Intrinsic upper bound on two-qubit polarization entanglement predetermined by pump polarization correlations in parametric down-conversion

Abstract

We study how one-particle correlations transfer to manifest as two-particle correlations in the context of parametric down-conversion (PDC), a process in which a pump photon is annihilated to produce two entangled photons. We work in the polarization degree of freedom and show that for any two-qubit generation process that is both trace-preserving and entropy-nondecreasing, the concurrence $C(\ensuremath{\rho})$ of the generated two-qubit state $\ensuremath{\rho}$ follows an intrinsic upper bound with $C(\ensuremath{\rho})\ensuremath{\le}(1+P)/2$, where $P$ is the degree of polarization of the pump photon. We also find that for the class of two-qubit states that is restricted to have only two nonzero diagonal elements such that the effective dimensionality of the two-qubit state is the same as the dimensionality of the pump polarization state, the upper bound on concurrence is the degree of polarization itself, that is, $C(\ensuremath{\rho})\ensuremath{\le}P$. Our work shows that the maximum manifestation of two-particle correlations as entanglement is dictated by one-particle correlations. The formalism developed in this work can be extended to include multiparticle systems and can thus have important implications towards deducing the upper bounds on multiparticle entanglement, for which no universally accepted measure exists.