An entangled state is defined as a state that is not separable. A separable state can be written as a probability distribution over uncorrelated states, product states,

ρ = ∑_ip_iρ_i^A ⊗ ρ_i^B.

Pure states

For pure states the above definition can be represented as follows. Consider two quantum systems A and B, with respective Hilbert spaces ℋ_A and ℋ_B. The Hilbert space of the composite system is the tensor product ℋ_A ⊗ ℋ_B. If the state |Ψ⟩_ABof the composite system can be represented in the form

|Ψ⟩_AB=|ψ⟩_A ⊗ |ϕ⟩_B,

where |ψ⟩_A ∈ ℋ_A and |ϕ⟩_B ∈ ℋ_B are the states of the systems A and B respectively, then this state is called a separable state. If a state is not separable, it is known as an entangled state.

Ralated papers

• R. F. Werner, Quantum states with Einstein-Rosen-Podolsky correlations admitting a hidden-variable model, Phys. Rev. A 40, pp. 4277-4281, 1989.
• D. Bruss, Characterizing Entanglement, Math. Phys. 43, pp. 4237, 2002.

Category:Entanglement Category:Handbook of Quantum Information