Simple Proof of Security of the BB84 Quantum Key Distribution Protocol

John Preskill (Caltech); Peter W. Shor (AT&T Labs Research)

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Simple Proof of Security of the BB84 Quantum Key Distribution Protocol

Peter W. Shor (AT&T Labs Research), John Preskill (Caltech)

Quantum Physics · Submitted 1 Mar 2000

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We prove the security of the 1984 protocol of Bennett and Brassard (BB84) for quantum key distribution.

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arXiv IDquant-ph/0003004 (version 2)

Pith IDDDFFMRJW, Pith's permanent record of this paper and its review

CitationJohn Preskill (Caltech), Peter W. Shor (AT&T Labs Research). "Simple Proof of Security of the BB84 Quantum Key Distribution Protocol." arXiv:quant-ph/0003004 (2000). https://pith.science/paper/DDFFMRJW

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What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.08 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.73 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We prove the security of the 1984 protocol of Bennett and Brassard (BB84) for quantum key distribution. We first give a key distribution protocol based on entanglement purification, which can be proven secure using methods from Lo and Chau's proof of security for a similar protocol. We then show that the security of this protocol implies the security of BB84. The entanglement-purification based protocol uses Calderbank-Shor-Steane (CSS) codes, and properties of these codes are used to remove the use of quantum computation from the Lo-Chau protocol.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We prove the security of the 1984 protocol of Bennett and Brassard (BB84) for quantum key distribution.	contribution 0.84	0.95	0.94	asserted 1.00
s1	We first give a key distribution protocol based on entanglement purification, which can be proven secure using methods from Lo and Chau's proof of security for a similar protocol.	method 0.59	0.88	0.05	asserted 0.94
s2	We then show that the security of this protocol implies the security of BB84.	result 0.35	0.92	0.24	asserted 1.00
s3	The entanglement-purification based protocol uses Calderbank-Shor-Steane (CSS) codes, and properties of these codes are used to remove the use of quantum computation from the Lo-Chau protocol.	method 0.94	0.84	0.05	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

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P abstract

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S sections
T body sentences
C citations
R cross-paper relations

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The paper

Original abstract

We prove the security of the 1984 protocol of Bennett and Brassard (BB84) for quantum key distribution. We first give a key distribution protocol based on entanglement purification, which can be proven secure using methods from Lo and Chau's proof of security for a similar protocol. We then show that the security of this protocol implies the security of BB84. The entanglement-purification based protocol uses Calderbank-Shor-Steane (CSS) codes, and properties of these codes are used to remove the use of quantum computation from the Lo-Chau protocol.

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References

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Entropy accumulation
quant-ph 2016-07 accept novelty 8.0 of 10

The smooth min-entropy of a correlated n-partite quantum system is bounded below by the sum of conditional von Neumann entropies of its parts, up to a square-root correction, without any independence assumption.
Learnt Attacks on Quantum Key Distribution under Channel Noise and Device Drift
quant-ph 2026-10 conditional novelty 7.0 of 10

Adaptive eavesdropping under device drift is formulated as a constrained Markov decision process over libraries of jointly searched attack circuits, with the value of adaptation bounded between fixed play and a dynami...
Optimal fidelity estimation when one state is pure via algorithmic Uhlmann transform
quant-ph 2026-08 accept novelty 6.0 of 10

When at least one of two quantum states is pure, the Uhlmann fidelity can be estimated with Θ(1/ε) queries and Θ(1/ε²) samples without knowing which state is pure, matching the optimal lower bounds.

How later papers used it

251 later papers cite it

Evidence: substantial. 251 of the citing papers share no author with it, and 41 of those carry a confident label from Pith's citation classifier.

Pith read 39 of the 409 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

8 later papers by other authors are listed below: 3 used its method or tool, 2 used its data or values and 3 compared their own results with it.

Uses its method or tool 3 of 17 papers with this label

Here, we follow the idea of the Shor-Preskill security proof to reduce phase-error correction into classical privacy amplification [ref] .

Stream privacy amplification for quantum cryptography (2021) · Reduction from quantum operations to classical ones · 0.98
Finally, in Sec. [ref], we reduce the entanglement-based scheme to the prepare-and-measure one in the main text via the Shor-Preskill argument [ref] .

Quantum key distribution surpassing the repeaterless rate-transmittance bound without global phase locking (2022) · Security of mode-pairing scheme · 0.98
Following the Shor-Preskill security argument, gave the key rate of the PM-QKD protocol for the sifted signals.

Phase-Matching Quantum Key Distribution (2018) · 0.88 · paraphrased: the licence does not allow quoting

Uses its data or values 2 of 6 papers with this label

The theoretical maximum QBER to still extract key is 11 $%$ [ref] ; we chose an LDPC matrix for $≤$ 4% as a compromise between correction efficiency and demands on polarization control.

Deployment of Entanglement-Based QKD in Financial Infrastructure (2026) · Performance evaluation · 0.94
Defined its weights using the BB84 security threshold of 0.011, adjusted for practical implementation losses.

Enhancing Satellite Quantum Key Distribution with Dual Band Reconfigurable Intelligent Surfaces (2025) · 0.83 · paraphrased: the licence does not allow quoting

Compares with it 3 of 12 papers with this label

Found that its proposed classical processing yields at least as high a key rate as the standard processing by Shor and Preskill for the QKD protocols.

Tomography increases key rates of quantum-key-distribution protocols (2008) · 0.99 · paraphrased: the licence does not allow quoting
Pointed out that reverse reconciliation often gives a different amount of secret key than direct reconciliation over Pauli channels with its modified protocol, contrasting with the standard BB84 protocol.

Narrow basis angle doubles secret key in the BB84 protocol (2009) · 0.96 · paraphrased: the licence does not allow quoting
Recovered the Shor-Preskill rate for θ = π/2 = 90°, corresponding to an ideal BB84 source.

Tight asymptotic key rate for the BB84 protocol with local randomisation and device imprecisions (2014) · 0.95 · paraphrased: the licence does not allow quoting

How the literature uses it

32 arXiv papers cite this in 64 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 1 paper

This paper provides a security proof of the Bennett-Brassard (BB84) quantum key distribution protocol in practical implementation.

Security proof of practical quantum key distribution schemes · 0.80

Papers citing it · 43 sentences without a confident label

Compares with it 4 papers

Combining the arguments in this section and Remark [ref], we find that our proposed classical processing yields at least as high key rate as the standard processing by Shor and Preskill [ref] for the QKD protocols.

Tomography increases key rates of quantum-key-distribution protocols · Relation to the conventional estimation procedure · 0.99
We have also pointed out that the reverse reconciliation often gives different amount of secret key to the direct reconciliation over Pauli channels with our modified protocol, which is contrasting to the standard BB84 protocol [ref] , and that there is difficulty to use the conventional channel parameter estimation if the angle between two bases is narrower than $π/4$.

Narrow basis angle doubles secret key in the BB84 protocol · Concluding remarks · 0.96
We note that the first-order rate term $I(X;Y)-I(X;E)$ is equal to the known asymptotic key rate for the BB84 protocol and coincides with the result from [ref] .

Second-order coding rates for key distillation in quantum key distribution · BB84 DV-QKD protocol · 0.95

Cites it as background 13 papers

The proofs by Lo and Chau [ref] , Shor and Preskill [ref] and Koashi [ref] are all based on the phase error correction and assume the basis choice to be unknown to Eve.

Security of the decoy-state BB84 protocol with imperfect state preparation · Introduction · 0.95
Conventionally, Alice and Bob discard mismatched measurement outcomes, which are transmitted and received by different bases [ref] .

Secure Key Rate of the BB84 Protocol using Finite Sample Bits · Accurate channel estimation · 0.93
Earlier works, e.g., [ref] , used a notion of security directly inspired from classical cryptography, where key techniques such as advantage distillation, error correction and privacy amplification were developed [ref] .

Security in Quantum Cryptography · Accessible information · 0.89

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