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“Anyone who can contemplate quantum mechanics without getting dizzy hasn’t understood it.” --Niels Bohr The Quantum Information Revolution Paul Kwiat Kwiat’s Quantum Clan (2012) Graduate Students: Rebecca Holmes Aditya Sharma Trent Graham Brad Christensen Kevin Zielnicki Mike Wayne Courtney Byard Undergraduates: Daniel Kumor David Schmid Jia Jun (“JJ”) Wong Cory Alford Joseph Nash David Rhodes Visit Prof: Hee Su Park Post-Doc: Jian Wang A New Science! Quantum Mechanics Information Science 20th Century Quantum Information Science 21st Century Quantum cryptography Secure key distribution (even between non-speaking parties) Fundamental physics Entanglement Decoherence Ultimate control over “large” systems Quantumclassical Quantum Information Quantum metrology Measurements beyond the classical limit Non-invasive measurements Measurements on quantum systems Quantum communciation Teleportation Linking separated quantum systems (“q. network”) Quantum computation Factoring Simulating other quantum systems (>30bits) Error correction Quantum Metrology Quantum Cryptography Quantum Computing “Things should be made as simple as possible, but not any simpler.” What I do… Unravel the mysteries of the universe… Quantum Optics ??? Light Quantum… a. very small b. very big (e.g., “quantum leap”) c. an unsplittable parcel/bundle of energy d. a cool buzzword to get more funding, more papers, more people at your Sat. am physics lecture, etc. e. all of the above 1905: Einstein made a ‘quantum leap’ and proposed that light was really made of particles with tiny energy given by E = h f = h c/l wavelength 6.6 x 10-34J-s frequency Physics 214: Lect. 7 Example: “Counting photons” How do we reconcile this notion that light comes in ‘packets’ with our view of an electromagnetic wave, e.g., from a laser?? Visible light Partially transmitting mirror Power input How many photons per second are emitted from a 1-mW laser (l=635nm)? E photon hc l 1240 eV -nm 2 eV 635 nm Power output: P = (# photons/sec) x Ephoton (# photons/sec) P E photon 10 3 s J 1 eV 1.6 10 -19 J 1 photon 2 eV 3.1 10 s 15 1 1 mW red laser 3 x 1015 photons/sec = 3,000,000,000,000,000/sec This is an incredibly huge number – your eye basically cannot resolve this many individual photons (though the rods can detect single photons!). And you MAY be able to see just one photon!! Formation of Optical Images For large light intensities, image formation by an optical system can be described by classical optics. l l However, for very low light intensities, one can see the statistical and random nature of image formation. l Use an extremely sensitive CCD camera that can detect single photons. A. Rose, J. Opt. Sci. Am. 43, 715 (1953) Exposure time But how do we *know* there’s only ONE photon… A beamsplitter… “1” “0” Photon only detected in one output. Equally likely to be transmitted or reflected – cannot tell which. "God does not play dice with the universe." Quantum random-number generator! “It •seems to me that the idea of a personal God is an completely unpredictable anthropological concept which I cannot take seriously.” • patented • commercially available “The important thing is not to stop questioning.” -A. Einstein Quantum Interrogation The problem… Measure -film -absorber -atom without -exposing -heating -exciting it “Yes, yes, already, Warren! … There is film in the camera!” WHY was Einstein’s 1905 proposal that light was made of particles such a profound leap that almost no one believed him? Because everyone KNEW that light was really waves. One of the strangest features of QM: all particles can behave like waves… Interference of waves (e.g., water, sound, …) Superposition (adding together) of waves Waves add up: “Constructive interference” Waves cancel: “Destructive interference” Light: Particle or Wave? 1675: Newton “proved” the light was made of “corpuscles” 1818: French Academy science contest l l Fresnel proposed interference of light. Judge Poisson knew light was made of particles: “Fresnel’s ideas ridiculous” If Fresnel ideas were correct, one would see a bright spot in the middle of the shadow of a disk. Judge Arago decided to actually do the experiment… Conclusion (at the time): Light must be a wave, since particles don’t interfere! Only, now we know that they must! Single-Photon Interference: Question: what if we reduce the source intensity so that at most one particle (photon) is in the apparatus at a time? ? Photons l Answer: Just like in the “optical image formation”, given enough time, the classical interference pattern will gradually build up from a huge # of seemingly random “events”! Exposure time l Optical Interferometers l l l Interference arises when there are two (or more) ways for something to happen, e.g., sound from two speakers reaching your ear. An interferometer is a device using mirrors and “beam splitters” (half light is transmitted, half is reflected) to give two separate paths for light to get from the source to the detector. Two common types: Mach-Zehnder: beamsplitter Michelson : mirror mirror beamsplitter Quantum Interrogation The problem… Measure -film -absorber -atom without -exposing -heating -exciting it “Yes, yes, already, Warren! … There is film in the camera!” The solution… (Elitzur & Vaidman, 1993) Use dual wave-particle nature of quantum objects (“wavicles”) Single photon always shows up at D1 (complete destructive interference to D2) Now place an absorbing object in one arm… 50% chance that photon is absorbed by object 50% chance it isn’t 25% chance D2 fires “interaction-free measurement” of object Quantum Interrogation • • • Optimizing reflectivities 50% efficiency By combining these techniques with the “quantum Zeno effect” (making repeated very weak interactions), the efficiency can in principle be pushed to 100%: no photons absorbed by the absorbing object! [85% demonstrated to date] Imaging semi-transparent objects does not readily yield a gray-scale Quantum Metrology Wpdrval Quantum Cryptography L&wz;xcuymnzx Quantum Computing Cryptography: Make messages so that only the intended recipient can understand them… 1. public key encryption: Standard, but not provably secure; relies on difficulty of factoring (e.g., 15 = 3x5) 2. secret key encryption: PROVABLY secure as long as a. no one else has the key b. the key is never reused Quantum Cryptography = Quantum Key Distribution Quantum Cryptography ALICE BOB KEY: …010001010011101001… Cipher: …0110010110100010… XOR(Cipher,Key) XOR(Message,Key) Message Cipher EVE Quantum Cryptography: Use a different property of light– polarization! Polarization: --the oscillation direction of the light --property of each photon --can measure with polarizers, calcite, etc. Prob(horizontally polarized photon pass horizontal polarizer): 1 Prob(horizontally polarized photon pass vertical polarizer): 0 Prob(diagonally pol. photon pass horizontal polarizer): 1/2 Prob(diagonally pol. photon pass vertical polarizer): 1/2 How to Make “Entangled” Coins “Spontaneous DownConversion”: high energy parent photon can split into two daughter photons (with same polarization) We don’t know WHICH crystal created the pair of photons, but we know they both came from the same crystal they MUST have the same polarization. What about Eavesdropping? • Eve cannot “tap” the line photons that don’t make it to Bob are not part of the key • Eve cannot “clone” the photon forbidden by basic quantum mechanics • Measurements by Eve necessarily have a chance (25%) to disturb the quantum state Alice and Bob can detect errors in the key! If the bit error rate is too high, they simply discard the key. No message is ever compromised. Current Free-Space QKD Distance Record: 144 km between LaPalma and Tenerife Last week news item: they used the entangled photons to teleport the state of a photon between the islands – world distance record for quantum teleportation! QKD Goes Commercial… Quantum Interrogation vs. Quantum Cryptography Since we can seemingly “see” without “looking” using quantum interrogation, does this mean an eavesdropper could use it to defeat quantum cryptography? No! It turns out that even making the gentlest measurement possible, if the eavesdropper gains any information, she disturbs the state. Or if she is so gentle so as not to disturb the state, then she gets no information. Quantum key distribution is secure against any attack allowed by the laws of physics! Imagination is more important than knowledge Moore’s Law Source: Intel The first solid-state transistor (Bardeen, Brattain & Shockley, 1947) The Ant and the Pentium ~100 million transistors INTEL Pentium 4 transistor Size of an atom ~ 0.1nm Binary digit Quantum bit “bit” “qubit” 0, 1 0101 Physical realization of qubits any 2 level system 2-level atom: ge spin-1/2: polarization: HV All 2-level systems are created equal, but some are more equal than others! Quantum communication photons Quantum storage atoms, spins Scaleable circuits superconducting systems “Quantum” phenomena Superposition Interference Waveparticle duality Intrinsic Entanglement randomness in measurement “Entanglement”, and the scaling that results, is the key to the power of quantum computing. • Classically , information is stored in a bit register: a 3-bit register can store one number, from 0 – 7. 1 0 1 • Quantum Mechanically, a register of 3 entangled qubits can store all of these numbers in superposition: a|000 + b|001 + c|010 + d|011 + e|100 + f|101 + g|110 + h|111 • Result: -- Classical: one N-bit number -- Quantum: 2N (all possible) N-bit numbers •N.B.: A 300-qubit register can simultaneously store 2300 ~ 1090 numbers That’s a BIG number 1090 = 1,000,000,000,000,000,000, 000,000,000,000,000,000, 000,000,000,000,000,000, 000,000,000,000,000,000, 000,000,000,000,000,000 This is more than the total number of particles in the Universe! Some important problems benefit from this exponential scaling, enabling solutions of otherwise insoluble problems. A hard problem: factoring large integers: For example, it is hard to factor 167,659 But an elementary school student can easily multiply 389 x 431 = 167,659 This asymmetry in the difficulty of factoring vs. multiplying is the basis of public key encryption, on which everything from on-line transaction security to ensuring diplomatic secrecy depends. Quantum Computing’s “killer app.” Quantum algorithms enable one to factor numbers into their prime constituents MUCH faster: RSA digits PC (1 GHz) Blue Waters (10PF) Quantum Computer (1 GHz) 129 4 months 1 sec 10 sec 225 300,000 yr 12 days 100 sec 300 1016 yr 20 million yr (>> universe) 200 sec The difficulty (impossibility) of factoring large numbers (and the ease of creating a large number from its factors) is the basis of public key encryption (which nearly everyone uses for secure transmission today). Atom in different energy states: energy states: state labels “ ”, “ ” atom in state atom in state atom atom in superposition state shorthand “wave function” representation = + Probability of measuring , P = ||2 Probability of measuring , P = ||2 Collective motion: the “quantum data bus” state of motion |rest |0 |0 + |1 |0 |0 |1 laser |rest + |moving |0 |0 |0 |0 |1 Science News Quantum Computing Explored Sep 12 2001 @ 08:10 American computer scientists are studying the possibility to build a super fast computer based on quantum physics. Why it might not work… Technology requirements •Set of qubits isolated from environment. •“Quantum information bus” to connect qubits. • Reliable read-out method. Essential Dichotomy Need WEAK coupling to environment to avoid decoherence, but you also need STRONG coupling to at least some external modes in order to ensure high speed and reliability. Quantum Information Timeline Difficulty/Complexity Quantum Computation The expected The unlikely – impossible? Quantum Widgets The known Quantum Sensors? Quantum Engineered Photocells? The as yet unimagined!!! Quantum Communication 0 5 Quantum Measurement 10 ~15 Time (years) Quantum Games & Toys 20? 25?? “Why is it that nobody understands me, and everybody likes me?” – A.E. Multiplexed Ion Trap Architecture control electrodes • Interconnected multi-trap structure • Route ions by controlling electrode potentials • Processor sympathetically cooled • No individual optical addressing during two-qubit gates (can do gates in strong trap fast) • One-qubit gates in subtrap • Readout in subtrap Quantum factoring and cryptography # of instructions the RSA cryptosystem: • polynomial work to encrypt/decrypt • exponential work to break = factoring • BUT quantum factoring is only polynomial work 24 1 10 23 1 10 22 1 10 21 1 10 20 1 10 19 1 10 18 1 10 17 1 10 16 1 10 15 1 10 14 1 10 13 1 10 12 1 10 11 1 10 10 1 10 9 1 10 8 1 10 7 1 10 6 1 10 5 1 10 4 1 10 1000 100 10 1 Classical ~ eAL ~ 1017 instructions: 8 months Quantum~ L3 ~ 109 operations: seconds 0 200 400 RSA129 •“latency”: will information encrypted today be secure against future quantum computers? 600 800 1000 # of bits, L, factored