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1. On an inequality of Lin, Kim and Hsieh and strong subadditivity

   https://doi.org/10.1007/s11005-024-01857-1  

   Carlen, Eric_A; Loss, Michael_P (September 2024, Letters in Mathematical Physics)

   Abstract We give an elementary proof of an inequality of Lin, Kim and Hsieh that implies strong subadditivity of the von Neumann entropy. 

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2. Subadditive femtosecond laser-induced electron emission from a GaAs tip

   Newman, William; Jones, Eric; Brunkow, Evan; Batelaan, Herman; Gay, Timothy (May 2024, Physical review B)

   Multiphoton emission of electrons has been observed from sharp tips of heavily p-doped GaAs caused by laser pulses with, nominally, 800-nm wavelength, 1-nJ/pulse energy, and 90-fs duration. The emission is mostly due to four-photon processes, with some contribution from three-photon absorption as well. When the electron emission current due to two pulses separated by delay 200 fs << τ << 1 ns is integrated over all electron energies, it is less than that observed for the sum of the emission from the two individual pulses. This subadditive behavior is consistent with a fast electron emission process, i.e., one in which the electron emission occurs over a time comparable to the laser pulse width. The subadditivity results from Pauli blocking of electron emission by the second pulse due to a population increase of the GaAs conduction band caused by the first pulse. Such subadditive photoemission is a sensitive probe of excited-carrier dynamics. We employ the use of an excited-level population model to characterize the photon absorption process and give us a clearer understanding of the electron dynamics in GaAs associated with multiphoton electron emission. Possible applications of this subadditivity effect to control photoemitted electron spin are discussed. 

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3. The holographic entropy cone from marginal independence

   https://doi.org/10.1007/JHEP09(2022)190  

   Hernández-Cuenca, Sergio; Hubeny, Veronika E.; Rota, Massimiliano (September 2022, Journal of High Energy Physics)

   A bstract The holographic entropy cone characterizes the relations between entanglement entropies for a spatial partitioning of the boundary spacetime of a holographic CFT in any state describing a classical bulk geometry. We argue that the holographic entropy cone, for an arbitrary number of parties, can be reconstructed from more fundamental data determined solely by subadditivity of quantum entropy. We formulate certain conjectures about graph models of holographic entanglement, for which we provide strong evidence, and rigorously prove that they all imply that such a reconstruction is possible. Our conjectures (except only for the weakest) further imply that the necessary data is remarkably simple. In essence, all one needs to know to reconstruct the holographic entropy cone, is a certain subset of the extreme rays of this simpler “subadditivity cone”, namely those which can be realized in holography. This recasting of the bewildering entanglement structure of geometric states into primal building blocks paves the way to distilling the essence of holography for the emergence of a classical bulk spacetime. 

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4. From Poincaré inequalities to nonlinear matrix concentration

   https://doi.org/https://doi.org/10.3150/20-BEJ1289  

   Huang, De; Tropp, Joel (January 2021, Bernoulli)

   null (Ed.)

   This paper deduces exponential matrix concentration from a Poincaré inequality via a short, conceptual argument. Among other examples, this theory applies to matrix-valued functions of a uniformly log-concave random vector. The proof relies on the subadditivity of Poincaré inequalities and a chain rule inequality for the trace of the matrix Dirichlet form. It also uses a symmetrization technique to avoid difficulties associated with a direct extension of the classic scalar argument. 

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5. Monotonicity Under Local Operations: Linear Entropic Formulas

   https://doi.org/10.1109/TIT.2020.2986728  

   Alhejji, Mohammad A.; Smith, Graeme (April 2020, IEEE Transactions on Information Theory)

   All correlation measures, classical and quantum, must be monotonic under local operations. In this paper, we characterize monotonic formulas that are linear combinations of the von Neumann entropies associated with the quantum state of a physical system that has n parts. We show that these formulas form a polyhedral convex cone, which we call the monotonicity cone, and enumerate its facets. We illustrate its structure and prove that it is equivalent to the cone of monotonic formulas implied by strong subadditivity. We explicitly compute its extremal rays for n ≤ 5. We also consider the symmetric monotonicity cone, in which the formulas are required to be invariant under subsystem permutations. We describe this cone fully for all n. We also show that these results hold when states and operations are constrained to be classical. 

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