Alice and Bob in theAlice and Bob in theQuantum WonderlandQuantum Wonderland

Two Easy SumsTwo Easy Sums

7873 x 6761 = ?7873 x 6761 = ?

? x ? = 26 292 671? x ? = 26 292 671

SuperpositionSuperpositionThe mystery of The mystery of ++

How can a particle be a How can a particle be a wave?wave?

PolarisationPolarisation

Three obstacles are easier Three obstacles are easier than twothan two

Addition of polarised lightAddition of polarised light

== ++

++==

The individual photonThe individual photon

MEASUREMENTMEASUREMENTPREPARATIONPREPARATION

YesYes

NoNo

How it looks to the photon in the How it looks to the photon in the stream (2)stream (2)

MEASUREMENTMEASUREMENTPREPARATIONPREPARATION

MAYBEMAYBE!!

States of being States of being

|N |N |NE |NE |NW|NW

|NE |NE |N |N |E|E

== ++

++==

Alive Alive Dead = ? Dead = ?

Quantum additionQuantum addition

++ =

++ =

++

SchrSchröödinger’s Catdinger’s Cat

|CAT = |ALIVE + |DEAD

EntanglementEntanglement

Observing Observing either side either side breaks the breaks the entanglemeentangleme

ntnt

++

Entanglement killed the catEntanglement killed the cat

According to quantum theory, if a cat can be in According to quantum theory, if a cat can be in

a state |ALIVE a state |ALIVE and a state |DEAD and a state |DEAD, it can also , it can also

be in a statebe in a state

|ALIVE|ALIVE + |DEAD + |DEAD..

Why don’t we see cats in Why don’t we see cats in such superposition statessuch superposition states??

++

Entanglement killed the catEntanglement killed the cat

++

ANSWER: because the theory actually ANSWER: because the theory actually predicts…..predicts…..

[[ ++]] ]][[

[[ ]]?

??

Entangled every which wayEntangled every which way

++ ++==

Einstein-Podolsky-Rosen Einstein-Podolsky-Rosen argumentargument

If one photon passes through the If one photon passes through the polaroid, so does the other one.polaroid, so does the other one.

Therefore each photon must already Therefore each photon must already have instructions on what to do at have instructions on what to do at

the polaroid.the polaroid.

The no-signalling theoremThe no-signalling theorem

I know what message Bob is

getting right nowQuantum entanglement

can never be used to send information that could not be sent by conventional means.

But I can’t make it be

my message!

Quantum cryptographyQuantum cryptography

0

1

0

0

1

0

1

0

0

1Alice and Bob now share a secret key which didn’t exist

until they were ready to use it.

Quantum informationQuantum information

θ

1 qubitΘ=0.0110110001

…

Yet a photon does this calculation!

1 bit0 or 1

YesYes

NoNo

To calculate the behaviour of a photon, infinitely many bits of

information are required

– but only one bit can be extracted.

Available information: one Available information: one qubitqubit

1 qubit

1

0

1 qubit

1 bit

y

x

1 bit

or

Available information: two Available information: two qubitsqubits

0 0

1 0

1 1

0 1

2 qubits 2 bits 2 qubits 2 bits

+

-

+

-

W

Z

Y

X

or

TeleportationTeleportation

Measurement ReconstructionTransmission Reception

?

Quantum TeleportationQuantum Teleportation

Measure

W,X,Y,Z?

Dan Dare, Pilot of the Future. Frank Hampson, Eagle (1950)

Dan Dare, Pilot of the Future. Frank Hampson, Eagle (1950)

Nature 362, 586-587 (15 Apr 1993)

ComputingComputing

INPUTN digits

COMPUTATIONRunning time T

OUTPUT

How fast does T grow as you increase N?

Quantum ComputingQuantum Computing

But you can choose your question

++ ++

In 1 unit of time, many calculations can be done but only one answer can be seen

E.g. Are all the answers the same?

6+4 20/3 100

Two Easy SumsTwo Easy Sums

7873 x 6761 = ?7873 x 6761 = ?

? x ? = 26 292 671? x ? = 26 292 671

53 229 353

Not so easy Not so easy ..

N

T for multiplying

two N-digitsT for factorising a 2N-digit number

1 1 2

2 4 4

3 9 8

4 16 16

5 25 32

10 100 1,024

20 400 1,048,576

30 900 1,073,741,824

40 1600 1,099,511,627,776

50 2500 1,125,899,906,842,620

T ≈ N 2 T ≈ 2 N

But on a quantum computer,

factorisation can be done in roughly the

same time as multiplication

T ≈ N 2

(Peter Shor, 1994)

No cats were harmed in the No cats were harmed in the preparation of this lecturepreparation of this lecture

Key Grip Lieven ClarisseKey Grip Lieven Clarisse

Visual Effects Bill HallVisual Effects Bill Hall

Focus Puller Paul ButterleyFocus Puller Paul Butterley

Best Boy Jeremy CoeBest Boy Jeremy Coe

Alice Sarah Alice Sarah PagePage

Bob Tim Olive-Bob Tim Olive-BeslyBesly