Quantum Cryptography, Teleportation & Sensing

Copying is the quiet foundation of the information age: files are duplicated constantly, and undersea cables boost their fading light pulses with amplifiers every 50 to 100 kilometres. Quantum information refuses to play along. In October 1982 William Wootters and Wojciech Zurek published a two-page Nature paper with a blunt title, 'A single quantum cannot be cloned', and Dennis Dieks reached the same result independently. The no-cloning theorem states that no physical process can take a system in an arbitrary unknown quantum state, plus a blank system, and leave both in that state.

The proof needs only linearity, the Chapter 10 property that a superposition of inputs evolves into the same superposition of outputs. Suppose a machine copies the basis states perfectly, turning |0⟩ into |0⟩|0⟩ and |1⟩ into |1⟩|1⟩, as the CNOT gate of Chapter 23 does. Feed it |+⟩ = (1/√2)(|0⟩ + |1⟩), and linearity forces the entangled output (1/√2)(|00⟩ + |11⟩), whereas two genuine copies of |+⟩ would be ½(|00⟩ + |01⟩ + |10⟩ + |11⟩). More generally, quantum evolution preserves the overlap s between two states, but copying would turn s into s², and s = s² only when s is 0 or 1. A copier can handle only states that are identical or perfectly distinguishable: classical information.

The theorem forbids less than it seems. You may copy a state you know, by preparing it again, and imperfect copies are allowed: the best universal qubit copier, found by Vladimír Bužek and Mark Hillery in 1996, makes two copies of fidelity 5/6, about 0.83. But three consequences drive this chapter: eavesdroppers cannot copy photons in transit, teleportation must destroy the original state, and quantum signals cannot be amplified without adding noise.

The only cipher proven unbreakable is the one-time pad, which grew out of Gilbert Vernam's 1917 teleprinter cipher and which Claude Shannon proved perfectly secret in 1949: combine the message with a random key as long as itself, use the key once, and the ciphertext reveals nothing. The catch is delivering the key, which the internet does with public-key methods that Shor's algorithm, run on a large enough quantum computer, would crack. Quantum key distribution, or QKD, delivers keys by physics instead. Charles Bennett of IBM and Gilles Brassard of the Université de Montréal presented the first protocol, BB84, in Bangalore, India, in December 1984, building on Stephen Wiesner's earlier idea of uncopyable quantum money.

BB84 reads photon polarisation in two bases. In the rectilinear basis, horizontal means 0 and vertical means 1; in the diagonal basis, 45° means 0 and 135° means 1. For each photon Alice picks a random bit and a random basis; Bob, ignorant of her choices, measures in a random basis of his own. When the bases match he reads her bit with certainty; when they differ, the photon meets his analyser at 45° and the Born rule gives cos²45° = ½, a coin toss. The bases are conjugate, or mutually unbiased: a state certain in one is perfectly random in the other, like spin along z and x in Chapter 17. That incompatibility is the whole defence: with one basis, Eve could read every photon and resend a perfect replacement.

Afterwards, over an ordinary public channel, Bob announces his bases, never his results, and Alice says which matched. They keep those bits, about half; this is sifting, and the survivors form the sifted key. They then sacrifice a random sample to compute the quantum bit error rate, or QBER, the fraction that disagree. Error correction repairs the remaining discrepancies, and privacy amplification, a hashing step that compresses the key, shrinks whatever partial knowledge an eavesdropper holds to essentially nothing. The public channel must also be authenticated, or Eve could impersonate Bob; that needs a short pre-shared secret, so QKD really grows a small shared seed into a long stream of fresh key.

Eve's simplest attack is intercept-resend: she measures each photon in a randomly chosen basis and sends Bob a fresh photon in the state she found. Look only at sifted bits, where Alice and Bob used the same basis. Half the time Eve chose that basis, learned the bit and resent it undisturbed. The other half she chose wrong, so her replacement photon is polarised in the wrong basis and Bob's measurement becomes a coin toss, wrong half the time. One half times one half is a quarter: a full intercept-resend attack stamps a 25 percent error rate on the sifted key, and an Eve who meddles with a fraction f of the photons leaves f/4.

Detection is statistical. Each compared bit exposes a full-time Eve with probability ¼, so she slips past n test bits with probability (3/4)ⁿ: about 0.3 percent for 20 bits, below one in a billion for 73. Copying photons to measure later is no escape; no-cloning forbids it. Since nobody can tell a spy from a dirty connector, Alice and Bob blame every error on Eve, and the security proof Peter Shor and John Preskill published in 2000 shows that ideal single-photon BB84 still yields a secret key for error rates up to about 11 percent. Above that, they abort.

The first prototype, in October 1989, sent a key across 32.5 centimetres of open air. In 2017 Jian-Wei Pan's team used the Chinese satellite Micius to deliver keys across up to 1,200 kilometres and then relayed a key between ground stations in China and Austria, 7,600 kilometres apart. In fibre, a 2023 twin-field experiment reached 1,002 kilometres, at about one secret bit per hundred billion pulses. Yet devices are not theorems: real lasers sometimes emit two photons at once, a leak now plugged with decoy pulses, and in 2010 researchers blinded the detectors of commercial systems with bright light and showed that the key could be stolen without leaving a trace.

In 1993 Charles Bennett, Gilles Brassard, Claude Crépeau, Richard Jozsa, Asher Peres and William Wootters posed a puzzle. Alice holds a qubit in an unknown state α|0⟩ + β|1⟩ and wants distant Bob to have it, but measuring would destroy the amplitudes and copying is forbidden. Their answer, quantum teleportation, uses an entangled pair shared in advance, one half each, plus an ordinary classical channel.

Alice makes a Bell-state measurement, a joint measurement asking which of the four Bell states of Chapter 20 her unknown qubit and her half of the pair are in. The blackboard algebra regroups the three-qubit state into four equally weighted terms, so each outcome has probability ¼ whatever α and β are, and each leaves Bob's qubit as the original state or a version with its sign flipped, its bits flipped, or both. Alice sends two classical bits naming her outcome, and Bob applies the matching gate from Chapter 23: nothing, Z, X, or X then Z. His qubit now holds the original state, while Alice's has lost its amplitudes, so no two copies ever coexist, and Alice never learns α or β.

Three myths fall at once. No matter moves: Bob's particle was already there, and only its state, the pattern of amplitudes, changes. Nothing outruns light: until the two bits arrive, Bob's qubit, averaged over Alice's four equally likely outcomes, is a featureless fifty-fifty mixture with no trace of α or β. And it is no transporter: the original is scrambled, and the destination must already hold the matter.

In December 1997 Anton Zeilinger's group at Innsbruck, with Dik Bouwmeester and Jian-Wei Pan among the authors, teleported a photon's polarisation, and Francesco De Martini's group in Rome soon reported a related experiment. In 2017 Pan's team teleported photon qubits from Ngari in Tibet up to Micius, as far as 1,400 kilometres, with an average fidelity of 0.80 ± 0.01, well above the two-thirds achievable without entanglement.

Shor's algorithm threatens the internet's public-key systems, and two remedies with confusingly similar names answer it. Post-quantum cryptography, or PQC, is classical: ordinary software on ordinary computers, built on mathematical problems believed hard even for quantum computers. In August 2024 the US National Institute of Standards and Technology, NIST, finalised its first three standards: the key-establishment scheme ML-KEM, derived from CRYSTALS-Kyber, and the signature schemes ML-DSA and SLH-DSA; the first two rest on structured lattices, the third on hash functions. In March 2025 it selected HQC, built on error-correcting codes, for standardisation as a backup to ML-KEM. PQC's security is computational: it assumes that no efficient algorithm, classical or quantum, solves these problems, which nobody has proved.

Quantum cryptography, with QKD as its flagship, uses quantum physics itself. Its security rests in principle on no-cloning and measurement disturbance, so it holds even against unlimited computing power, a guarantee called information-theoretic security. The price is steep: dedicated photon sources, detectors and links, range limited by loss, point-to-point operation, a continuing need for authentication, and hardware hardened against side channels. Citing these limits, the US National Security Agency and the UK's National Cyber Security Centre advise against relying on QKD for government systems and favour PQC, while China and European research programmes keep building QKD networks. In short: post-quantum means new mathematics on old hardware; quantum cryptography means new hardware, with physics in place of mathematics.

Everything that makes qubits hard to protect makes them superb sensors: a quantum sensor is a system whose energy levels or phase respond strongly to the quantity being measured, so the sensitivity behind decoherence becomes the signal. The oldest keeps time. Atoms of one isotope are identical, so a transition frequency is a constant of nature. Louis Essen and Jack Parry built the first practical caesium clock at Britain's National Physical Laboratory in 1955, and since 1967 the SI second has been 9,192,631,770 periods of the radiation from a hyperfine transition in caesium-133. The best caesium fountain clocks now reach uncertainties of one or two parts in 10¹⁶.

Optical clocks use transitions near 10¹⁵ hertz, tens of thousands of times faster than caesium's microwave tick, so each cycle slices time more finely. A strontium lattice clock, its atoms held in a lattice of laser light, ticks at 429,228,004,229,873 Hz. In 2024 JILA in Boulder reported a strontium clock with systematic uncertainty 8.1×10⁻¹⁹, and in 2025 NIST reached 5.5×10⁻¹⁹ with one aluminium ion; at 8.1×10⁻¹⁹, a clock started at the Big Bang would now be off by about a third of a second. General relativity makes a clock raised by Δh tick faster by the fraction g·Δh/c², about 1.1×10⁻¹⁶ per metre, and in 2022 JILA resolved this shift across a millimetre-tall cloud of atoms.

Atom interferometers aim the matter waves of Chapter 6 at gravity. In 1991 Mark Kasevich and Steven Chu used laser pulses as beam splitters and mirrors, splitting each falling atom's wavefunction into two paths with one pulse, redirecting the paths with a second pulse after a time T, and recombining them with a third after another T. Gravity shifts the phase difference by k·g·T², where k is the light's effective wavenumber; for rubidium with T = 0.1 seconds that is about 1.6 million radians, so reading the phase to a milliradian fixes g to about six parts in 10¹⁰. With N independent atoms, phase noise falls only as 1/√N, the standard quantum limit; entanglement or squeezing can in principle approach 1/N, the Heisenberg limit.

A SQUID, or superconducting quantum interference device, is a superconducting loop broken by Josephson junctions, the tunnelling barriers of Chapter 12. First built at Ford in 1964, the device gives an output that repeats with every flux quantum threading the loop, h/2e, about 2.07×10⁻¹⁵ webers, and because it resolves a tiny fraction of one quantum, a SQUID cooled by liquid helium detects femtotesla fields, tens of billions of times weaker than Earth's, enough to map the brain's magnetic activity. Nitrogen-vacancy centres, a nitrogen atom beside a missing carbon in diamond, work at room temperature: green light makes them glow more brightly in one spin state, so their spin is read optically, and a magnetic field shifts their 2.87 GHz spin resonance by about 28 GHz per tesla, letting atom-sized sensors map fields inside living cells.

The most famous quantum sensor is a ruler. LIGO's 4-kilometre arms register gravitational waves that change their length by about 4×10⁻¹⁸ metres, a four-hundredth of a proton's width, where light's graininess matters: random photon arrivals blur the phase reading and random photon kicks jostle the mirrors. In 1981 Carlton Caves traced this noise to vacuum fluctuations leaking into the interferometer and proposed injecting squeezed light, whose phase uncertainty is pushed below the vacuum level while its amplitude uncertainty grows. LIGO has done so since 2019, cutting high-frequency noise by up to 3 decibels, and since 2023 its 300-metre filter cavities have spread the benefit across the band, raising the expected detection rate by up to 65 percent.

Telecom fibre loses about 0.2 decibels per kilometre, so the surviving fraction of photons falls exponentially: one percent after 100 kilometres, 10⁻²⁰ after 1,000. Classical networks rescue fading signals with amplifiers, but a perfect amplifier would be a copier, which no-cloning outlaws, and any real one adds noise that swamps single-photon signals. Today's long links therefore use trusted nodes, relay stations that decrypt and re-encrypt the key and must be physically guarded, as on China's 2,000-kilometre backbone from Beijing to Shanghai, opened in 2017, or satellites like Micius, whose path is mostly absorption-free vacuum.

The real fix is the quantum repeater, proposed in 1998 by Hans Briegel, Wolfgang Dür, Ignacio Cirac and Peter Zoller. Divide the distance into short links, entangle each, store the halves in quantum memories, and join the links by entanglement swapping, teleportation applied to entanglement itself: a Bell measurement on halves of two different pairs at a middle node leaves the far ends entangled although they never met. Purification distils good pairs from noisy ones, and end-to-end entanglement then lets teleportation carry any qubit across.

As of 2026 quantum networks are few-node testbeds. In 2022 Ronald Hanson's team at Delft teleported a qubit between non-neighbouring nodes of a three-node network of nitrogen-vacancy centres, and in 2024 a Harvard team entangled two quantum memories across 35 kilometres of deployed fibre around Boston. A full quantum internet would deliver entanglement on demand between any two points, enabling Bell-certified key distribution, linked quantum processors, blind computing on servers that cannot see your data, and networks of entangled clocks and telescopes. Continent-spanning repeater chains remain a goal, not a result.