Revival and instabilities of entanglement in monitoring maps with indefinite causal order

In this proceeding, we revisit the discussion presented in Ref. [Commun Phys 7, 373 (2024)], which examines the behavior of a quantum switch involving two arbitrary quantum operations when the control is exposed to environmental effects. Our study extends this analysis by focusing on the evolution of entanglement in the target system within the quantum switch framework, taking into account the influence of environmental conditions and control post-selection. We find that entanglement evolution is highly sensitive to these factors. While entanglement sudden death occurs under definite causal order, indefinite causal order can reverse this loss. We observe entanglement revival in high-temperature regimes and a sudden reappearance of entanglement under weak monitoring conditions at low temperatures. These findings provide insights into the resilience of the quantum switch in the presence of environmental disturbances and highlight its potential for applications where preserving entanglement is essential.