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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 

We report two conjugates of gem-diethyl pyrroline nitroxide radicals with D-mannosamine as potential metabolic organic radical contrast agents, mORCAs, circumventing the need for biorthogonal reactions. In-cell EPR spectroscopy, using Jurkat cells and analogous conjugate, based on a pyrrolidine nitroxide radical, shows an efficient incorporation of highly immobilized nitroxides, with a correlation time of τcor = 20 ns. In vivo MRI experiments in mice show that the paramagnetic nitroxide radical shortens the T1 and T2 relaxation times of protons in water located in the kidney and brain by only up to ~10% after 3 d. Ex vivo EPR spectroscopic analyses indicate that the contrast agents in mouse tissues are primarily localized in the kidney, lung, liver, heart, and blood, which primarily contain immobilized nitroxide radicals with τcor = 4–9 ns. The spin concentrations in tissues remain low (1–3 nmol g⁻1) at 24 h after the third mORCA injection, approximately one to two orders of magnitude lower than those of ORCAFluor and BASP-ORCA (measured at ~24 h post-injection). These low spin concentrations explain the small proton T1 and T2 relaxation changes observed in in vivo MRI. 

Abstract Cisco (Coregonus artedi) are a widespread, cold‐water zooplanktivore native to North America. Although Cisco are generally referred to as an “obligate zooplanktivore,” there is some evidence that the species exhibits considerable variability in trophic niche. Here, we assessed how Cisco body size relates to trophic position, that is, trophic ontogeny. We analysed¹³C and¹⁵N isotopes from Cisco ranging from 127 to 271 mm in body length (n = 66) from Trout Lake, Vilas County, Wisconsin, USA.¹⁵N isotopes showed smaller Cisco had a trophic position of ~3, which steadily increased to ~3.5 for larger Cisco. Further,¹³C isotope signatures showed Cisco transitioned to be more pelagically reliant (lower¹³C signatures). Using gillnet catch data, we found that larger Cisco were using deeper habitats than smaller Cisco. Our results support that Cisco have significant variability in trophic niche even though they are traditionally thought of as an obligate planktivore. Overall, we emphasize that researchers should be cautious when generalizing Cisco trophic function, particularly when considering the broader food web. 

We investigate the effect of three-dimensionality on the synchronisation characteristics of the wake behind an oscillating circular cylinder at$${\textit {Re}} = 300$$. Cylinder oscillations in rotation, transverse translation and streamwise translation are considered. We utilise phase-reduction analysis, which quantifies the phase-sensitivity function of periodic flows, to examine the synchronisation properties. Here, we present an ensemble-based framework for phase-reduction analysis to handle three-dimensional wakes that are not perfectly time-periodic. Based on the phase-sensitivity functions, synchronisability to three types of cylinder oscillations is evaluated. In spite of similar trends, we find that phase-sensitivity functions involving three-dimensional wakes are lower in magnitude compared with those of two-dimensional wakes, which leads to narrower conditions for synchronisation to weak cylinder oscillations. We unveil that the difference between the phase-sensitivity functions of two- and three-dimensional flows is strongly correlated to the amplitude variation of the three-dimensional flow by the cylinder motions. This finding reveals that the cylinder motion modifies the three-dimensionality of the wake as well as the phase of vortex shedding, which leads to reduced phase modulation. The synchronisation conditions of three-dimensional wakes, predicted by phase-reduction analysis, agree with the identification by parametric studies using direct numerical simulations for forced oscillations with small amplitudes. This study presents the potential capability of phase-reduction to study synchronisation characteristics of complex flows. 

Toric $t$-designs, or equivalently $t$-designs on the diagonal subgroup of the unitary group, are sets of points on the torus over which sums reproduce integrals of degree $t$monomials over the full torus. Motivated by the projective structure of quantum mechanics, we develop the notion of $t$-designs on the projective torus, which have a much more restricted structure than their counterparts on full tori. We provide various new constructions of toric and projective toric designs and prove bounds on their size. We draw connections between projective toric designs and a diverse set of mathematical objects, including difference and Sidon sets from the field of additive combinatorics, symmetric, informationally complete positive operator valued measures and complete sets of mutually unbiased bases (MUBs) from quantum information theory, and crystal ball sequences of certain root lattices. Using these connections, we prove bounds on the maximal size of dense $B_{t}modm$sets. We also use projective toric designs to construct families of quantum state designs. In particular, we construct families of (uniformly-weighted) quantum state $2$-designs in dimension $d$of size exactly $d(d+1)$that do not form complete sets of MUBs, thereby disproving a conjecture concerning the relationship between designs and MUBs (Zhu 2015). We then propose a modification of Zhu's conjecture and discuss potential paths towards proving this conjecture. We prove a fundamental distinction between complete sets of MUBs in prime-power dimensions versus in dimension $6$(and, we conjecture, in all non-prime-power dimensions), the distinction relating to group structure of the corresponding projective toric design. Finally, we discuss many open questions about the properties of these projective toric designs and how they relate to other questions in number theory, geometry, and quantum information. 

Managing fisheries in a changing socio-ecological environment may require holistic approaches for identifying and adapting to novel ecosystem dynamics. Using 32 years of Ceded Territory of Wisconsin (CTWI) walleye ( Sander vitreus) data, we estimated production ( P), biomass ( B), biomass turnover ( P/B), yield ( Y), and yield over production ( Y/P) and tested for hyperstability in walleye yield. Most CTWI walleye populations showed low P and B, and Y/P < 1 . Yet, production overharvest ( Y/P > 1) was prevalent among Wisconsin walleye recruitment-based management approaches (natural recruitment (NR), sustained only by stocking, combination). Production, B, and P/B have declined in NR populations, while Y and Y/P have remained constant. Walleye Y was hyperstable along a production gradient among all management approaches and fishery types (i.e., angling only, angling/tribal harvest combined). Diminishing productivity and hyperstable yield may be jointly contributing to observed walleye declines. We classified lakes into management groups of low, moderate, or high vulnerability to harvest based on Y/P and P/B dynamics and identify that harvest may benefit from declines to maintain or increase the adaptive capacity of CTWI walleye. 

ABSTRACT Ecosystems are abruptly changing due to invasive species and global climate change. In lakes, invasive Rainbow Smelt Osmerus mordax can cause negative ecosystem effects through competitive and predatory interactions with native species leading to food web shifts away from native species dominance, altered zooplankton communities, and the decline or extirpation of native cool and coldwater fishes. We conducted two whole-lake removals of invasive Rainbow Smelt and simultaneous introductions of native Cisco Coregonus artedi through stocking. About 327 and 1.6 adult Rainbow Smelt/ha were removed and about 45 adult Cisco/ha were stocked over 4 years into the two experimental lakes. In one system, native Yellow Perch Perca flavscens relative abundance and density significantly increased by 556% and 143% post-manipulation, respectively. In the other system, native Walleye Sander vitreus relative abundance increased by 26% and became consistently present in the pelagic zone post-manipulation (allowing for density estimation). Rainbow Smelt relative abundance and density decreased by >85% in both experimental lakes. The two ecosystems shifted to native species dominance while invasive Rainbow Smelt became insignificant components of the food webs. In these two intensive whole-lake manipulations, we applied the Resist–Accept–Direct (RAD) climate adaptation framework to test an applicable ecological adaptation strategy and used panarchy theory as an ecologically grounded pathway to purposefully direct ecosystem transformation. We used this holistic management framework to better understand and manage undesired ecological change—“food web thinking.” In the context of our study, two ecosystems were purposefully directed towards native food web structures, species interactions, and processes, which mitigated Rainbow Smelt driven negative effects.