Alice and Bob in the Quantum Wonderland. Two Easy Sums 7873 x 6761 = ? 7873 x 6761 = ? ? x ? = 26 292 671 ? x ? = 26 292 671.

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Alice and Bob in the Quantum Wonderland

Two Easy Sums 7873 x 6761 = ? 7873 x 6761 = ? ? x ? = 26 292 671 ? x ? = 26 292 671

Superposition The mystery of +

How can a particle be a wave?

Polarisation

Three obstacles are easier than two

Addition of polarised light =+ += 

The individual photon MEASUREMENT PREPARATION Yes No

How it looks to the photon in the stream (2) MEASUREMENT PREPARATION MAYBE!

States of being |N  |N  |NE  |NW  |NE  |N  |N  |E  =+ +=

Alive Dead = ? Quantum addition + ++ + = + = +

Schrödinger’s Cat |CAT  = |ALIVE  + |DEAD 

Entanglement Observing either side breaks the entanglement +

Entanglement killed the cat According to quantum theory, if a cat can be in a state |ALIVE  and a state |DEAD , it can also be in a state |ALIVE  + |DEAD . Why don’t we see cats in such superposition states ? +

Entanglement killed the cat + ANSWER: because the theory actually predicts….. [ + ]][ [] ? ? ?

Entangled every which way + + =

Einstein-Podolsky-Rosen argument If one photon passes through the polaroid, so does the other one. Therefore each photon must already have instructions on what to do at the polaroid.

The no-signalling theorem I know what message Bob is getting right now Quantum 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 cryptography 0 1 0 0 1 0 1 0 0 1 Alice and Bob now share a secret key which didn’t exist until they were ready to use it.

Quantum information θ 1 qubit Θ=0.0110110001… Yet a photon does this calculation! 1 bit 0 or 1 Yes No To calculate the behaviour of a photon, infinitely many bits of information are required – but only one bit can be extracted.

Available information: one qubit 1 qubit 1 0 1 bit y x or

Available information: two qubits 0 1 0 1 0 1 2 qubits  2 bits + - + - W Z Y X or

Teleportation Measurement Reconstruction TransmissionReception ?

Quantum Teleportation Measure W,X,Y,Z?

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

Nature 362, 586-587 (15 Apr 1993)

Computing INPUT N digits COMPUTATION Running time T OUTPUT How fast does T grow as you increase N?

Quantum 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+420/3100

Two Easy Sums 7873 x 6761 = ? 7873 x 6761 = ? ? x ? = 26 292 671 ? x ? = 26 292 671 53 229 353

Not so easy. N T for multiplying two N-digits T for factorising a 2N-digit number 112 244 398 416 52532 101001,024 204001,048,576 309001,073,741,824 4016001,099,511,627,776 5025001,125,899,906,842,620 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 preparation of this lecture Key Grip Lieven Clarisse Visual Effects Bill Hall Focus Puller Paul Butterley Best Boy Jeremy Coe Alice Sarah Page Bob Tim Olive-Besly

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