Local predictability and coherence versus distributed entanglement in entanglement swapping from partially entangled pure states

TL;DR

This paper explores the relationship between local predictability, coherence, and distributed entanglement in entanglement swapping of pure states, extending previous results and experimentally verifying some cases using IBM quantum computers.

Contribution

It generalizes the complementarity relations in entanglement swapping to broader pure states and provides experimental validation using quantum computing.

Findings

Extended complementarity relations to general pure states in ESP.

Experimental verification of theoretical results on IBM quantum computers.

Demonstrated the connection between local properties and distributed entanglement.

Abstract

Complete complementarity relations, as e.g. $P(\rho_{A})^{2} + C(\rho_{A})^{2} + E(|\Psi\rangle_{AB})^{2}=1$, constrain the local predictability, $P$, and local coherence, $C$, and the entanglement, $E$, of bipartite pure states. For pairs of qubits prepared initially in a particular class of partially entangled pure states with null local coherence, these relations were used in Ref. [Phys. Lett. A, 451, 128414 (2022)] to provide an operational connection between local predictability of the pre-measurement states with the probability of the maximally entangled components of the states after the Bell-basis measurement of the entanglement swapping protocol (ESP). In this article, we extend this result for general pure initial states establishing the relation between $P$, $C$ and the distributed entanglement in the ESP. We use IBM's quantum computers to verify experimentally some instances of these general theoretical results.