Operational connection between predictability and entanglement in entanglement swapping from partially entangled pure states

TL;DR

This paper establishes an operational link between predictability and entanglement in quantum entanglement swapping, revealing how measurements affect these properties in partially entangled states.

Contribution

It introduces a novel connection between predictability and entanglement during entanglement swapping from partially entangled states, grounded in complementarity relations.

Findings

Predictability of the pre-measurement state relates to post-measurement probabilities.

Entanglement can increase after Bell-basis measurement in certain cases.

Predictability decreases when entanglement increases post-measurement.

Abstract

Complementarity and entanglement are fundamental features of Quantum Mechanics that were recently related in triality equalities that involve quantum coherence, the wave aspect of a qubit, and quantum predictability and quantum entanglement, the particle aspect of a qubit. In this article, we give an operational connection between redictability and entanglement in entanglement swapping from initially partially entangled states. For this, we show that the predictability of the pre-measurement one-qubit density matrix is directly related to the probability of the partially entangled component of the post-measurement state. Going even further, we analyze the entanglement swapping for partially entangled states in the light of complementarity relations and show that, in the cases where the entanglement increases after a Bell-basis measurement, the predictability is consumed when compared to the initially prepared state.