A beginner’s guide to quantum information · A beginner’s guide to quantum communication and information Sarah Croke School of Physics & Astronomy University of Glasgow Stirling

A beginner’s guide to quantum communication and information

Sarah Croke

School of Physics & Astronomy

University of Glasgow

Stirling Teachers Meeting 09/05/2018

Outline

• A little bit about information

• Development of quantum computing

• Quantum communications:

– A little bit about cryptography

– A little bit about quantum theory

– Quantum key distribution

– Classroom demonstration (lo-tech)

• Summary: quantum information

A LITTLE BIT ABOUT INFORMATION

What is information?


• Facts provided or learned about something or someone: ‘a vital piece of information’



• What is conveyed or represented by a particular arrangement or sequence of things: ‘genetically transmitted information’



• What is conveyed or represented by a particular arrangement or sequence of things: ‘genetically transmitted information’ – Computing: Data as processed, stored, or

transmitted by a computer.

(source: Oxford Dictionaries)

Information processing

• Do the ways in which we can transform information depend on the physical system in which the information is encoded?



Elementary operations

IN OUT

0 1

1 0

NOT

A B OUT

0 0 0

0 1 0

1 0 0

1 1 1

A B OUT

0 0 0

0 1 1

1 0 1

1 1 1

AND OR A A

B B

Moore’s Law

A “bit”: an elementary (classical) information carrier

DEVELOPMENT OF QUANTUM COMPUTING

“Nature isn't classical, dammit, and if you want to make a simulation of

nature, you'd better make it quantum mechanical.”

Richard Feynman, after dinner speech 1982

Image: NASA Imagine the Universe

• Suppose one atom has two possible states: “g” and “e”


• Two atoms have four possible states: “gg”, “ge”, “eg”, “ee”.


• Superposition principle: a “gg” + b “ge” + c “eg” + d “ee”. • To simulate, need to store the four numbers a, b, c, d. • For N atoms, need to store 2N numbers: exponential!

What else are quantum processors good for?

• 1980s: quantum key distribution

• 1994: Shor’s algorithm (factoring)

• 1997: Grover’s algorithm (search)

Image: IBM: 50 qubits

Image: Google: 72 qubits

Image: Intel: 49 qubits

And in the last 6 months:

A LITTLE BIT ABOUT CRYPTOGRAPHY

Cryptography: Caesar cipher

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

D E F G H I J K L M N O P Q R S T U V W X Y Z A B C

Plain:

Cipher:

Caesar cipher: Shift = +3

• (See also: http://www.simonsingh.net/The_Black_Chamber/caesar.html)

B O B , M E E T M E A T

E I G H T - A L I C E

Plain text:

Caesar cipher: Shift = +3



E R E , P H H W P H D W


H L J K W - D O L F H

Plain text:

Cipher text:

Caesar cipher: encrypted text




Plain text:

Cipher text:

Decryption: Shift = -1


D Q D ,



Plain text:

Cipher text:



C P C ,



Plain text:

Cipher text:



B O B ,



Plain text:

Cipher text:







Plain text:

Cipher text:

Encryption: Variable shift


E A E , L C C F L C R F


C J N I F - R Q J B C

Plain text:

Cipher text:


R E B G C K N I J O M Q L U A S X Z D F T P H Y V W

Plain:

Cipher:

Decryption: Variable shift



Plain text:

Cipher text:

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Cipher:

Plain:


, E E E


E - E


Plain text:

Cipher text:


E

Cipher:

Plain:


, E E M E


E - E


Plain text:

Cipher text:


E M

Cipher:

Plain:


, M E E M E


E - E


Plain text:

Cipher text:


E M

Cipher:

Plain:


, M E E T M E T


E T - E


Plain text:

Cipher text:


E T M

Cipher:

Plain:


, M E E T M E A T


E T - A E


Plain text:

Cipher text:


E T M A

Cipher:

Plain:


, M E E T M E A T


E T - A L I C E


Plain text:

Cipher text:


C E T I M L A

Cipher:

Plain:


, M E E T M E A T


E I T - A L I C E


Plain text:

Cipher text:


C E T I M L A

Cipher:

Plain:






Plain text:

Cipher text:


O C E B T H I M G L A

Cipher:

Plain:

A secure scheme: Random shift

B O B , M E E T M E A T 17 13 2 4 7 13 16 4 20 3 8

S B D Q L R J Q Y D B

E I G H T - A L I C E 19 21 13 3 18 2 5 22 17 3

X D T K L C Q E T H

Plain text:

Shift:

Cipher text:

Plain text:

Shift:

Cipher text:

A secure scheme: Random shift

B O B , M E E T M E A T 17 13 2 4 7 13 16 4 20 3 8

S B D Q L R J Q Y D B

E I G H T - A L I C E 19 21 13 3 18 2 5 22 17 3

X D T K L C Q E T H

Plain text:

Shift:

Cipher text:

Plain text:

Shift:

Cipher text:

Private key cryptography: One-time pad

0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0

1 0 0 1 1 0 1 0 1 0 0 0 1 0 1 1 1 0 0

Plain text:

Key:

One-time pad: encryption

0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0

1 0 0 1 1 0 1 0 1 0 0 0 1 0 1 1 1 0 0

1

Plain text:

Cipher text:

Key:


0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0

1 0 0 1 1 0 1 0 1 0 0 0 1 0 1 1 1 0 0

1 0

Plain text:

Cipher text:

Key:


0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0

1 0 0 1 1 0 1 0 1 0 0 0 1 0 1 1 1 0 0

1 0 0

Plain text:

Cipher text:

Key:


0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0

1 0 0 1 1 0 1 0 1 0 0 0 1 0 1 1 1 0 0

1 0 0 0

Plain text:

Cipher text:

Key:


0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0

1 0 0 1 1 0 1 0 1 0 0 0 1 0 1 1 1 0 0

1 0 0 0 0

Plain text:

Cipher text:

Key:


0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0

1 0 0 1 1 0 1 0 1 0 0 0 1 0 1 1 1 0 0

1 0 0 0 0 1 1 0 1 1 1 1 1 0 1 0 0 1 0

Plain text:

Cipher text:

Key:

One-time pad: decryption

0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0

1 0 0 1 1 0 1 0 1 0 0 0 1 0 1 1 1 0 0

1 0 0 0 0 1 1 0 1 1 1 1 1 0 1 0 0 1 0

Plain text:

Cipher text:

Key:

1 0 0 1 1 0 1 0 1 0 0 0 1 0 1 1 1 0 0 Key:

Plain text:


0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0

1 0 0 1 1 0 1 0 1 0 0 0 1 0 1 1 1 0 0

1 0 0 0 0 1 1 0 1 1 1 1 1 0 1 0 0 1 0

Plain text:

Cipher text:

Key:

1 0 0 1 1 0 1 0 1 0 0 0 1 0 1 1 1 0 0

0

Key:

Plain text:


0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0

1 0 0 1 1 0 1 0 1 0 0 0 1 0 1 1 1 0 0

1 0 0 0 0 1 1 0 1 1 1 1 1 0 1 0 0 1 0

Plain text:

Cipher text:

Key:

1 0 0 1 1 0 1 0 1 0 0 0 1 0 1 1 1 0 0

0 0

Key:

Plain text:


0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0

1 0 0 1 1 0 1 0 1 0 0 0 1 0 1 1 1 0 0

1 0 0 0 0 1 1 0 1 1 1 1 1 0 1 0 0 1 0

Plain text:

Cipher text:

Key:

1 0 0 1 1 0 1 0 1 0 0 0 1 0 1 1 1 0 0

0 0 0

Key:

Plain text:


0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0

1 0 0 1 1 0 1 0 1 0 0 0 1 0 1 1 1 0 0

1 0 0 0 0 1 1 0 1 1 1 1 1 0 1 0 0 1 0

Plain text:

Cipher text:

Key:

1 0 0 1 1 0 1 0 1 0 0 0 1 0 1 1 1 0 0

0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0

Key:

Plain text:

Key distribution problem

0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0

1 0 0 1 1 0 1 0 1 0 0 0 1 0 1 1 1 0 0

1 0 0 0 0 1 1 0 1 1 1 1 1 0 1 0 0 1 0

Plain text:

Cipher text:

Key:

A LITTLE BIT ABOUT QUANTUM THEORY

Polarisation

Polarisation

Polarisation

Polarisation measurement: H/V basis

Polarising beam splitter

I(V)

I(H)

Polarisation measurement: A/D basis


I(A)

I(D)

Single photon polarisation


P(V)

P(H)

Probabilities

H 1 0 ½ ½

V 0 1 ½ ½

Single photon polarisation

QUANTUM KEY DISTRIBUTION

Quantum communication

0:

1:

Quantum key distribution


• For each photon, Alice chooses at random in which basis, H/V or A/D, to encode her bit. She prepares H (or A) for “0” and V (or D) for “1”.

1: 0:


• Alice sends her photons to Bob using a quantum channel.


• When Bob receives them, he chooses at random whether to measure H/V or A/D in each case, and writes down the bit found: “0” for H (or A), “1” for V (or D).

Quantum key distribution H/V, A/D,

A/D…

H/V, A/D, H/V…


• Case 1: Alice and Bob choose the same basis.


• Case 1: Alice and Bob choose the same basis.


• Case 2: Alice and Bob choose different bases.





Quantum key distribution with an eavesdropper

Assumptions on the eavesdropper

Quantum key distribution with an eavesdropper

01001

01101

• Eve must introduce errors

• This is a fundamental feature of quantum mechanics

• Alice and Bob can detect the presence of Eve

KEY DISTRIBUTION WITH MAGIC BOXES

Magic boxes

Properties of magic boxes

• One “photon” is made up of two boxes, each containing a coin.

• Whenever one box is opened, the other one shakes so that the coin is flipped with probability ½.

Key distribution with magic boxes

• Alice chooses at random in which box, red or yellow, to place her bit. She places the coin heads up for “0” and tails for “1”.

1: 0:

Key distribution with magic boxes

• Alice sends the magic boxes to Bob (possibly via Eve, need a moderator)

Key distribution with magic boxes • When Bob receives the boxes, he

chooses at random whether to open the red or the yellow box in each case, and writes down the bit found there: “0” for heads, “1” for tails.

Key distribution with magic boxes Red, Yellow,

Yellow…

Red, Yellow, Red…

Quantum Technology school

• For: your budding Alices and Bobs taking highers or advanced highers

• Taster sessions in Physics, Computer Science and Engineering

• Look out for announcements via Sputnik mailing list

When: September 4-5 2018 Where: Glasgow University Theme: Quantum technology

Contact: [email protected] [email protected]

mailto:[email protected]

mailto:[email protected]

Documents

A beginner’s guide to quantum information · A beginner’s guide to quantum communication and information Sarah Croke School of Physics & Astronomy University of Glasgow Stirling