Alice and Bob in the Quantum Wonderland

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## Alice and Bob in the Quantum Wonderland

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**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)