Shallow random quantum circuits, specifically 2D geometrically local ones, exhibit limited long-range correlations in their output states due to the inherent lightcone structure. However, upon measuring a subset of qubits, the measurement process can induce long-range entanglement, resulting in conditional correlations between distant qubits1. This phenomenon is a key aspect of quantum computing, as it highlights the complex interplay between measurement and entanglement in quantum systems. The study of conditional dependence in these circuits can provide valuable insights into the underlying mechanisms governing quantum information processing. Researchers have employed Scrooge ensembles to investigate this phenomenon, shedding light on the intricate relationships between qubits in shallow random quantum circuits. This understanding is crucial for the development of robust quantum computing architectures, as it can inform the design of quantum error correction protocols and optimize quantum information processing tasks, making it essential for practitioners to consider the implications of conditional dependence in quantum circuit design.