From Topological to Quantum Entanglement

Understand

Entanglement is a special feature of the quantum world that reflects the existence of subtle, often non-local, correlations between local degrees of freedom.

• In topological theories such non-local correlations can be given a very intuitive interpretation: quantum entanglement of subsystems means that there are "strings" connecting them.
• More generally, an entangled state, or similarly, the density matrix of a mixed state, can be represented by cobordisms of topological spaces.
• Using a formal mathematical definition of TQFT we construct basic examples of entangled states and compute their von Neumann entropy.