Waldhausen Additivity: classical and quasicategorical
نویسندگان
چکیده
منابع مشابه
Waldhausen Additivity: Classical and Quasicategorical
We give a short proof of classical Waldhausen Additivity, and then prove Waldhausen Additivity for an ∞-version of Waldhausen K-theory. Namely, we prove that Waldhausen K-theory sends a split-exact sequence of Waldausen quasicategories A → E → B to a stable equivalence of spectra K(E) → K(A) ∨ K(B) under a few mild hypotheses. For example, each cofiber sequence in A of the form A0 → A1 → ∗ is r...
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Information theory quantifies the optimal rates of resource interconversions, usually in terms of entropies. However, nonadditivity often makes evaluating entropic formulas intractable. In a few auspicious cases, additivity allows a full characterization of optimal rates. We study uniform additivity of formulas, which is easily evaluated and captures all known additive quantum formulas. Our com...
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We develop a theory of Spanier–Whitehead duality in categories with cofibrations and weak equivalences (Waldhausen categories, for short). This includes L–theory, the involution on K–theory introduced by [Vo] in a special case, and a map Ξ relating L–theory to the Tate spectrum of Z/2 acting on K–theory. The map Ξ is a distillation of the long exact Rothenberg sequences [Sha], [Ra1], [Ra2], inc...
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Abstract We show that for the tensor product of an entanglement-breaking quantum channel with an arbitrary quantum channel, both the minimum entropy of an output of the channel and the Holevo-Schumacher-Westmoreland capacity are additive. In addition, for the tensor product of two arbitrary quantum channels, we give a bound involving entanglement of formation for the amount of subadditivity (fo...
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ژورنال
عنوان ژورنال: Journal of Homotopy and Related Structures
سال: 2018
ISSN: 2193-8407,1512-2891
DOI: 10.1007/s40062-018-0206-6