What Is Quantum Entanglement?
Non-Separable Quantum States
Two quantum systems are entangled when their joint quantum state cannot be written as a product of individual states. Measuring one instantly determines a correlated property of the other — regardless of the physical distance separating them.
This is not a signal travelling faster than light. No usable information is transmitted in the act of measurement; the correlations only become apparent when the results are compared via a classical channel. What is non-classical is the strength of those correlations — they exceed any possible explanation involving pre-agreed hidden variables.
Einstein, Podolsky, and Rosen identified this as a seeming paradox in 1935, arguing quantum mechanics must be "incomplete." John Bell's 1964 theorem proved that any local hidden variable theory makes different predictions to quantum mechanics. Decades of experiments — culminating in the 2022 Nobel Prize in Physics — have consistently confirmed the quantum prediction, ruling out local realism.
Bell Test Experiments
Key Concepts
Bell States
The four maximally entangled two-qubit states form a complete orthonormal basis. Example: |Φ+⟩ = (|00⟩ + |11⟩)/√2. Measuring either qubit in the computational basis immediately determines the state of the other.
CHSH Inequality
The CHSH variant of Bell's inequality: |E(a,b) − E(a,b') + E(a',b) + E(a',b')| ≤ 2 for classical systems. Entangled quantum systems achieve up to 2√2 ≈ 2.83, providing a clear experimental signature of quantum non-locality.
Quantum Teleportation
Transfer an unknown quantum state from Alice to Bob using: (1) a pre-shared entangled pair, (2) a Bell-state measurement by Alice, (3) two classical bits sent to Bob, (4) a corrective unitary by Bob. The original state is destroyed at Alice's end.
Superdense Coding
With one pre-shared entangled qubit, Alice can encode and transmit two classical bits to Bob by sending only a single qubit. Entanglement effectively doubles the classical capacity of a quantum channel.
The Quantum Teleportation Protocol
Entanglement in Cryptographic Security
Device-Independent QKD
Conventional QKD assumes that Alice and Bob's devices behave as described. Device-independent QKD (DI-QKD) makes no such assumption. Security is certified entirely by observing that the devices violate a Bell inequality — if they do, the underlying quantum correlations cannot have been pre-programmed by an adversary, regardless of who manufactured the hardware.
This provides the strongest possible cryptographic security guarantee: it holds even against an adversary who supplied the devices. The E91 protocol is the paradigmatic example.
Current status: Theoretically proven and experimentally demonstrated in small-scale settings (~2021–2022). Scaling to practical key rates remains an active research challenge requiring very high detector efficiencies and loophole-free Bell tests.
Implementation Challenges