• 沒有找到結果。

From Einstein's questions to Quantum bits: a new quantum era?

N/A
N/A
Protected

Academic year: 2022

Share "From Einstein's questions to Quantum bits: a new quantum era?"

Copied!
56
0
0

加載中.... (立即查看全文)

全文

(1)

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

(2)

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

(3)

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)

4

Quantum information

a flourishing field

(5)

Quantum information how did it emerge?

Entanglement is different!

(6)

6

Quantum information how did it emerge?

Entanglement is more!

(7)

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)

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??)

(9)

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)

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

(11)

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)

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 = +

(13)

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)

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?

(15)

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)

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

= +

= −

(17)

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)

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 1

ρ

∫ 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

(19)

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)

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

(21)

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 ba 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)

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

(23)

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)

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)

(25)

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)

26

Orsay’s source of pairs of entangled photons (1981)

J = 0

551 nm

ν

1

ν

2

423 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)

(27)

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)

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

(29)

Experiment with variable

polarizers

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

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)

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

(31)

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)

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).

(33)

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

1

changes (instantaneously) the real situation of S

2

Quantum 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.

(34)

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

(35)

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)

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…

(37)

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

(38)

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

(39)

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)

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

(41)

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)

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

(43)

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)

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)

(45)

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

(46)

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

(47)

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

(48)

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!

(49)

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)

50

Bell’s inequalities at the lab classes of the

Institut d’Optique Graduate School

http://www.institutoptique.fr/telechargement/inegalites_Bell.pdf

(51)

Appendix

No faster than light signaling with

EPR pairs

(52)

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

(53)

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)

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…

(55)

« 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)

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

Quantum optics provides means of safe key distribution (QKD)

參考文獻

相關文件

Theorem 3.1, together with some algebraic manipulations, implies that the quantum corrections attached to the extremal ray exactly remedy the defect caused by the classical product

In part II (“Invariance of quan- tum rings under ordinary flops II”, Algebraic Geometry, 2016), we develop a quantum Leray–Hirsch theorem and use it to show that the big

To proceed, we construct a t-motive M S for this purpose, so that it has the GP property and its “periods”Ψ S (θ) from rigid analytic trivialization generate also the field K S ,

Population: the form of the distribution is assumed known, but the parameter(s) which determines the distribution is unknown.. Sample: Draw a set of random sample from the

double-slit experiment is a phenomenon which is impossible, absolutely impossible to explain in any classical way, and.. which has in it the heart of quantum mechanics -

We compare the results of analytical and numerical studies of lattice 2D quantum gravity, where the internal quantum metric is described by random (dynamical)

In an Ising spin glass with a large number of spins the number of lowest-energy configurations (ground states) grows exponentially with increasing number of spins.. It is in

* Anomaly is intrinsically QUANTUM effect Chiral anomaly is a fundamental aspect of QFT with chiral fermions.