Biological invasions are a form of global change threatening biodiversity, ecosystem stability, and human health, and cost government agencies billions of dollars in remediation and eradication programs. Attempts to eradicate introduced species are most successful when detection of newly established populations occurs early in the invasion process. We review existing and emerging tools -specifically environmental DNA (eDNA), chemical approaches, remote sensing, citizen science, and agency-based monitoring -for surveillance and monitoring of invasive species. For each tool, we consider the benefits provided, examine challenges and limitations, discuss data sharing and integration, and suggest best practice implementations for the early detection of invasive species. Programs that promote public participation in large-scale biodiversity identification and monitoring (such as iNaturalist and eBird) may be the best resources for early detection. However, data from these platforms must be monitored and used by agencies that can mount appropriate response efforts. Control efforts are more likely to succeed when they are focused on early detection and prevention, thereby saving considerable time and resources.

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A ternary ring of operators (TRO) in finite dimensions is a diagonal sum of spaces of rectangular matrices. TRO as operator space corresponds to quantum channels that are diagonal sums of partial traces, which we call TRO channels. TRO channels admits simple, single-letter capacity formula. Using operator space and complex interpolation techniques, we give perturbative capacities estimates for a wider class of quantum channels by comparison to TRO channels. Our estimates applies mainly for quantum and private capacity and also strong converse rates. The examples includes random unitary from group representations which in general are non-degradable channels.

We revisit the connection between index and relative entropy for an inclusion of finite von Neumann algebras. We observe that the Pimsner-Popa index connects to sandwiched p-Rényi relative entropy for all 1/2 ≤ p ≤ ∞, including Umegaki's relative entropy at p = 1. Based on that, we introduce a new notation of relative entropy to a subalgebra which generalizes subfactors index. This relative entropy has application in estimating decoherence time of quantum Markov semigroup.

Quantum capacity, the ultimate transmission rate of quantum communication, is characterized by regularized coherent information. In this work, we reformulate approximations of the quantum capacity by operator space norms and give both upper and lower estimates on quantum capacity and potential quantum capacity using complex interpolation techniques from operator space theory. Upper bounds are obtained by a comparison inequality for Rényi entropies. Analyzing the maximally entangled state for the whole system and for error-free subsystems provides lower bounds for the "one-shot" quantum capacity. These two results combined give upper and lower bounds on quantum capacity for our "nice" classes of channels, which differ only up to a factor 2, independent of the dimension. The estimates are discussed for certain classes of channels, including group channels, generalized Pauli channels and other highdimensional channels.where σ AB = id A ⊗ Φ(ρ AA ) and the maximum runs over all pure bipartite state ρ AA . I c (A B) σ is the coherent information of bipartite σ given by H(σ B ) − H(σ AB ), with H(σ) = −tr(σ log σ) being the von Neumann entropy, and Q (1) is the "one-shot" quantum capacity. Let us also recall that the negative cb-entropy (also called the reverse coherent information) of a channel Φ is defined similarly as −S cb (Φ) = max ρ H(A) ρ − H(AB) ρ (see Section 2 for formal definitions). *