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Discovering Physics, Nov. 5, 2003
Is This the Dawn of the Quantum
Information Age?
Quantum Theory
• In the 1920s, Bohr, Heisenberg,
Schrodinger, Dirac and others developed
a radically new kind of physics to
understand the strange world of the atom:
Quantum Theory.
• In quantum theory randomness and
uncertainty play a fundamental role.
• Although strange and counterintuitive,
quantum theory is arguably the most
successful theory in physics.
“God does not play dice with the
universe!”
– Albert Einstein
“Stop telling God what do to!”
– Niels Bohr
Learning Quantum Mechanics
The student begins by learning the tricks of the trade. He learns how to make
calculations in quantum mechanics and get the right answers...to learn the
mathematics of the subject and to learn how to use it takes about six
months. This is the first stage in learning quantum mechanics, and it is
comparatively easy and painless. The second stage comes when the student
begins to worry because he does not understand what he has been doing. He
worries because he has no clear physical picture in his head. He gets
confused in trying to arrive at a physical explanation for each of the
mathematical tricks he has been taught. He works very hard and gets
discouraged because he does not seem able to think clearly. This second
stage often lasts six months or longer, and it is strenuous and unpleasant.
Then, quite unexpectedly, the third stage begins. The student suddenly says
to himself, "I understand quantum mechanics," or rather he says, "I understand
now that there really isn't anything to be understood."
Freeman Dyson
Information Theory
In 1948 Claude Shannon introduces the
concept of the bit as the fundamental
unit of information.
Using the fact that all information can
be represented by bits, Shannon and
others develop the Mathematical
Theory of Information.
This theory is the basis of modern
information technology.
BIT = 0 , 1
Pentium Chip
Information is Physical!
• In practice, bits are always represented by the state of
some physical system.
• At its most fundamental level, the physical world is
described by quantum theory.
• Does quantum theory change our understanding of
information theory?
• Recent discoveries over the past 10 years say the
answer is YES!
The Classical Bit
=0
=1
The Classical Box
C
The Quantum Box
Q
The Quantum Box
Q
The Quantum Box
If I know what’s in Door #1
There is a 50% chance I will
find a red ball behind Door #2
Q
And a 50% chance I will find
a black ball behind Door #2.
The Quantum Box
If I know what’s in Door #2
There is a 50% chance I will
find a red ball behind Door #1
Q
And a 50% chance I will find
a black ball behind Door #1
What’s Inside the Box?
• A two-level quantum system.
• Simple example: Quantum mechanical Spin.
z
Opening Door #1 = measuring
spin along z-axis.
Down
Up ==
What’s Inside the Box?
• A two-level quantum system.
• Simple example: Quantum mechanical Spin.
x
Opening Door #2 = measuring
spin along x-axis.
Right
Left ==
Two Perspectives
• The glass is half empty (pessimistic).
Nature has shortchanged us. Uncertainty is built into
the laws of nature. We can’t ever know everything
about what’s inside the box.
• The glass is half full (optimistic).
Nature has given us a gift. Uncertainty is built into the
laws of nature. Maybe we can use it!
Sending a Secret Message
Message: 1 0 1 0
A
Random Key: 1 0 0 1
0011
+
E
B
1
01?
0
0011
0011
Random Key: 1 0 0 1
Message: 1 0 1 0
+
Classical Key Distribution
A
1 0 0 1
C
C
C
C
C
B
C
C
1 0 0 1
C
Classical Key Distribution
A
1 0 0 1
C
C
C
C
C
E
C
C
1 0 0 1
C
C
C
C
C
1 0 0 1
B
Bond has no way of knowing if
Dr. Evil has intercepted the key.
Quantum Key Distribution
A
Q
Q
Q
Q
Q
B
Q
Q
Q
After Bond receives the boxes, Austin calls
to tell him which doors to open.
1 0 0 1
Quantum Key Distribution
A
Q
Q
Q
Q
Q
E
Q
Q
Q
Dr. Evil doesn’t know which doors to open.
He can only guess.
1 0 1 1
Q
B
Q
Q
Q
Bond can tell if Dr. Evil has looked in the
boxes by comparing some fraction of the
key with Austin.
1 0 1 1
Charles Bennett
Gilles Brassard
The first quantum key
distribution device
(1989)
Exploiting Quantum "Spookiness" to Encrypt an Image
Jennewein et al., Physical Review Letters (2000)
“Classical” Technology
C
The Transistor – a “switch” which
can be either “on” or “off”
The Integrated Circuit
Pentium Processor
Moore’s Law
“Quantum” Technology?
Q
The Quantum Dot – an artificial
structure which traps a single
electron which can either be spin
“up” or spin “down”
The Quantum Dot Computer
Prime Factorization
• Given two prime numbers p and q,
pxq=C
Easy
C
p, q
Hard
• Best known factoring algorithm scales as
time = exp(Number of Digits)
• Mathematical Basis for Public Key Cryptography.
Quantum Factorization
• In 1994 Peter Shor showed that a Quantum
Computer in which C-bits are replaced with Qbits could factor an integer exponentially faster
than a classical computer!
time = (Number of Digits)
3
• Shor’s algorithm exploits something called
Massive Quantum Parallelism.
Q-bits
Number of C-bits
Q
2
Q Q
4
Q Q Q
8
Q Q Q Q
16
Q-bits
Number of C-bits
Q Q Q Q Q
32
250
# of atoms in
the universe
The Real Mystery: Entanglement
• Why does it take so many C-bits to specify the
state of a small number of Q-bits?
• Q-bits can be correlated in ways which have no
analog in the classical world. They can be
“entangled.”
• When factoring a large integer, a quantum
computer will be in a highly entangled state.
Other Uses of Entanglement
• Entanglement can be used to transmit a
Q-bit from one place to another without
actually moving the box!
Quantum Teleportation
• Entanglement can be used to protect Qbits from error.
Quantum Error Correction
Conclusions
• On paper, a qualitatively new kind of
technology based on the weird behavior of
the quantum world appears to be possible.
• It is a problem for the current generation of
scientists (i.e. us!) to find out whether this
is possible in practice.
Discovering Physics, Nov. 5, 2003
Is This the Dawn of the Quantum
Information Age?