Is This the Dawn of the Quantum Information Age?

Discovering Physics, Nov. 5, 2003

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

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."

Learning Quantum Mechanics

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!

C

The Classical Bit

= 1= 0

The Classical Box

CC

Q

The Quantum Box

QQQQ

Q

The Quantum Box

QQQQ

The Quantum Box

QQQQ

If I know what’s in Door #1

There is a 50% chance I will find a red ball behind Door #2

And a 50% chance I will find a black ball behind Door #2.

Q

The Quantum Box

QQQQ

If I know what’s in Door #2

There is a 50% chance I will find a red ball behind Door #1

And a 50% chance I will find a black ball behind Door #1

Q

What’s Inside the Box?

• A two-level quantum system.• Simple example: Quantum mechanical Spin.

Opening Door #1 = measuringspin along z-axis.

z

Up =Down =

What’s Inside the Box?

• A two-level quantum system.• Simple example: Quantum mechanical Spin.

Opening Door #2 = measuringspin along x-axis.

Right =Left =

x

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!

Message: 1 0 1 0

Random Key: 1 0 0 1

Sending a Secret Message

A

B

E

0 0 1 1+

Message: 1 0 1 0

0 0 1 1

Random Key: 1 0 0 1 +

1 0 1 00011 ?

CCCC

Classical Key Distribution

1 0 0 1

CCCCC C C C

A

CC C C

B 1 0 0 1

CCCC

Classical Key Distribution

1 0 0 1

CCCCC C C C

A

CC C C

E1 0 0 1

CC C C

B1 0 0 1

Bond has no way of knowing if Dr. Evil has intercepted the key.

Quantum Key Distribution

QQ Q Q

A

B1 0 0 1

QQ Q Q

After Bond receives the boxes, Austin calls to tell him which doors to open.

Quantum Key Distribution

QQ Q Q

A

1 0 1 1

QQ Q

E Dr. Evil doesn’t know which doors to open.

He can only guess.

Q

B

1 0 1 1

QQ Q Q

Bond can tell if Dr. Evil has looked in the boxes by comparing some fraction of the

key with Austin.

Charles Bennett

Gilles Brassard

The first quantum keydistribution 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,

p x q = 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 Q-bits could factor an integer exponentially faster than a classical computer!

time = (Number of Digits)

• Shor’s algorithm exploits something called

Massive Quantum Parallelism.

3

Q

Q

QQ

Q Q

Q Q Q Q

Q-bits Number of C-bits

2

4

8

16

Q Q Q Q Q

Q-bits Number of C-bits

32

250 # of atoms inthe 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 Q-bits 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.

Is This the Dawn of the Quantum Information Age?

Discovering Physics, Nov. 5, 2003