Polarisation entanglement
The quantum polarisation state of an intense light field can be succinctly described by the quantum Stokes operators [4,15,16]. These are derived by analogy to the classical Stokes parameters [17]. Ifâ x/y andâ † x/y denote the photon annihilation and creation operators of two orthogonal polarisation modes x and y, andn x andn y are the photon number operators of these modes, the quantum Stokes operators read as followŝ The operatorsŜ 1 ,Ŝ 2 , andŜ 3 follow the operator valued commutation relation of the SU(2) Lie algebra TheŜ 0 operator, which represents the total intensity, commutes with all other Stokes operators. This formalism corresponds to the well known derivation of Schwinger [18]. It gives rise to a set of three state dependent Heisenberg-type uncertainty relations Thus a state which obeys is a polarisation squeezed state (see Refs. [5,10] and references therein). In the experiments presented in this paper we consider a fully circularly polarized state, i.e. Ŝ 3 = 0. The Stokes parameters orthogonal toŜ 3 are given bŷ all of which have the property Ŝ (θ) = 0. Physically speaking these parameters are dark. This plane contains an infinite family of maximally conjugate Stokes parameters, generally given byŜ(θ) andŜ(θ + π/2) which obey the uncertainty relation Thus the values ofŜ(θ) andŜ(θ + π/2) cannot be simultaneously determined with arbitrary accuracy. That is, the variance ∆ 2Ŝ (j) ofŜ(j) cannot vanish for j = θ and j = θ + π/2 simultaneously. The variance V sq of a polarisation squeezed state is minimised for a particular angle θ sq , i. e.Ŝ(θ sq ) =Ŝ sq is squeezed, the variance V asq of the corresponding conjugate parameterŜ(θ sq + π/2) =Ŝ asq is anti-squeezed. Such polarisation squeezed states can be used for the generation of polarisation entanglement. Polarisation entanglement can be quantified and characterised in many ways, depending on the application and precise system under consideration [20]. However, the most common measures used for the experimental demonstration of continuous variable entanglement are the EPR criterion [21] and the non-separability criterion [22]. Although originally derived for the characterisation of quadrature entanglement these criteria have equivalents in the polarisation variables [5]. In general, let us consider a pair of Stokes parametersŜ(θ) andŜ(θ + π/2) which form a conjugate pair. Consider a composite quantum system that consists of two modes which we label C and D. 
### Language ###
English

### Assessment ###
The text discusses quantum physics concepts, specifically about Stokes operators. A basic query could focus on their fundamental commutation property.

### Query ###
What kind of algebraic relation do Stokes operators follow?
What kind of algebraic relation do Stokes operators follow?