Superposition + The mystery of
= + = + 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 |W |NE |N |NW |N |NE
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 the theory actually predicts…..
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 0 1 1 0 0 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… 1 bit 0 or 1 To calculate the behaviour of a photon, infinitely many bits of information are required – but only one bit can be extracted. Yet a photon does this calculation!
Available information: one qubit 0 1 qubit 1 bit 1 or x 1 qubit 1 bit y
+ W X - + Y - Z or 2 qubits 2 bits Available information: two qubits 0 0 0 1 1 0 1 1 2 qubits 2 bits
Teleportation Transmission Reception Reconstruction Measurement ?
Quantum Teleportation Measure W,X,Y,Z?
Computing INPUT N digits COMPUTATION Running time T OUTPUT How fast does T grow as you increase N?
+ + 100 In 1 unit of time, many calculations can be done but only one answer can be seen Quantum Computing 6+4 20/3 But you can choose your question E.g. Are all the answers the same?
Two Easy Sums 7873 x 6761 = ? ? x ? = 26 292 671 53 229 353
Not so easy . But on a quantum computer, factorisation can be done in roughly the same time as multiplication T ≈ N 2 (Peter Shor, 1994)