Thermalization and information scrambling in out-of-equilibrium quantum many-body systems are deeply intertwined: Local subsystems dynamically approach thermal density matrices while their entropies track nonlocal information spreading. Projected ensembles, i.e., ensembles of pure states conditioned on measurement outcomes of complementary subsystems, provide higher-order probes of thermalization, converging at late times to universal maximum-entropy ensembles constrained by conservation laws. In this work we introduce the partial projected ensemble (PPE) as a framework to study how the spatiotemporal structure of information scrambling is imprinted on projected ensembles. The PPE consists of an ensemble of mixed states induced on a subsystem by measurements on a spatially separated part of its complement, while tracing out the remainder, naturally capturing scenarios involving discarded outcomes or noise-induced losses. We show that the statistical fluctuations of the PPE faithfully track the causal lightcone of information spreading, thereby revealing how scrambling dynamics is encoded in the ensemble structure. In addition, we demonstrate that the probabilities of bit-string probabilities (PoPs) associated with the PPE exhibit distinct dynamical regimes and provide an experimentally accessible probe of scrambling. Both the PPE fluctuations and PoPs display exponential sensitivity to the size of the discarded region, reflecting an exponential degradation of quantum correlations under erasure or loss. We substantiate these findings using the nonintegrable kicked Ising chain, combining numerics in the ergodic regime with exact results at its self-dual point, and extend our analysis to the many-body localized (MBL) regime using simulations supported by analytical results for the $\ell$-bit model. The linear and logarithmic light cones characteristic of ergodic and MBL regimes, respectively, emerge naturally from the PPE dynamics, establishing it as a powerful tool for probing scrambling and deep thermalization.

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• Information scrambling
• Many-body localization
• Quantum chaos
• Quantum circuits
• Quantum correlations in quantum information
• Quantum measurements
• Quantum statistical mechanics
• Disordered systems
• Quantum chaotic systems
• Qubits
• Diagrammatic methods
• Direct numerical simulations
• Exact diagonalization
• Random field Ising model