BB84 Quantum Key Distribution

Buffalo Astronomical Association · Hands-on outreach worksheet

Instructions

This packet lets two players (Alice and Bob) run the BB84 protocol with dice and pen-and-paper. After enough rounds, they encrypt a short message with their shared secret key.

What you need

One red 6-sided die (for choosing the basis: + or ×)
One black 8-sided die (for Alice's bits: 0 or 1)
The bench setup: laser, Alice's λ/2 plate, free-space link, Bob's λ/2 plate, PBS, two detectors
Two worksheets (Alice's and Bob's) plus the Sifting & Encryption sheet

Dice conventions

Red d6 (basis)	odd (1,3,5) → + basis	even (2,4,6) → × basis
Black d8 (bit)	1–4 → bit 0	5–8 → bit 1

What Alice and Bob each do (per round)

Alice (sender)

Roll red d6 → record basis (+ or ×)
Roll black d8 → record bit (0 or 1)
Look up the λ/2 angle below and set the waveplate
Fire the laser. Bob takes his reading.

Bob (receiver)

Roll red d6 → record basis (+ or ×)
Set his λ/2 to the angle for that basis
Watch which detector fires:
det 0 → bit 0 · det 1 → bit 1
Record the bit on his sheet

λ/2 plate angles to set

Alice

Basis	Bit	Output polarization	λ/2 physical angle
+	0	0° (horizontal)	0°
+	1	90° (vertical)	45°
×	0	−45°	−22.5°
×	1	+45°	+22.5°

A λ/2 plate rotates polarization by 2× its physical angle, which is why each setting is half of the target.

Bob

Basis	λ/2 physical angle	Effect
+	0°	PBS already analyzes H vs V — no rotation
×	22.5°	Rotates ±45° back to 0°/90° so PBS reads it

Bob doesn't choose a bit — the detectors decide. det 0 fires → bit 0, det 1 fires → bit 1.

Polarization quick reference

+ · bit 0
0°

+ · bit 1
90°

× · bit 0
−45°

× · bit 1
+45°

5-bit alphabet (for encryption)

A	00000	B	00001	C	00010	D	00011	E	00100	F	00101	G	00110
H	00111	I	01000	J	01001	K	01010	L	01011	M	01100	N	01101
O	01110	P	01111	Q	10000	R	10001	S	10010	T	10011	U	10100
V	10101	W	10110	X	10111	Y	11000	Z	11001

After the rounds: sifting & encryption

Alice and Bob compare their bases publicly (round by round). Keep rounds where the bases match; cross out rounds where they differ.
The kept bits form the sifted key — Alice's and Bob's should agree (in a clean channel they do).
Encode the message in 5-bit binary using the alphabet table.
XOR (binary add) the message with the key, bit by bit: 0+0=0, 0+1=1, 1+0=1, 1+1=0.
Bob decrypts the same way: ciphertext XOR key → original message.

Binary XOR rules: 0⊕0=0 · 0⊕1=1 · 1⊕0=1 · 1⊕1=0

Alice's worksheet

Record your dice rolls, set the λ/2 angle, fire the laser.

ALICE

Reminder. Roll the red d6 to pick a basis (odd → +, even → ×). Roll the black d8 to pick a bit (1–4 → 0, 5–8 → 1). Set your λ/2 to the angle in the rightmost column, then signal Bob.

#	Red d6 (1–6)	Basis + or ×	Black d8 (1–8)	Bit 0 or 1	λ/2 angle 0° / 45° / −22.5° / +22.5°	Notes
1	3	+	7	1	45°	(example row)
2	4	×	2	0	−22.5°	(example row)
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30

Quick reference: +·0 → 0° · +·1 → 45° · ×·0 → −22.5° · ×·1 → +22.5°

Bob's worksheet

Roll for a basis, set your λ/2, see which detector fires.

BOB

Reminder. Roll the red d6 to pick a basis (odd → +, even → ×). Set your λ/2 to 0° for +, or 22.5° for ×. When Alice fires the laser, see which detector goes off: det 0 → bit 0, det 1 → bit 1.

#	Red d6 (1–6)	Basis + or ×	λ/2 angle 0° or 22.5°	Detector det 0 or det 1	Bit 0 or 1	Notes
1	2	×	22.5°	det 1	1	(example row)
2	5	+	0°	det 0	0	(example row)
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30

Reminder: + basis → λ/2 at 0° · × basis → λ/2 at 22.5°. The detector that fires tells you the bit.

Sifting & encryption

Compare bases publicly, build the sifted key, encrypt the message.

BOTH

Step 1 — Public basis comparison

Copy each round's basis and bit from Alice's and Bob's worksheets. Mark "keep" (✓) if Alice and Bob used the same basis, "discard" (✗) otherwise.

#	Alice basis	Alice bit	Bob basis	Bob bit	Same? ✓ / ✗	#
1	+	1	+	1	✓	16
2	×	0	+	1	✗	17
3						18
4						19
5						20
6						21
7						22
8						23
9						24
10						25
11						26
12						27
13						28
14						29
15						30

Step 2 — Sifted key

Write Alice's bits from the kept (✓) rounds, in order, in the cells below. This is the shared secret key (Bob's bits in those same rounds should match).

Sifted key

Step 3 — Encode the message

Write the message letter-by-letter, then encode each letter in 5 bits using the alphabet table.

Letter

Data bit

Key bit (⊕)

Ciphertext

XOR rules: 0⊕0=0 · 0⊕1=1 · 1⊕0=1 · 1⊕1=0

Step 4 — Decrypt (Bob)

Bob XORs the ciphertext with his copy of the key, then looks up each 5-bit chunk in the alphabet table.

Ciphertext

Key bit (⊕)

Decoded bit

Letter

If Alice and Bob used a clean channel, the decoded message should match the original. If an eavesdropper was intercepting, ~25% of same-basis bits will disagree → the decoded message will be garbled.

#	Alice basis	Alice bit	Bob basis	Bob bit	Same? ✓ / ✗	#
1	+	1	+	1	✓	16
2	×	0	+	1	✗	17
3						18
4						19
5						20
6						21
7						22
8						23
9						24
10						25
11						26
12						27
13						28
14						29
15						30

#	Alice basis	Alice bit	Bob basis	Bob bit	Same? ✓ / ✗	#
1	+	1	+	1	✓	16
2	×	0	+	1	✗	17
3						18
4						19
5						20
6						21
7						22
8						23
9						24
10						25
11						26
12						27
13						28
14						29
15						30

#	Alice basis	Alice bit	Bob basis	Bob bit	Same? ✓ / ✗	#
1	+	1	+	1	✓	16
2	×	0	+	1	✗	17
3						18
4						19
5						20
6						21
7						22
8						23
9						24
10						25
11						26
12						27
13						28
14						29
15						30