The Three Upcoming Revolutions in Physics and Astronomy that will Affect Everyone. Quantum Information Nov. 12, 2002

Transcription

1 The Three Upcoming Revolutions in Physics and Astronomy that will Affect Everyone Quantum Information Nov. 12, 2002

2 The History of Secrecy Enemy of the State You re being watched Big Brother You are captured on video 8-10 times per day Greater interconnectivity requires greater privacy protection Will continue to grow with growth of the internet The grid Protection of privacy Numbers instead of names Passwords

3 Warm up Decrypt this following message K ycpv vq igv cp c kp vjku eqwtug. How d you do it? Look for one-letter words Look for commonly used letters Knowledge about frequency and location of vowels in words Answer I want to get an A in this course.

4 The History of Secrecy The battle between cryptography and cryptanalysis Simple encryption Crypto-quote Earliest cryptography Deciphering hieroglyphs in Egyptian crypts Rosetta stone was the key Story of Queen Mary s treason against Queen Elizabeth (1586) The Babington plot

5 The History of Secrecy The battle between cryptography and cryptanalysis World War I Why did the U.S. enter World War I? World War II German Enigma (U-571) Alan Turing and the Bombes

6 The History of Secrecy The battle between cryptography and cryptanalysis How do we protect our secrets now? Encryption Basic encryption schemes are easily broken One time pad Public key Authentication Background checks Thumb and retinal scans» Voice? 2001 Secure telephones

7 The History of Secrecy The battle between cryptography and cryptanalysis RSA & public key encryption One-way functions Secure internet commerce How public key cryptography works Multiplying two prime numbers is easy 23 x 47 =? Factoring a number into its two prime cofactors is hard 1961 =? x? If N-digit key can be factored, increase N to increase security

8 The History of Secrecy The battle between cryptography and cryptanalysis The internet and the rise of personal secrecy Not just needed by the government Secrecy on the internet How its done Where its used Credit cards Personal information Protected sites

9 The History of Secrecy How am I being tracked every day? Communication Telephone & Cell phone Two way TV & Internet browsing Security Cameras everywhere Card-key entry Credit & debit cards Purchases & carbons Electronic verification Fingerprints and DNA matching Travel GPS in cars and trucks On Star Ticket & Hotel reservations

10 The History of Secrecy How am I protecting myself everyday? Communication Secure web sites (https) Security Passwords Travel Class/work Honor code? How long could I go untracked, if I wanted to?

11 Interlude: How does a computer work? Bits Information storage Bytes Memory Binary Logic Basic operations AND, OR, NOT Universal Operations NAND, NOR Processing Retrieve bits Operate binary logic Store bits l Classical Computer Classical bits must be either 0 or 1. N bits represent any number [0, 2 N -1]. Loop over all numbers in 2 N operations.

12 Interlude: How does a computer work? Classical computers Moore s law Devices continue to halve in size every 2-3 years Pentium IV has gate length 260 atoms across! Bits are being stored in fewer and fewer atoms The end of Moore s law Moore s law will end before we reach atomic scale computing Quantum mechanical limit will be reached in the next decade

13 Do you really expect me to understand quantum mechanics? Quantum mechanics Heisenberg Uncertainty Principle What it means, and what it doesn t mean Measurement Electron Waves 10 nm Wave-particle duality Is light a wave or a particle? Is matter made of waves or particles? Decoherence and collapse Every interaction with nature is a measurement

14 Do you really expect me to understand quantum mechanics? Quantum mechanics Tunneling How to pass through walls Example: Fusion and how the sun works This is how Moore s law fails Atomic-scale transistors can t contain electrons - -

15 Do you really expect me to understand quantum mechanics? Quantum mechanics Superposition How to be in two places at the same time Example: Quantum mechanical light switch Superposition and Measurement Measurement Measurement destroys the superposition System must end up in one state or the other Probability of final state depends on the way the superposition is structured

16 Do you really expect me to understand quantum mechanics? Quantum computers Quantum bits Can represent both values simultaneously Compare with classical operations Example of exponential scaling Do-loop Number of bits necessary to represent the universe l Quantum Computer Superposition allows Qbits to be between 0 and 1. N Qbits represent all of [0, 2 N -1] simultaneously. Loop over all numbers in 1 operation.

17 Do you really expect me to understand quantum mechanics?

18 Do you really expect me to understand quantum mechanics?

19 Do you really expect me to understand quantum mechanics? Quantum computers Decoherence Q-bits are fragile Every interaction with nature is a measurement Quantum error correction How do you fix an error you can t look at? How it works Vulnerable storage Quantum state represented simply as superposition. Bit flip creates error. Step 1: Redundant storage Encode Qbit in state of 3 Qbits Step 2: Bit flip error occurs. a 0>+b 1> a 1>+b 0> a 000>+b 111> a 100>+b 011> Step 3: Error detected. Qbits compared to each other, 2 at a time, for discrepancies. a 100>+b 011> Step 4: Error corrected. Comparative measurments reveal error on Qbit 1; Qbit flipped. a 000>+b 111>

20 Do you really expect me to understand quantum mechanics? Quantum computers Quantum logic How to compute using Qbits Controlled-NOT Using one Q-bit to control another Universal operation Comparison of two Qbits Necessary for error correction Controlled Not Target Qbit not flipped if control Qbit is 0. Target Qbit flipped if control Qbit is 1. How it works Collective Measurement Qbits A and B are compared using two C-NOTs and a third ancilla bit

21 Do you really expect me to understand quantum mechanics? Shor s Code-breaking Quantum Algorithm How fast can you factor a number? Difficulty grows exponentially with number of digits Q computer advantage Code-breaking can be done in minutes, not millennia Public key encryption, based on factoring, will be vulnerable!!!

22 Do you really expect me to understand quantum mechanics? Grover s Search Quantum Algorithm Sequentially try all N possibilities Average search takes How quickly can you find a needle in a haystack? Difficulty grows exponentially with number of items (N) Q computer advantage Search 106 items 500X faster Classical Search N/2 steps Quantum Search Simultaneously try all N possibilities Refining process reveals answer Average search takes N1/2 steps

23 Do you really expect me to understand quantum mechanics?. Quantum Computing Hardware Ion Trap QC Semiconductor Qdot QC Atom Trap QC Semiconductor Spin QC NMR QC Superconductor QC AMO QC Ion trap and cavity QED Optical lattice NMR QC Semiconductor QC Spin-based Doped Silicon Quantum dots Quantum Hall regime Superconductor QC Charge and Flux JJs Other Physical Systems Quantum Computing Software H NH 3 Algorithms Q. Information Theory Q. Error Correction Architectures C O C RF SQUID Bext Josephson Junction C H3 I OH Energy Quantum Hall Regime Electrons on LHe Molecular systems I "1" "0" F0 0.5 Flux / F 1 1.5

24 Beam me up, Scotty! Quantum mechanics Entanglement Can you beat the speed of light??? Example: Linked quantum mechanical light switches Quantum Key Generation How it works Step 1: Alice and Bob start. Polarization entangled photon pairs are generated. Quantum cryptography How it works Agree on a key by sharing entangled photons Guaranteed to be secure by the laws of physics! An eaves dropper reveals himself! Step 2: Alice sets key. Alice measures polarization of one entangled photon. Result of measurement is key Step 3: Bob reads key. Alice tells Bob what measurement she made. Bob gets key. Step 4: Message sent. Alice encodes message and sends it to Bob through open channels. Bob decodes message

25 Beam me up, Scotty! Science Fiction Faster than light ( superluminal ) effects Science Fact Quantum key distribution Working systems since 1994 Free space experiments 67 km achieved Fiber experiments 23 km achieved

26 Beam me up, Scotty! Quantum teleportation How it works Send message, not key Entangle message with entangled photon Quantum Teleportation How it works Step 1: Alice and Bob start. Polarization entangled photon pairs are generated. What it can t do Doesn t break speed of light barrier Requires classical communication channel Can t teleport matter Could reconstruct state of matter Step 2: Alice sends message. Alice entangles message photon with one entangled photon. Step 3: Bob receives message. Alice s message is destroyed as it is teleported to Bob on second entangled photon. Step 4: Bob reads message Alice tells Bob how to measure second entangled photon to read message.

27 Beam me up, Scotty! Science Fiction Matter teleportation Science Fact Quantum state teleportation

28 Should we be able to keep secrets secret? Warm up Sneakers

29 Should we be able to keep secrets secret? The impact of the quantum information revolution Information security National interests Should this be the next Manhattan project? If we built it, should we tell?

30 Should we be able to keep secrets secret? The impact of the quantum information revolution Information security Financial and personal commerce Will quantum computers be widely available? Should there be secrets the government can t read?

31 Should we be able to keep secrets secret? The impact of the quantum information revolution Information security Freedom of personal communications vs Wiretapping, crime prevention, and antiterrorism What is the boundary between Personal privacy and national security? Health vs insurance Who should know what about you? Who shouldn t? Who decides?