# Quantum Key Distribution works like an unsophisticated candy machine Scott Shepard Louisiana Tech University.

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Quantum Key Distribution works like an unsophisticated candy machine Scott Shepard Louisiana Tech University

What the Physicists do with Entangled Photons

“Spooky Action at a Distance” If measure along same axis perfectly anticorrelated If measure along different axis no correlation BA

Unsophisticated Candy Machine measures size or magnetic – not both Q C N F magnetic (x+) non-magnetic (x-) big (y+) non-big (y-) F = Franc C = Canadian nickel Q = US quarter N = US nickel

As a Table Q C N F magnetic (x+) non-magnetic (x–) big (y+) non-big (y–) Detector aDetector b F (x+ y+)N (x– y–) C (x+ y–)Q (x– y+) Q (x– y+)C (x+ y–) N (x– y–)F (x+ y+) There is no EPR “paradox.”

Measuring Along 3 Directions Detector aDetector bProbability (x+ n + y+)(x– n – y–) P1 + + – – – + P2 + – + – + – P3 + – – – + + P4 – + + + – – P5 – + – + – + P6 – – + + + – P7 – – – + + + P8 n can be along any direction perfect “anti-correlation” built into this LHV model

Measuring Along 3 Directions Detector aDetector bProbability (x+ n + y+)(x– n – y–) P1 + + – – – + P2 + – + – + – P3 + – – – + + P4 – + + + – – P5 – + – + – + P6 – – + + + – P7 – – – + + + P8 P(x+,y+) = P2 +P4

Measuring Along 3 Directions Detector aDetector bProbability (x+ n + y+)(x– n – y–) P1 + + – – – + P2 + – + – + – P3 + – – – + + P4 – + + + – – P5 – + – + – + P6 – – + + + – P7 – – – + + + P8 P(x+,y+) = P2 +P4 P(y+,n+) = P3 + P7

Measuring Along 3 Directions Detector aDetector bProbability (x+ n + y+)(x– n – y–) P1 + + – – – + P2 + – + – + – P3 + – – – + + P4 – + + + – – P5 – + – + – + P6 – – + + + – P7 – – – + + + P8 P(x+,y+) = P2 +P4 P(y+,n+) = P3 + P7 P(x+,n+) = P3 + P4

Measuring Along 3 Directions Detector aDetector bProbability (x+ n + y+)(x– n – y–) P1 + + – – – + P2 + – + – + – P3 + – – – + + P4 – + + + – – P5 – + – + – + P6 – – + + + – P7 – – – + + + P8 P(x+,y+) = P2 +P4 P(y+,n+) = P3 + P7 P(x+,n+) = P3 + P4 so P(x+,y+) + P(y+,n+) ≥ P(x+,n+) Bell’s Inequality

Measuring Along 3 Directions Detector aDetector bProbability (x+ n + y+)(x– n – y–) P1 + + – – – + P2 + – + – + – P3 + – – – + + P4 – + + + – – P5 – + – + – + P6 – – + + + – P7 – – – + + + P8 P(x+,y+) = P2 +P4 P(y+,n+) = P3 + P7 P(x+,n+) = P3 + P4 so P(x+,y+) + P(y+,n+) ≥ P(x+,n+) Bell’s Inequality Bell’s must be true if LHV exists

SO WHAT’S THE PROBLEM? So Bell’s inequality must hold if we are to have one of these “it’s all built in (like classical correlations) but we just can’t see it yet” type of models that Einstein wanted. But (for n along some directions) the quantum calculation violates Bell’s inequality. Therefore, they can’t both be right (incompatable). So do experiments => quantum wins every time. These quantum correlations are NOT classical. “They break the rules.”

What the Engineers do with Entangled Photons

SO WHAT’S THE PROBLEM? So Bell’s inequality must hold if we are to have one of these “it’s all built in (like classical correlations) but we just can’t see it yet” type of models that Einstein wanted. But (for n along some directions) the quantum calculation violates Bell’s inequality. Therefore, they can’t both be right (incompatable). So do experiments => quantum wins every time. These quantum correlations are NOT classical. “They break the rules.”

THAT’S NOT A PROBLEM that’s a solution!! Quantum computers also break the rules. They do the “impossible,” such as break encryption codes in minutes that would take thousands of years on a supercomputer. This threatens all aspects of computer security. Quantum correlations to the rescue!! In quantum encryption the security is based on the laws of physics, rather than computation time, thereby restoring security.

The oft ignored, but amazing XOR A BXOR 0 0 0 0 1 1 10 1 1 1 0 A BXOR 0 0 0 0 1 1 10 1 1 1 0 } A=0 pass B } A=1 invert B } A≠B send 1 (A=B send 0) XOR as a correlator XOR as a controlled inverter

ASIDE A BXOR 0 0 0 0 1 1 10 1 1 1 0 SOP rep. of XOR 0 10 1 01 0 1 A B AXB = AB’+A’B 0

ASIDE A BXOR 0 0 0 0 1 1 10 1 1 1 0 SOP rep. of XOR 0 10 1 01 0 1 A B AXB = AB’+A’B 0 and POS rep. via DeMorgan’s thrm… “Dan’s thrm”

ASIDE A BXOR 0 0 0 0 1 1 10 1 1 1 0 but what’s the XOR rep. of NAND…? SOP rep. of XOR 0 10 1 01 0 1 A B AXB = AB’+A’B 0 and POS rep. via DeMorgan’s thrm… “Dan’s thrm”

ASIDE A BXOR 0 0 0 0 1 1 10 1 1 1 0 A B AB A+B 0 0 0 1 10 0 1 1 1 but what’s the XOR rep. of NAND…? SOP rep. of XOR 0 10 1 01 0 1 A B AXB = AB’+A’B 0 and POS rep. via DeMorgan’s thrm… “Dan’s thrm” notice: and/or point at one makes it easy to implement arbitrary function from table

END OF THE ASIDE A BXOR 0 0 0 0 1 1 10 1 1 1 0 } A=0 pass B } A=1 invert B The XOR as a controlled inverter means that we can use it to scramble/encrypt a bit stream… and then use it to de-scramble/un-encrypt the scrambled bits back into the original stream… if both XOR gates share the same encryption key…

When Transmitter and Receiver know the same key:

How to Safely Distribute the Key? Essential ingredient #1: –no “quantum cloning” (you can clone a sheep, but you can’t clone a photon) Essential ingredient #2: –you measure it => you change it (1/2 the time) initial state = y+state = x+state = x– measure along x, get => or

Quantum Key Distribution (QKD) i.e., A sends x+, x–, y+, or y– (spin1/2 vs spin 1 … angles differ by 2) i.e., B measures along x or y if B’s basis was not same one that A used, then both throw away this bit.

Quantum Key Distribution (QKD) notice that B announces his basis AFTER his measurement if he announced it BEFORE his measurement, then Eve could use the same basis and go undetected. notice also that EVE can’t store these up and look at them later, because she can’t copy them in the first place (no-cloning)

ISSUES OF TECHNOLOGY (Note: this part is outdated now)

LASER SOURCES within each pulse (of chosen polarization) there should only be one photon –otherwise Eve could steal one !! so “single photon” sources are desired we don’t have any, so we approximate: –weak laser still Poisson, but @ P(1) ~.1 then P(2) ~.005 –entangled photon source, gating detector

WEAK LASER SOURCES @ P(1) ~.1 (1/10 th of a photon per T) –dark current a problem –low data rate with P(2) ~.005 –“Eve’s dropping” error 5% –a BER of 5x10^(-2) is horrible by telecom standards

ENTANGLED PHOTON SOURCES Parametric Down-conversion –one pump photon @ f comes in –two correlated photons each @f/2 come out Still pumped with weak laser (not 1 photon) –so multiple photon pairs can still come out –but can mitigate dark current problems –gate B’s detector only when A saw one too Still low data rates

ENTANGLED PHOTON SOURCES Once the realm of only the best research labs These are now being generated in undergraduate physics labs !! Rather than testing LHV/Bell…put the tech. spin on it for undergraduate eng. technology labs !! –NIST is doing it (IST labs) –LANL wants it to happen Technological advances make it affordable –5mW violet (400nm) laser diodes for pump –puts us at 800nm where commercial Si APD photoncounting modules exist

DETECTORS Commercial single-photon counting modules employing Si APDs at 800nm –High efficiency (50%) –Low dark current –But fiber losses at 800nm are 2dB/km at 1330nm, where fiber loss is.35dB/km –No commercial modules –Cooled InGaAs APDs built in lab (10% efficiency) at 1550nm, where fiber loss is.2dB/km –No commercial modules –Cooled InGaAs APDs built in lab (2% efficiency)

ISSUES OF TECHNOLOGY Better sources !! Better detectors !!

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