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 wave-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