Beyond key distribution
Quantum communication transmits quantum states or uses entanglement between distant parties. QKD is only one application. Others include teleporting qubits, connecting quantum computers, distributed sensing and clock synchronisation, blind and secure delegated computation, and secure identification.
Superdense coding
Alice and Bob share $|\Phi^+\rangle$. To send two classical bits Alice applies $I$, $X$, $Z$ or $XZ$ to her qubit, turning the pair into one of the four orthogonal Bell states, then sends her single qubit. Bob performs a Bell measurement on both qubits and recovers both bits. Entanglement doubles the classical capacity of a noiseless qubit channel. Without shared entanglement, the Holevo bound allows only one bit per qubit.
Quantum teleportation
Alice holds an unknown qubit $|\psi\rangle_C=\alpha|0\rangle+\beta|1\rangle$ and shares $|\Phi^+\rangle_{AB}$ with Bob. Rewriting the joint state in the Bell basis of $C$ and $A$,
Alice’s Bell measurement yields one of four equally likely outcomes. She sends the two classical bits to Bob, who applies $\sigma_k$ to recover $|\psi\rangle$. Teleportation does not clone (Alice’s qubit is destroyed) and does not signal faster than light (the classical message is required). First demonstrated in 1997; satellite-to-ground teleportation over ~1400 km was reported in 2017.
Entanglement swapping and purification
Swapping. Given pairs $A$–$B_1$ and $B_2$–$C$, a Bell measurement on $B_1B_2$ projects $A$ and $C$ into an entangled state, though they never interacted. This is how a repeater chain extends entanglement. Purification (distillation). Several noisy pairs are converted by local operations and classical communication (LOCC) into fewer higher-fidelity pairs. The central cost is the exponential photon loss, which cannot be fixed by amplification because amplification would violate no-cloning.
The repeaterless bound (PLOB)
For a pure-loss bosonic channel with transmittance $\eta$, the maximum secret-key rate achievable without repeaters is (Pirandola, Laurenza, Ottaviani, Banchi 2017)
bits per channel use. At 0.2 dB/km this is about $1.4\times10^{-2}$ at 100 km, $10^{-10}$ at 500 km and $10^{-20}$ at 1000 km. Beating this scaling needs quantum repeaters, or protocols such as twin-field QKD that use a middle node to effectively halve the distance, giving $\sqrt\eta$ scaling.
Quantum repeaters and memories
(Briegel, Dür, Cirac, Zoller 1998.) Divide the link into short segments, create entanglement in each (heralded), store it in memories, then swap and purify, so cost scales polynomially in distance instead of exponentially. Generations (Muralidharan et al. 2016):
| Generation | Loss handled by | Errors handled by | Requirement |
|---|---|---|---|
| 1st | Heralded entanglement generation + memories | Entanglement purification | Memories with long coherence; two-way classical signalling |
| 2nd | Heralded entanglement generation | Quantum error correction | Fault-tolerant local operations |
| 3rd | Quantum error correction | Quantum error correction | No heralding; very high-fidelity operations, fastest in principle |
Free-space and satellite quantum links
Free-space entanglement distribution uses an SPDC source, transmitter telescope, atmospheric channel and receiver. Total loss $\eta=\eta_{\rm geo}\eta_{\rm atm}\eta_{\rm opt}$. Practical needs: ultra-precise pointing, adaptive optics against turbulence, narrow spectral/temporal filtering for background rejection and polarization reference-frame alignment. The Micius satellite demonstrated entanglement distribution over about 1200 km, teleportation to orbit and intercontinental key exchange; microsatellites (Jinan-1) show a path to lower cost. Satellites currently act as trusted relays for QKD; entanglement-based satellite links could remove that trust.
Stages of a quantum internet
(Wehner, Elkouss, Hanson, Science 2018.) A roadmap with increasing capability:
- Trusted-repeater networks: QKD with trusted nodes (today).
- Prepare-and-measure networks: end users send qubits, no entanglement.
- Entanglement-distribution networks: end-to-end entanglement; enables device-independent protocols.
- Quantum-memory networks: storage, enabling repeaters and blind computing.
- Few-qubit fault-tolerant networks: distributed sensing, clock sync, leader election.
- Quantum-computing networks: networked fault-tolerant quantum computers.
Milestones: loophole-free Bell test across 1.3 km (Delft 2015); multi-node networks of solid-state qubits (Delft 2021); metropolitan entanglement testbeds with commercial vendors.