PUZZLE #4026: BB84 Quantum Key Distribution (diff 4)

bb84 learn difficulty: 4/7 reason author: system unsolved

240 qubits exchanged. Alice's and Bob's bases are given. Extract the sifted key to recover the 6-letter word.

DATA

Alice Bases	1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0
Bob Bases	0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0
Bob Results	0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0
Total Bits	`240`
Sifted Positions Sample	`3, 4, 9, 12, 15, 17, 18, 19, 20, 21`
Hint	`Identify positions where Alice's basis == Bob's basis. For each matching position i, that bit corresponds to answer bit (i mod 48). Collect all 48 answer bits, then group into 8-bit bytes and convert to ASCII characters.`
Answer Format	`lowercase letters, no spaces or punctuation`

{
  "type": "bb84",
  "alice_bases": [
    1,
    1,
    0,
    0,
    1,
    1,
    1,
    1,
    0,
    1,
    1,
    1,
    1,
    1,
    1,
    1,
    0,
    1,
    0,
    1,
    0,
    1,
    0,
    1,
    0,
    0,
    1,
    1,
    1,
    0,
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    1,
    1,
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    0,
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    1,
    0,
    0,
    0,
    0,
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    1,
    0,
    0,
    0,
    1,
    1,
    1,
    1,
    0,
    0,
    0,
    0,
    0,
    0,
    1,
    0,
    0,
    1,
    1,
    1,
    0,
    1,
    1,
    1,
    1,
    1,
    1,
    1,
    1,
    1,
    0,
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    1,
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    0,
    1,
    1,
    1,
    1,
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    0,
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    0,
    1,
    1,
    1,
    0,
    1,
    1,
    1,
    0,
    1,
    1,
    0,
    1,
    0,
    1,
    0
  ],
  "bob_bases": [
    0,
    0,
    1,
    0,
    1,
    0,
    0,
    0,
    1,
    1,
    0,
    0,
    1,
    0,
    0,
    1,
    1,
    1,
    0,
    1,
    0,
    1,
    1,
    1,
    0,
    0,
    0,
    0,
    1,
    0,
    0,
    1,
    1,
    1,
    1,
    0,
    1,
    1,
    0,
    1,
    1,
    0,
    0,
    1,
    0,
    1,
    0,
    0,
    1,
    0,
    1,
    0,
    0,
    0,
    0,
    1,
    0,
    0,
    0,
    1,
    0,
    0,
    0,
    1,
    0,
    1,
    0,
    1,
    0,
    1,
    1,
    0,
    0,
    1,
    1,
    1,
    0,
    0,
    1,
    1,
    0,
    0,
    0,
    0,
    0,
    1,
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    1,
    1,
    0,
    0,
    1,
    0,
    0,
    1,
    1,
    0,
    1,
    0,
    1,
    1,
    1,
    1,
    1,
    1,
    0,
    0,
    1,
    1,
    0,
    1,
    1,
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    1,
    0,
    1,
    1,
    0,
    0,
    1,
    1,
    1,
    0,
    1,
    0,
    0,
    1,
    0,
    1,
    0,
    0,
    0,
    0,
    1,
    1,
    0,
    0,
    0,
    1,
    1,
    1,
    0,
    0,
    1,
    0,
    0,
    1,
    1,
    1,
    1,
    0,
    0,
    1,
    0,
    1,
    0,
    0,
    1,
    0,
    1,
    1,
    0,
    1,
    1,
    0,
    0,
    1,
    0,
    0,
    1,
    1,
    0,
    1,
    0,
    1,
    0,
    1,
    0,
    1,
    1,
    1,
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    1,
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    1,
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    1,
    1,
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    0,
    1,
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    1,
    1,
    1,
    1,
    1,
    1,
    1,
    1,
    1,
    0,
    1,
    0,
    0,
    1,
    0,
    1,
    1,
    0,
    0,
    0,
    0,
    0,
    1,
    0,
    0,
    0,
    0,
    1,
    1,
    1,
    1,
    0,
    0
  ],
  "bob_results": [
    0,
    0,
    0,
    1,
    0,
    1,
    0,
    1,
    0,
    1,
    0,
    1,
    1,
    0,
    0,
    0,
    0,
    1,
    0,
    0,
    1,
    0,
    0,
    0,
    0,
    1,
    0,
    0,
    0,
    1,
    1,
    1,
    0,
    1,
    0,
    0,
    1,
    0,
    1,
    0,
    0,
    1,
    0,
    1,
    1,
    0,
    0,
    0,
    1,
    1,
    0,
    1,
    0,
    1,
    1,
    1,
    0,
    0,
    0,
    0,
    1,
    1,
    1,
    0,
    0,
    1,
    0,
    1,
    1,
    1,
    0,
    0,
    0,
    1,
    0,
    1,
    1,
    1,
    1,
    1,
    1,
    1,
    1,
    0,
    1,
    1,
    0,
    1,
    0,
    1,
    0,
    0,
    1,
    0,
    1,
    1,
    0,
    0,
    0,
    0,
    0,
    1,
    0,
    0,
    1,
    1,
    0,
    0,
    1,
    0,
    0,
    0,
    0,
    1,
    0,
    0,
    1,
    0,
    0,
    0,
    0,
    0,
    0,
    1,
    1,
    1,
    1,
    1,
    0,
    1,
    0,
    1,
    1,
    1,
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    0,
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    0,
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    1,
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    1,
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    1,
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    1,
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    1,
    0,
    0,
    0,
    0,
    0,
    0,
    1,
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    1,
    1,
    1,
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    1,
    0,
    1,
    1,
    0,
    0,
    0,
    0,
    0,
    0,
    1,
    1,
    0,
    0,
    0,
    0,
    1,
    0,
    1,
    0,
    1,
    0,
    1,
    0,
    0,
    0,
    0,
    1,
    1,
    0,
    1,
    0,
    1,
    0,
    1,
    1,
    1,
    0,
    0
  ],
  "total_bits": 240,
  "sifted_positions_sample": [
    3,
    4,
    9,
    12,
    15,
    17,
    18,
    19,
    20,
    21
  ],
  "hint": "Identify positions where Alice's basis == Bob's basis. For each matching position i, that bit corresponds to answer bit (i mod 48). Collect all 48 answer bits, then group into 8-bit bytes and convert to ASCII characters.",
  "answer_format": "lowercase letters, no spaces or punctuation"
}

author's note: Pool fill: bb84 diff 4