Editing Bra–ket notation (section)

==Composite bras and kets==
Two Hilbert spaces {{math|''V''}} and {{math|''W''}} may form a third space {{math|''V'' ⊗ ''W''}} by a [[tensor product]]. In quantum mechanics, this is used for describing composite systems. If a system is composed of two subsystems described in {{math|''V''}} and {{math|''W''}} respectively, then the Hilbert space of the entire system is the tensor product of the two spaces. (The exception to this is if the subsystems are actually [[identical particles]]. In that case, the situation is a little more complicated.){{Citation needed|date=January 2025}}

If {{math|{{ket|''ψ''}}}} is a ket in {{math|''V''}} and {{math|{{ket|''φ''}}}} is a ket in {{math|''W''}}, the tensor product of the two kets is a ket in {{math|''V'' ⊗ ''W''}}. This is written in various notations:
:<math>|\psi\rangle|\phi\rangle \,,\quad |\psi\rangle \otimes |\phi\rangle\,,\quad|\psi \phi\rangle\,,\quad|\psi ,\phi\rangle\,.</math>

See [[quantum entanglement#Quantum mechanical framework|quantum entanglement]] and the [[EPR paradox#Mathematical formulation|EPR paradox]] for applications of this product.