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