A topic in the Open Knowledge Graph — a free, open map of 15,290 topics and the order to learn them in.

Quantum Key Distribution (BB84)

Research Depth 158 in the knowledge graph I know this Set as goal
1topic build on this
957prerequisites beneath it
See this on the map →
No-Cloning TheoremQuantum Measurement and the Born Rule+1 moreQuantum Communication Networks
BB84 QKD cryptography eavesdropping information-theoretic-security

Core Idea

Quantum key distribution (QKD) enables two parties to establish a shared secret key whose security is guaranteed by the laws of quantum mechanics, not computational hardness assumptions. The BB84 protocol (Bennett-Brassard 1984) works by encoding random bits in one of two conjugate bases (rectilinear or diagonal). An eavesdropper measuring the qubits inevitably disturbs them (by the no-cloning theorem and measurement disturbance), introducing detectable errors. After basis reconciliation and error estimation, the parties distill a secure key. BB84 achieves information-theoretic security — it is provably secure even against adversaries with unlimited computational power, including quantum computers.

Explainer

Classical cryptography faces a fundamental problem: the security of widely used public-key systems (RSA, elliptic curves) rests on assumptions about the computational hardness of certain mathematical problems — assumptions that Shor's algorithm would break. Quantum key distribution offers a qualitatively different kind of security: one based on physics rather than mathematics. The BB84 protocol, proposed by Bennett and Brassard in 1984, uses quantum mechanics to distribute a shared secret key between two parties in a way that any eavesdropping attempt is detectable.

The protocol works as follows. Alice prepares random qubits, each encoding a random bit in a randomly chosen basis: either the Z basis (|0> for 0, |1> for 1) or the X basis (|+> for 0, |-> for 1). She sends these qubits to Bob, who measures each in a randomly chosen basis (Z or X). When their bases match (about 50% of the time), their bit values agree perfectly. When bases mismatch, Bob's result is completely random. Alice and Bob publicly compare their basis choices (not bit values) and keep only the rounds where they used the same basis — this is sifting, producing the raw key.

Eavesdropping detection comes next. Suppose Eve intercepts qubits, measures them, and resends them to Bob (an intercept-resend attack). Eve does not know Alice's basis, so she guesses randomly. When Eve guesses wrong (50% of the time), her measurement disturbs the qubit, and when Bob subsequently measures in Alice's correct basis, he gets a random result instead of Alice's bit. This introduces an error rate of approximately 25% in the sifted key. Alice and Bob sacrifice a random subset of their sifted key bits, compare them publicly, and check the error rate. An error rate significantly above the channel noise threshold indicates eavesdropping, and they abort.

If the error rate is acceptably low, Alice and Bob apply error correction (to fix the remaining errors) and privacy amplification (to eliminate any partial information Eve may have gained). The result is a shorter but provably secure shared secret key. The security proof, formalized by Lo, Chau, Shor, Preskill, and others, shows that any eavesdropping strategy — including sophisticated quantum attacks beyond intercept-resend — is detectable. The proof relies on the no-cloning theorem (Eve cannot copy the qubits and keep them for later analysis) and the information-disturbance tradeoff (gaining information about a quantum state necessarily disturbs it). QKD has been commercially deployed over fiber-optic links and demonstrated via satellite (the Micius experiment), making it the most mature application of quantum information science.

Practice Questions 3 questions

Prerequisite Chain

Understanding ZeroThe Number ZeroCounting to FiveCounting to 10Counting to 20Counting a Set of Objects Up to 20Cardinality: The Last Number CountedMatching Numerals to QuantitiesSubitizing Small QuantitiesAddition Within 10Number Bonds to 10Addition Within 20Doubles and Near DoublesDoubles Facts Within 10Near Doubles Facts Within 20Mental Math Strategies for AdditionMental Math: Adding and Subtracting TensAddition Within 100Repeated Addition as MultiplicationMultiplication as Equal GroupsMultiplication: ArraysBasic Multiplication Facts (0s, 1s, 2s, 5s, 10s)Multiplication Facts Within 100Division as Equal SharingDivision as Grouping (Measurement Division)Division: Grouping (Repeated Subtraction) ModelDivision: Fair Sharing ModelDivision as Equal SharingDivision as GroupingBasic Division FactsDivision Facts Within 100Multiplication and Division Fact FamiliesRelationship Between Multiplication and DivisionDivision Facts as Inverse of MultiplicationRemainders and Quotients in DivisionDivision Word ProblemsMulti-Step Word ProblemsSolving Multi-Step Word ProblemsMultiplication Word ProblemsDivision Word ProblemsIntroduction to Long DivisionFactors and MultiplesPrime and Composite NumbersEquivalent FractionsRelating Fractions and DecimalsDecimal Place ValueIntegers and the Number LineComparing and Ordering IntegersAbsolute ValueAdding IntegersSubtracting IntegersMultiplying IntegersDividing IntegersUnit RatesProportionsPercent ConceptConverting Between Fractions, Decimals, and PercentsOperations with Rational NumbersTwo-Step EquationsSolving Multi-Step EquationsEquations with Variables on Both SidesAngle Pairs: Complementary, Supplementary, and VerticalParallel Lines and TransversalsCorresponding AnglesAlternate Interior AnglesTriangle Angle Sum TheoremExterior Angle TheoremTriangle Inequality TheoremSimilar Triangles: AA SimilaritySimilar Triangles: SSS and SAS SimilarityProportions in Similar TrianglesRight Triangle Trigonometry IntroductionSine, Cosine, and Tangent RatiosTrigonometric Ratios ReviewRadian MeasureConverting Between Degrees and RadiansThe Unit CircleGraphing Sine and CosineGraphing Tangent and Reciprocal Trigonometric FunctionsDerivatives of Trigonometric FunctionsAntiderivativesIndefinite IntegralsBasic Integration RulesRiemann SumsDefinite Integral DefinitionDouble Integrals: Definition and SetupIterated Integrals and Fubini's TheoremDouble Integrals over Rectangular RegionsDouble Integrals over General RegionsApplications of Double Integrals: Area, Mass, and MomentsTriple Integrals in Cartesian CoordinatesTriple Integrals in Cylindrical and Spherical CoordinatesChange of Variables and the Jacobian DeterminantApplications of Triple Integrals: Volume and MassVector Fields and Their RepresentationsLine Integrals of Vector FieldsWork and CirculationLine Integrals of Scalar and Vector FunctionsFundamental Theorem for Line IntegralsConservative Vector FieldsConservative Vector Fields and Potential FunctionsCurl and Divergence of Vector FieldsCurl and DivergenceDivergence TheoremElectric Flux and Divergence TheoremGauss's Law: Integral Form and MeaningSolving Problems with Gauss's LawConductors in Electrostatic EquilibriumCapacitance and CapacitorsDielectricsDielectric Constant and Relative PermittivityElectric Field Inside Dielectric MaterialsDielectric Materials and PolarizationDielectric Susceptibility and PermittivityEnergy Density in Electric FieldsElectric Current and Current DensityElectrical Resistance and ResistivityOhm's Law and Circuit ElementsElectromotive Force (EMF) and BatteriesKirchhoff's Circuit Laws: Voltage and CurrentDC Circuit Network Analysis MethodsTransient Response in RC CircuitsRC CircuitsLC and RLC CircuitsAC Circuits: FundamentalsImpedance and ReactanceAC Power and ResonanceElectromagnetic WavesPostulates of Special RelativityTime DilationLength ContractionLorentz TransformationRelativistic Velocity AdditionRelativistic Momentum and EnergyMass-Energy Equivalence and E=mc²Photons as Particles with Energy and MomentumPlanck-Einstein Relation: Energy and FrequencyPhotoelectric EffectThe Photon: Light as QuantaCompton ScatteringWave-Particle Dualityde Broglie WavelengthThe Schrödinger EquationState Vectors and WavefunctionsQuantum SuperpositionQuantum EntanglementBell Theorem and Bell InequalitiesPostulates of Quantum MechanicsObservables and Quantum OperatorsCommutators and Commutation RelationsQuantum Angular MomentumQuantum Mechanical Treatment of HydrogenSolving the Schrödinger Equation for Hydrogen AtomQuantum NumbersSpin-1/2 SystemsPauli MatricesQuantum GatesNo-Cloning TheoremQuantum Key Distribution (BB84)

Longest path: 159 steps · 957 total prerequisite topics

Prerequisites (3)

Leads To (1)