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

TL;DR

This paper establishes an intrinsic upper bound on two-qubit polarization entanglement generated via parametric down-conversion, linking maximum entanglement to the pump photon’s polarization correlations.

Contribution

It derives a fundamental upper bound on two-qubit entanglement based on pump polarization, revealing how one-particle correlations limit two-particle entanglement in PDC.

Findings

Concurrence is bounded by (1+P)/2, where P is pump polarization.

For certain states, the upper bound simplifies to the degree of polarization P.

The formalism can extend to multi-particle systems and entanglement bounds.

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 $C(\rho)$ of the generated two-qubit state $\rho$ follows an intrinsic upper bound with $C(\rho)\leq (1+P)/2$, 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 non-zero diagonal elements such that the effective dimensionality of the two-qubit state is same as the dimensionality of the pump polarization state, the upper bound on concurrence is the degree of polarization itself, that is, $C(\rho)\leq P$. 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 multi-particle systems and can thus have important implications towards deducing the upper bounds on multi-particle entanglement, for which no universally accepted measure exists.