Alice and Bob in the Quantum Wonderland Two

Alice and Bob in the Quantum Wonderland

Two Easy Sums 7873 x 6761 = ? = 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 PREPARATION MEASUREMENT Yes No

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

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

Quantum addition + = + Alive + Dead = = ?

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 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 But I can’t make it be my message! Quantum entanglement can never be used to send information that could not be sent by conventional means.

Quantum cryptography 0 0 1 1 Alice and Bob now share a secret key which didn’t exist until they were ready to use it.

Quantum information Yes θ No 1 qubit Θ=0. 0110110001… To calculate the behaviour of a photon, infinitely many bits of information are required 1 bit 0 or 1 – but only one bit can be extracted. Yet a photon does this calculation!

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

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

Teleportation Measurement Transmission ? Reception Reconstruction

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 6+4 + 20/3 + 100 In 1 unit of time, many calculations can be done but only one answer can be seen But you can choose your question E. g. Are all the answers the

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

Not so easy N T for multiplying two N-digits T for factorising a 2 N-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)

Key Grip Visual Effects Focus Puller Lieven Clarisse Bill Hall Paul Butterley No Best cats. Boywere harmed the Jeremyin Coe preparation of this lecture Alice Bob Sarah Page Tim Olive-Besly