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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”
  AB AB
A
B
If measure along same axis
perfectly anticorrelated
If measure along different
axis
no correlation
Unsophisticated Candy Machine
measures size or magnetic – not both
F
C
magnetic (x+)
Q
N
non-magnetic (x-)
F = Franc
C = Canadian nickel
big
(y+)
non-big
(y-)
Q = US quarter
N = US nickel
As a Table
F
C
magnetic (x+)
Q
N
non-magnetic (x–)
big
(y+)
non-big
(y–)
There is no EPR “paradox.”
Detector a
Detector 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+)
Measuring Along 3 Directions
Detector a
(x+ n + y+)
+ + –
+ – +
+ – –
– + +
– + –
– – +
– – –
Detector b
(x– n – y–)
– – +
– + –
– + +
+ – –
+ – +
+ + –
+ + +
Probability
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 a
(x+ n + y+)
+ + –
+ – +
+ – –
– + +
– + –
– – +
– – –
Detector b
(x– n – y–)
– – +
– + –
– + +
+ – –
+ – +
+ + –
+ + +
P(x+,y+) = P2 +P4
Probability
P1
P2
P3
P4
P5
P6
P7
P8
Measuring Along 3 Directions
Detector a
(x+ n + y+)
+ + –
+ – +
+ – –
– + +
– + –
– – +
– – –
Detector b
(x– n – y–)
– – +
– + –
– + +
+ – –
+ – +
+ + –
+ + +
P(x+,y+) = P2 +P4
Probability
P1
P2
P3
P4
P5
P6
P7
P8
P(y+,n+) = P3 + P7
Measuring Along 3 Directions
Detector a
(x+ n + y+)
+ + –
+ – +
+ – –
– + +
– + –
– – +
– – –
Detector b
(x– n – y–)
– – +
– + –
– + +
+ – –
+ – +
+ + –
+ + +
P(x+,y+) = P2 +P4
Probability
P1
P2
P3
P4
P5
P6
P7
P8
P(y+,n+) = P3 + P7
P(x+,n+) = P3 + P4
Measuring Along 3 Directions
Detector a
(x+ n + y+)
+ + –
+ – +
+ – –
– + +
– + –
– – +
– – –
Detector b
(x– n – y–)
– – +
– + –
– + +
+ – –
+ – +
+ + –
+ + +
P(x+,y+) = P2 +P4
Probability
P1
P2
P3
P4
P5
P6
P7
P8
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 a
(x+ n + y+)
+ + –
+ – +
+ – –
– + +
– + –
– – +
– – –
Detector b
(x– n – y–)
– – +
– + –
– + +
+ – –
+ – +
+ + –
+ + +
P(x+,y+) = P2 +P4
Probability
P1
P2
P3
P4
P5
P6
P7
P8
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
XOR as a controlled inverter
A
0
0
1
1
B
0
1
0
1
XOR
0
1
1
0
} A=0
pass B
} A=1 invert B
XOR as a correlator
A
0
0
1
1
B
0
1
0
1
XOR
0
1
1
0
} A≠B send 1
(A=B send 0)
ASIDE
A
0
0
1
1
B
0
1
0
1
XOR
0
1
1
0
SOP rep. of XOR
A
0
1
B
0
0
1
1
1
0
0
AXB = AB’+A’B
ASIDE
A
0
0
1
1
B
0
1
0
1
XOR
0
1
1
0
SOP rep. of XOR
A
0
1
B
0
0
1
1
1
0
0
AXB = AB’+A’B “Dan’s thrm”
and POS rep. via DeMorgan’s thrm…
ASIDE
A
0
0
1
1
B
0
1
0
1
SOP rep. of XOR
A
0
1
B
XOR
0
1
1
0
0
0
1
1
1
0
0
AXB = AB’+A’B “Dan’s thrm”
and POS rep. via DeMorgan’s thrm…
but what’s the XOR rep. of NAND…?
ASIDE
A
0
0
1
1
B
0
1
0
1
SOP rep. of XOR
A
0
1
B
XOR
0
1
1
0
0
0
1
1
1
0
0
AXB = AB’+A’B “Dan’s thrm”
and POS rep. via DeMorgan’s thrm…
but what’s the XOR rep. of NAND…?
A
0
0
1
1
B
0
1
0
1
AB A+B
0
0
0
1
0
1
1
1
notice: and/or point at one
makes it easy to implement
arbitrary function from table
END OF THE ASIDE
The XOR as a controlled inverter
A
0
0
1
1
B
0
1
0
1
XOR
0
1
1
0
} A=0
pass B
} A=1 invert B
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)
or
measure along x, get =>
initial state = y+
state = x+
state = x–
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 (1/10th 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 !!