Transcription
What the # *! Do We (K)now!?about Quantum MechanicsCarlton M. CavesCenter for Quantum Information and ControlUniversity of New Mexicohttp://info.phys.unm.edu/ cavesCenter for Quantum Information and ControlView from Cape HauyTasman Peninsula,TasmaniaAspens in the Sangre de Cristo RangeNorthern New Mexico
There is magic in the worldof the very small.I don’t care if you are atHogwarts, Harry. You can’tviolate the uncertainty principle.Fifty points from Gryffindor.Use your quantummechanics, Harry. Feelthe quantum reality.And that magic isdescribed by quantummechanics.
Quantum mechanics governs the behavior of thevery small, but how small are we talking about?1 metermhuman height10-3 metermillimeter (mm)10-6 metermicrometer (μm)10-9 meternanometer (nm)human hairsize of eukaryotic plant cellsize of eukaryotic animal cellsize of Escherichia coliwavelength of visible lightthickness of cell membranesize of amino acid, X-ray wavelengthsize of an atom10-12 meterpicometer (pm)gamma-ray wavelength10-15 meterfemtometer (fm)size of atomic nucleus
What’s strange about the behavior ofquantum systems?Waves vs. particlesIndeterminacyUncertainty principleComplementarity
What’s strange about the behavior ofquantum systems?Waves vs. particlesIndeterminacyUncertainty principleComplementarity
What’s strange about the behavior ofquantum systems?Max Planck(1858-1947)Niels Bohr(1885-1962)Given a proton and an electron, balancing the electron’s(positive) energy of motion with its (negative) electricalbinding energy, within the constraints of the uncertaintyprinciple, determines the size of an atom to be about 0.1nanometer. Putting the mass of the proton in each volumeof this size gives the density of ordinary matter.
What’s strange about the behavior ofquantum systems?EntanglementQuantum correlations“Great! But I might be more impressed if I had a cluewhat a correlation is, much less a quantum correlation.”Erwin Schrödinger(1881-1961)John S. Bell(1928-1990)N. David Mermin(1935-)
Cable BeachWestern AustraliaGet ready! I’m going to tryto explain why entanglementis weird, but we’ll need amajor detour to get there.
CorrelationsStudent atHarvard UniversityLung cancerSmokingPolitically leftDrinking lattesGood teeth
Perfect correlationLeft footRight footCowboy bootCowboy bootSandalSandalBiking shoeBiking shoeSki bootSki boot
A correlation is anassociation between things.It’s perfect when theassociation always occurs.Oljeto WashSouthern Utah
A correlation gameSacagawea was a Lemhi Shoshone woman, whoaccompanied the Lewis and Clark Expedition, actingas an interpreter and guide, in their exploration ofthe Western United States. She traveled thousandsof miles from North Dakota to the Pacific Oceanbetween 1804 and 1806.Sacagawea 1US coinSculpture, in Bismarck, NorthDakota,of Sacagawea andher baby, Jean-BaptisteCharbonneau.Heads0UpBitTails1DownThe face on the coin was modeled on aShoshone-Bannock woman namedRandy'L He-dow Teton, then a studentat the University of New Mexico.
A correlation gameCorrelations between coins held by Alice andBob can be used to “teleport” the state ofVictor’s coin to Bob.Sacagawea 1US coin1.2.3.Heads0UpBitTails1DownAlice only needs to know thather and Bob’s coins arecorrelated, not whether theyare both heads or both tails.Alice doesn’t need todetermine whether Victor’scoin is heads or tails.The message she sends toBob doesn’t reveal whetherVictor’s coin is heads or tails.
Correlations can beused to sendinformation withoutactually sending it.Echidna GorgeBungle Bungle RangePurnululu National ParkWestern Australia
Polarization of lightA source ofpolarized lightNo polarized glassesPolarized glasses
Polarization of a single photon(particle of light)Photon10Photon polarization
Photon polarizationX polarization10Photon10X
Photon polarizationY polarization10PhotonQuantum coinTwo-state quantum systemQubits rX Y10Y
Quantum coinPhoton polarizationQubit10PhotonQuantum rules1. Only one polarization at a time canbe prepared or measured.2. When one polarization is measured,the other is randomized.0s 1rX Y
Classical bit vs. qubitA classical bit is either on or off.A few electrons on a capacitorA pit on a compact diskA 0 or 1 on the printed pageA smoke signal rising from a distant mesaA qubit has a continuum of on-off properties.VYA quantum state tells youUthe odds for getting 0 or 1when you examine any ofXthese one-bit coinscontinuum of one-bit coins (linear polarizations).(linear polarizations)
What happened to Planck’s constant?Planck initiated the study of quantummechanics when he announced in1900 the results of his theoreticalresearch into the radiation andabsorption of a “black body.”Max Planck (1858-1947)Planck’s constant is the scale on whichphysical phenomena are discrete (orgrainy); for example, photons are theexpression of the discreteness of theelectromagnetic field.
World of classical physicsContinuous, smooth(analogue)World of quantum physicsI don’t care if you areat Hogwarts, Harry.You can’t violate theuncertainty principle.Discrete, grainy(digital)Information-processing perspectiveDigital devices(on-off)Use your quantummechanics, Harry. Feelthe quantum reality.Continuum ofdigital properties
A qubit (photon polarization) is a wholebunch of one-bit coins, but we will onlyneed the two coins corresponding to Xand Y polarization. A quantum stategives the odds for each of these coins.Tent RocksKasha-Katuwe National MonumentNorthern New Mexico
Entanglement (at last):quantum correlationsPerfect correlation, with the tworesults, 00 or 11, being equally likely.1100Photon AXAliceParametricdownconverterBell entangledquantum statePhoton BBobX polarization1100X
Entanglement (at last):quantum correlationsPerfect correlation, with the tworesults, 00 or 11, being equally likely.10Photon A10YAliceParametricdownconverterBell entangledquantum statePhoton BBobY polarization1010Y
A quantum correlation game:Quantum teleportationVictorPhoton VPhoton AAliceAlice makes a special fouroutcome polarizationmeasurement on V and A andthen sends one of fourmessages (two bits) to Bob.Alice never finds out thequantum state of V, theDo nothing.Y polarization.Flipyour XandY polarizations.messagedoesn’treveal it, andV’s initial quantum state isdestroyed by the game.Bell entangledquantum statePhoton BVictor runs over to Bob andfinds that B now has the samequantum state as V had.Bob
What’s strange about the behaviorof quantum systems?EntanglementQuantum correlationsWe cannot account for quantum teleportation in termsof the photons’ having pre-existing polarizations that arediscovered by the measurements.But we haven’t shown that yet. Everything so far can beexplained in terms of two 1-bit coins (for X and Ypolarizations). But to teleport all polarization, not just X andY, Alice needs to communicate only two bits to Bob; thecorrelations of all these coins are too strong be explained interms of coins with pre-existing properties.
Claret cup cactiNew MexicoQuantum entanglement can beused for useful tasks such asteleportation of quantum states.
Greenberger-Horne-Zeilinger (GHZ) entanglement3-qubit GHZ entangled state:qubit1st qubitx1 y1XY2nd qubit3rd qubitx2 y2x3 y3XXYYxyXYLet’s tell a story: a qubitbecomes a two-bit personx 0 (heads) is a MAN.x 1 (tails) is a WOMAN.y 0 (heads) drinks BEER.y 1 (tails) drinks WINE.
WOMANMANx1 y1Xx1 y1ORYXYx2 y2x3 y3x2 y2x3 y3XXXXYYDrinking ANTAGONISTSAsk one person for gender, theother two for drinking preference.YYDrinking COMPATRIOTS2 heads and 1 tail or 3 tails2 zeroes and 1 one or 3 ones
SummarizeAsk one person for gender, theother two for drinking preference.2 heads and 1 tail or 3 tails2 zeroes and 1 one or 3 onesx1 y1XYx2 y2x3 y3XXYYA MAN is always accompanied by two ANTAGONISTS.A WOMAN is always accompanied by two COMPATRIOTS.
Ask one person for gender, theother two for drinking preference.2 heads and 1 tail or 3 tails2 zeroes and 1 one or 3 onesx1 y1XYx2 y2x3 y3XXYYNow ask all three persons for gender.2 heads and 1 tail or 3 tails2 zeroes and 1 one or 3 onesThere must be two MEN and a WOMAN or three WOMEN.
Here’s whyMANMANMANx1 y1x1 y1XXYWOMANMANYWOMANx2 y2x3 y3x2 y2x3 y3XXXXYANTAGONISTSYYANTAGONISTSYA MAN is always accompanied by two ANTAGONISTS.A WOMAN is always accompanied by two COMPATRIOTS.There must be two MEN and a WOMAN or three WOMEN.
Quantum mechanics: only what wejust showed to be impossible occurs.2 heads and 1 tail or 3 tails2 zeroes and 1 one or 3 onesx1 y1XY2 heads and 1 tail or 3 tails2 zeroes and 1 one or 3 onesx2 y2x3 y3XXYY2 tails and 1 head or 3 heads2 ones and 1 zero or 3 zeroesA MAN is always accompanied by two ANTAGONISTS.A WOMAN is always accompanied by two COMPATRIOTS.There must be two MEN and a WOMAN or three WOMEN.There must be two WOMEN and a MAN or three MEN.
What’s strange about the behavior ofquantum systems?EntanglementQuantum correlationsCorrelations—even perfectcorrelations— that violate therules of ordinary existence.We cannot account for the behavior of quantumsystems by imagining that properties have preexisting values that are discovered by observation.
Bungle Bungle RangeWestern AustraliaObjects in the world of the very small violate therules of ordinary existence: either they are notindividual objects, or they do not have realisticproperties. The result is magic.
It’s not only dogs thatcan’t understand quantummechanics.Quantum physics leads youto a world of magic,beyond your imagination,but provides a set of rulesto manage and control themagic.Quantum informationscience is the disciplinethat explores informationprocessing within thequantum world, where themundane constraints ofrealism and determinism nolonger apply.
Why not extend the magicinto the world of theeveryday?I don’t care if you are atHogwarts, Harry. You can’tbuild a quantum computer. Fiftypoints from Gryffindor.Use your quantummechanics, Harry. Aquantum computer wouldbe real magic.The more magic youattempt, the harder itgets.
Quantum information science.Engineering the magic.Truchas from East Pecos BaldySangre de Cristo RangeNorthern New Mexico
Private communicationAlice and Bob share a one-time pad(secret random key).But where do Alice and Bob get the key?
Quantum key distribution using entanglementAlice measures X, Y,U, or V polarization.Photon AAliceAlice and Bob share the type ofmeasurement they did, not theresult. If they measured the samething, they keep the shared randombit for their key. Otherwise, they usethe results to verify a Bell inequality,which can be used to rule out thepresence of an eavesdropper.Bell entangledquantum statePhoton BBobBob measures X, Y,U, or V polarization.
Quantum key distribution usingentanglementExperiment at Los Alamos National Laboratory (2000): D. S.Naik, C. G. Peterson, A. G. White, A. J. Berglund, and P. G. Kwiat
Why is quantum key distribution secure?An unmeasured qubit has no bit valuewaiting to be discovered. Alice and Bobcreate the key by measuring thepolarizations. Before that, there is nokey for an eavesdropper to steal.“There is no there there.”Gertrude Stein damning her native Oakland andinadvertently describing quantum systems.Essential ingredient: Entanglement between qubits
Quantum mechanics governs the behavior of the very small, but how small are we talking about? 1 meter m human height. 10-3. meter millimeter (mm) human hair. size of eukaryotic plant cell. size of eukaryotic animal cell. 10-6 meter micrometer (μm) size of Escherichia coli. wavelength of visible light. thickness of cell membrane
