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Recently, many experiments have been conducted with the goal of demonstrating a quantum advantage over classical computation. One popular framework for these experiments is Gaussian boson sampling, where quadratic photonic input states are interfered via a linear optical unitary and subsequently measured in the Fock basis. In this paper, we study the modal entanglement of the output states in this framework just before the measurement stage. Specifically, we compute Page curves as measured by various Rényi- $\alpha$entropies, where the Page curve describes the entanglement between two partitioned groups of output modes averaged over all linear optical unitaries. We derive these formulas for $\alpha =1$(i.e., the von Neumann entropy) and, more generally, for all positive integer $\alpha$, in the asymptotic limit of infinite number of modes and for input states that are composed of single-mode-squeezed-vacuum state with equal squeezing strength. We then analyze the limiting behaviors when the squeezing is small and large. Having determined the averages, we then explicitly calculate the Rényi- $\alpha$variance for integers $\alpha >1$and are able to show that these entropies are weakly typical. Published by the American Physical Society2025 

High-resolution awake mouse functional magnetic resonance imaging (fMRI) remains challenging despite extensive efforts to address motion-induced artifacts and stress. This study introduces an implantable radio frequency (RF) surface coil design that minimizes image distortion caused by the air/tissue interface of mouse brains while simultaneously serving as a headpost for fixation during scanning. Furthermore, this study provides a thorough acclimation method used to accustom animals to the MRI environment minimizing motion-induced artifacts. Using a 14 T scanner, high-resolution fMRI enabled brain-wide functional mapping of visual and vibrissa stimulation at 100 µm×100 µm×200 µm resolution with a 2 s per frame sampling rate. Besides activated ascending visual and vibrissa pathways, robust blood oxygen level-dependent (BOLD) responses were detected in the anterior cingulate cortex upon visual stimulation and spread through the ventral retrosplenial area (VRA) with vibrissa air-puff stimulation, demonstrating higher-order sensory processing in association cortices of awake mice. In particular, the rapid hemodynamic responses in VRA upon vibrissa stimulation showed a strong correlation with the hippocampus, thalamus, and prefrontal cortical areas. Cross-correlation analysis with designated VRA responses revealed early positive BOLD signals at the contralateral barrel cortex (BC) occurring 2 s prior to the air-puff in awake mice with repetitive stimulation, which was not detected using a randomized stimulation paradigm. This early BC activation indicated a learned anticipation through the vibrissa system and association cortices in awake mice under continuous exposure of repetitive air-puff stimulation. This work establishes a high-resolution awake mouse fMRI platform, enabling brain-wide functional mapping of sensory signal processing in higher association cortical areas. 

Abstract High‐field preclinical functional MRI (fMRI) is enabled the high spatial resolution mapping of vessel‐specific hemodynamic responses, that is single‐vessel fMRI. In contrast to investigating the neuronal sources of the fMRI signal, single‐vessel fMRI focuses on elucidating its vascular origin, which can be readily implemented to identify vascular changes relevant to vascular dementia or cognitive impairment. However, the limited spatial and temporal resolution of fMRI is hindered hemodynamic mapping of intracortical microvessels. Here, the radial encoding MRI scheme is implemented to measure BOLD signals of individual vessels penetrating the rat somatosensory cortex. Radial encoding MRI is employed to map cortical activation with a focal field of view (FOV), allowing vessel‐specific functional mapping with 50 × 50 µm²in‐plane resolution at a 1 to 2 Hz sampling rate. Besides detecting refined hemodynamic responses of intracortical micro‐venules, the radial encoding‐based single‐vessel fMRI enables the distinction of fMRI signals from vessel and peri‐vessel voxels due to the different contribution of intravascular and extravascular effects.