Lecture 21 Photon Statistics (detecting sub-poissoinian light) application 1 of single photons: quantum communication Read: FQ5, FQ12

Quantum Optics of Photons FQ’Chap5 FQ’Chap6 Chap 7-8: coherent, squeezed, & number states

Photon Statistics FQ’Chap5 Single photon detector: PMT (photomultiplier tube) APD (avalanche photodiode)

Subpoissonian Light But: any (random) loss will randomize the photons (det. Subpoissonian challenging)

Theory of Photodetection (semiclasical) If I(t)=I constant If I(t) fluctuating, superpoissonian

Theory of Photodetection (quantum) But: any (random) loss will randomize the photons (det. Subpoissonian challenging) Key: high Q.E.

Noise in Photodiodes

Shot Noise (“quantum noise”)

(classical) Noise Reduction Also: feed-forward

Experimental Observation of quantum nature of light: sub-poissonian light Use sub-poissonian electrons to gernerate SubP-light Sub-poissonian counting statistics

Sub-shot noise photocurrent

Shapiro-Wong Group: http://www.rle.mit.edu/qoptics/ Quantum Information Science 1: quantum (secure) communication & quantum cryptography (photon based) (cf. *FQ Chap12) Learn more: M. Le Blanc: A Short Introduction to Quantum Information and Quantum Computation Chuang & Nielson, QCQI David Mermin, Quantum Computer Science: An Introduction Good to reach on beach or train: J. Dowling’s Schrodinger’s Killer App L. Susskind, Quantum Mechanics: The Theoretical Minimum (see also Stanford course lectures/videos of same title) N. Gisin et al. Rev. Mod. Phys. 74, 145–195 (2002) J.W.Pan Lecture: http://quantuminformation.physi.uni-heidelberg.de/pic/LEC430.pdf MIT 6.453 course on quantum communication http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-453-quantum-optical-communication-fall-2008/ Shapiro-Wong Group: http://www.rle.mit.edu/qoptics/

See also http://www.youtube.com/ watch?v=tKfyw-uAgac From :C. Bennett lecture “Information is quantum” [highly recommended to read] http://researcher.watson.ibm.com/researcher/files/us-bennetc/QInfWeb.pdf

Classical Cryptography (Secure Communication) ENIGMA RSA-100=37975227936943673922808872755445627854565536638199 × 40094690950920881030683735292761468389214899724061 Earn $200,000 to factorize RSA-2048 Later quantum computing will break this RSA RSA-100 =15226050279225333605356183781326374297180681149613 80688657908494580122963258952897654000350692006139

The purpose of quantum cryptography is to provide a reliable method for transmitting a secret key and knowing that no-one has intercepted it along the way. The method is founded on the fundamental laws of quantum physics, and the process of sharing a secret key in a secure way is called quantum key distribution. Two basic schemes for quantum cryptography, using basic principles of quantum measurements on single particles (photons) The properties of entangled photon properties of entangled states.

Classical communication & evesdropper

Photon polarization qbits

Review 2-state QM (d=2 Hilbert space) R2 representation

Quantum No Cloning Theorem http://courses.cs.washington.edu/courses/ cse599d/06wi/lecturenotes4.pdf

QKD by BB84 Protocol (ex.12.3) Interesting read on B&B http://www1.cse.wustl.edu/~jain/cse571-07/ftp/quantum/index.html At 57, Gilles Brassard has won a multitude of awards, but the Nobel Prize would be a crowning achievement at an international level. The young mathematics prodigy initially discovered by his brother Robert, his elder by six years, Brassard mastered differential and integral calculus in elementary school. Université de Montréal opened its door to Brassard when he was just 13 years old, and he entered into a bachelor's program. The "mathematical elegance" of cryptography captivated him during his doctoral studies at Cornell University, and he immediately redirected his attention to the science of coding, until then the preserve of the military. His meeting with Charles Bennett in November 1979 was decisive and is the stuff of cinema. A few days before delivering a lecture on cryptography in Puerto Rico, Brassard was bathing in the ocean when he saw a stranger swimming toward him. The man approached him saying that he knew how to duplicate banknotes that are otherwise impossible to duplicate, using quantum mechanics. "That meeting in the middle of the ocean changed my life," says Brassard. Twelve years his elder, Bennett had read the title of Brassard's paper in the program and wanted to meet him. The two men became friends and worked together actively, leading to a famous brainstorming session in November 1992. Inspired by an article on quantum physics he had just read, Brassard invited one of the authors, William Wootters, to present his findings in Montreal. He took the occasion to invite Charles Bennett and Claude Crépeau. During the presentation, a question was raised by Bennett that Wootters was unable to answer. The researchers locked themselves in Brassard's office to discuss the matter. "Twenty-four hours later, the theory of quantum teleportation was born," recalls the scientist. Returning to their daily lives, the researchers exchanged papers between North America, Europe, and Israel: according to Brassard, the six authors were in a continuum of movement on which the sun never set. It took only 11 days to prepare and submit the article. "I think the principle of quantum teleportation would have been discovered sooner or late because it was inevitable. Our collaboration saved a few years," he says. Never tiring of his teaching career after 33 years - first as lecturer at the University at 24, then as full professor nine years later, becoming the youngest faculty member to receive such a promotion in the modern history of the Université de Montréal - Gilles Brassard relishes the freedom afforded by his position. As head of the Canada Research Chair in quantum computing, he continues his work in theoretical and quantum computer science. He currently supervises some ten graduate students, mostly doctoral candidates, half of whom are from abroad. His greatest professional pride comes from learning that a former student has obtained a professorship at a university somewhere in the world, a pleasure he has known more than twenty times already. Without hesitation, he refuses offers from abroad, enjoying above all the quality of life of Montreal, his hometown. An avid cyclist and hiker, the Nobel contender also loves cooking and listening to music. Most of all, he has an undying sense of humour, peppering his remarks on quantum physics with spontaneous laughter. - See more at: http://www.noodls.com/view/C72E62DBAF2DB94324F14C95042A47D40F3E72EF#sthash.bG0zAaq7.dpuf Interesting read on B&B http://researcher.watson.ibm.com/researcher/view.php?person=us-bennetc http://www.noodls.com/view/C72E62DBAF2DB94324F14C95042A47D40F3E72EF (also discovered q. teleportation)

Reality Complications Reduced key length Missing photons .. Reduce # of useful bits Birefringence (change polarization during transmission) Detector dark counts (false click even with missing photons) address by (classical) Error correction General Read: “Quantum cryptography: Seeking absolute security” http://www.nature.com/nature/journal/v447/n7143/full/447372a.html

Hardware requirements/complications (reliable) Single photon source [multiphoton emission compromises security by giving Eve more chances to evade detection (both Eve’s detectors click  knows basis wrong)] Attenuated single-freq laser: photon Poisson distr, subject to multi-photons “on-demand” single photon source [current research] (will revisit this when discussing QO) (reliable) single photon detectors, polarization rotators, medium

Transmission Media for quantum communication/cryptography Subject to environmental noise (air turb. stray light etc.) <possible project/essay> Phase (vs polarization) encoding Subject to loss and birefringence (at long distance)

See also : http://qwcap.com (potential essay topic, explain how these work, or market analysis)