quantum key distribution

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Quantum key distribution (QKD) is a method of generating a shared secret key whose security is based on the laws of quantum mechanics rather than computational complexity. The BB84 protocol uses four photon states grouped into two non-orthogonal bases (rectilinear and diagonal). Non-orthogonal states cannot be distinguished with certainty, so interception introduces errors. After transmission, the parties perform bit reconciliation and privacy amplification to eliminate information leakage. Today, systems operate over optical fiber for distances up to hundreds of kilometers, and satellite communication extends the range to thousands.

History

In the 1970s, Stephen Wiesner proposed the idea of quantum money that cannot be counterfeited. Quantum cryptography gained widespread recognition in 1984 after Charles Bennett and Gilles Brassard published the BB84 protocol.

How it works

An analogy with two alphabets: one uses dots and dashes (vertical/horizontal polarization), the other uses zigzags (diagonal directions). Alice writes a bit with a random alphabet, and Bob reads it, also choosing an alphabet at random. If the alphabets match, the result is correct; if not, a random value is obtained. Then they exchange information about the chosen alphabets for each sent symbol, keeping bits only for cases of matching. Eve, not knowing the alphabet, disturbs the transmitted states, and her interference manifests as additional errors during verification.

💡 The first bank transfer protected by a quantum key took place in 2004 in Vienna; now quantum networks connect entire cities.

Quantum key distribution is a cryptographic primitive that generates a key through the exchange of quantum states and guarantees unconditional security. Secrecy relies on the uncertainty principle: an eavesdropper cannot reliably distinguish non-orthogonal states, such as a photon with polarization 0° and 45°, without introducing errors when the basis is mismatched. In the BB84 protocol, Alice randomly selects a bit and a basis, sending one of four states; Bob measures in a random basis. After the sifting stage, bits with matching bases form the raw key. Estimating the quantum bit error rate (QBER) by sacrificing a portion of bits gives an upper bound on Eve’s information; if QBER is below the threshold, error correction and privacy amplification are performed to obtain the final key. Entanglement-based protocols (E91) verify the violation of Bell's inequality. The decoy state method protects against attacks on weakened laser pulses.

History

Quantum cryptography traces its origins to the concept of quantum money proposed by Stephen Wiesner in 1970 (published in 1983). In 1984, Charles Bennett and Gilles Brassard introduced the BB84 protocol, which became a turning point. In 1991, Artur Ekert proposed the E91 protocol based on entangled particles, opening up prospects for satellite communication. Today, QKD is a commercial technology with deployed networks.

How it works

The security of QKD stems from the disturbance of quantum states upon measurement (wavefunction collapse). If Eve guesses the basis, she introduces no errors, but she cannot guess correctly every time. For BB84, secure key extraction is possible when the quantum error rate e < 11%. Mathematically, after error correction and privacy amplification, the length of the final key is L = n·r, where n is the raw key size, r = 1 − h(e_x) − h(e_z) (asymptotic limit), h is binary entropy, and e_x, e_z are errors in the bases. Practical limitations include losses and detector noise.

r = 1 - h(e_x) - h(e_z)

r — fraction of bits that become secret key (dimensionless, 0 to 1); h(p) = -p \log_2 p - (1-p) \log_2 (1-p) — binary entropy; e_x, e_z — error probabilities in the X- and Z-bases, respectively (dimensionless, 0 to 0.5)

Open problems & fun facts

Range without quantum repeaters is limited by attenuation in optical fiber (≈100–200 km); Vulnerabilities of real detectors (side-channel attacks, blinding); Low key generation rate compared to classical methods; Integration into existing network infrastructures and high cost

💡 The Micius satellite, launched in 2016, enabled the first intercontinental QKD between China and Europe using entangled photons from orbit.

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quantum key distribution

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How it works

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How it works

History

How it works

Open problems & fun facts

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