Ja n 20 06 A comment on “ A semiconductor source of entangled photons ”
نویسندگان
چکیده
When basic tools of quantum information are applied to the quantum tomography data presented in [1], none of their devices appears to be a source of entangled photons. In a paper titled " A semiconductor quantum source of triggered entangled photon pairs " Stevenson et. al. [1] claim to find evidence for the emission of polarization entangled photons from certain quantum dots. A density matrix completely specifies all properties of the quantum state [2]. Using quantum tomography [3], the authors of [1] construct the density matrices representing the polarization state of the photons emitted by each of their devices. We show that subjecting their quantum states to the basic definition of entanglement leads to the inevitable conclusion that none of their devices produced entangled light. In all the dots investigated in [1], quantum tomography yielded real density matrices of the form ρ = α 0 0 γ 0 β 0 0 0 0 β ′ 0 γ 0 0 α ′ , (1) with β ≈ β ′ and the zeros stands for terms that are comparable to the measure-ments' noise. (The matrix is written in the basis {|HH , |HV , |V H, |V V }.) A straightforward test for entanglement is the Peres separability criterion [4]. For the matrix ρ of Eq. (1), (we set β = β ′ for simplicity) this involves looking if the matrix ρ P = α 0 0 0 0 β γ 0 0 γ β 0 0 0 0 α ′ . (2) has negative eigenvalues. If it does, the state is entangled; otherwise [6] it is not. The state (1) is entangled if and only if γ > β. The reader will easily convince 1
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