defined elementary microscopic objects (photons, atoms, ions,
molecules…) to solid state devices (and continuous variables?) … First quantum revolution
(wave particle duality):
lasers, transistors, integrated circuits ⇒
“information society”
Will quantum computing and quantum communication systems lead to the “quantum information society”?
(8 Juillet 1960, New York Times) (8 Juillet 1960, New York Times)
+
_ Métal Métal
N N
N P
n
couche active dopée p SiO2
zone émettrice 1 x 10 µm2
+
_ Métal Métal
N N
N P
n
couche active dopée p SiO2
zone émettrice 1 x 10 µm2
Visionary fathers of the second quantum revolution
48
• Einstein discovered a new quantum feature, entanglement, different in nature from wave- particle duality for a single particle
• Schrödinger realized that entanglement is definitely different
• Bohr had the intuition that interpreting
entanglement according to Einstein's views was incompatible with Quantum Mechanics
• Bell found a proof of Bohr's intuition
• Feynman realized that entanglement could be used for a new way to process information
We stand on the shoulders of giants!
We need the contribution of many people
Thanks to the 1982 team
and to the atom optics group, who makes
quantum simulation and
quantum atom optics an experimental
reality
Philippe Grangier
Jean Dalibard Gérard Roger André Villing
50
Bell’s inequalities at the lab classes of the
Institut d’Optique Graduate School
http://www.institutoptique.fr/telechargement/inegalites_Bell.pdf
Appendix
No faster than light signaling with
EPR pairs
52
No faster than light signaling with EPR entangled pairs
Alice changes the setting of polarizer I from a to a’: can Bob instantaneously observe a change on its measurements at II ?
Single detections: P+( )b = P−( ) 1/ 2b = No information about a
+1 ν2 +1
+1 +1 -1
ν1 +1 -1
I a b II
S
Joint detections:
Instantaneous change ! Faster than light signaling ?
1 2
( , ) ( , ) cos ( , ) etc.
P++ a b = P−− a b = 2 a b
No faster than light signaling with EPR entangled pairs
Alice changes the setting of polarizer I from a to a’: can Bob instantaneously observe a change on its measurements at II ?
+1 ν2 +1
+1 +1 -1
ν1 +1 -1
I a b II
S
Joint detections:
Instantaneous change ! Faster than light signaling ?
1 2
( , ) ( , ) cos ( , ) etc.
P++ a b = P−− a b = 2 a b
To measure P++(a,b) Bob must compare his results to the results at I: the transmission of these results from I to Bob is done on a classical channel, not faster than light.
54
So there is no problem ?
ν2
-1 +1
ν1
-1
+1 I a b II
S
View a posteriori onto the experiment:
During the runs, Alice and Bob carefully record the time and result of each measurement.
… and they find that P++(a,b) had changed instantaneously when Arthur had changed his polarizers orientation…
Non locality still there, but cannot be used for « practical telegraphy » After completion of the experiment, they meet and compare
their data…
« It has not yet become obvious to me that there is no real problem. I cannot define the real problem, therefore I
suspect there’s no real problem, but I am not sure there is no real problem. So that’s why I like to investigate
things. »*
R. Feynman:
Simulating Physics with Computers, Int. Journ. of Theoret. Phys. 21, 467 (1982)**Is it a real problem ?
* This sentence was written about EPR correlations
** A founding paper on quantum computers
56
Mathematically proven safe cryptography:
sharing two identical copies of a secret key
The goal: distribute to two partners (Alice et Bob) two identical secret keys (a random sequence of 1 and 0), with absolute certainty that no spy (Eve) has been able to get a copy of the key.
Using that key, Alice and Bob can exchange (publicly) a coded message with a mathematically proven safety (Shannon theorem) (provided the message is not longer than the key)
Alice Bob
Eve
110100101 110100101