Entanglement and Nonlocal Correlations
Correlations beyond classical intuition
What entanglement is
A composite system is entangled when its state cannot be written as a simple product of states of its parts. Entangled subsystems may each appear random while the joint state is highly structured.
Bell states
The maximally entangled two-qubit states provide canonical examples of entanglement and are central resources in quantum communication.
Bell inequalities
Bell's theorem shows that no local hidden-variable theory can reproduce all quantum predictions. Violations of Bell inequalities demonstrate that quantum correlations are stronger than any classical local model.
Important nuance
Entanglement does not allow faster-than-light communication, even though the correlations are nonclassical.
Reduced states
For an entangled system, each part can be described by a reduced density matrix obtained by tracing out the other part. The local state can be mixed even if the total state is pure.
What is a defining feature of entanglement?
Entangled states are not separable into product states of the subsystems.
Correct answer: The joint state cannot be factorized into separate states
What does a Bell inequality test?
Experimental violations rule out a broad class of classical explanations.
Correct answer: whether local hidden-variable models can explain the correlations
Does entanglement allow instant communication?
Quantum correlations are nonlocal, but usable information cannot be sent faster than light.
Correct answer: No
Why can a subsystem of an entangled pair appear mixed?
Tracing out the partner removes access to joint information.
Correct answer: because the partner system carries correlated information
Applications
Entanglement powers quantum cryptography, teleportation, superdense coding, and many quantum algorithms.