ﻻ يوجد ملخص باللغة العربية
We study quantum dichotomies and the resource theory of asymmetric distinguishability using a generalization of Strassens theorem on preordered semirings. We find that an asymptotic variant of relative submajorization, defined on unnormalized dichotomies, is characterized by real-valued monotones that are multiplicative under the tensor product and additive under the direct sum. These strong constraints allow us to classify and explicitly describe all such monotones, leading to a rate formula expressed as an optimization involving sandwiched Renyi divergences. As an application we give a new derivation of the strong converse error exponent in quantum hypothesis testing.
Given two pairs of quantum states, a fundamental question in the resource theory of asymmetric distinguishability is to determine whether there exists a quantum channel converting one pair to the other. In this work, we reframe this question in such
The distillable entanglement of a bipartite quantum state does not exceed its entanglement cost. This well known inequality can be understood as a second law of entanglement dynamics in the asymptotic regime of entanglement manipulation, excluding th
The existence of a positive log-Sobolev constant implies a bound on the mixing time of a quantum dissipative evolution under the Markov approximation. For classical spin systems, such constant was proven to exist, under the assumption of a mixing con
We show that the new quantum extension of Renyis alpha-relative entropies, introduced recently by Muller-Lennert, Dupuis, Szehr, Fehr and Tomamichel, J. Math. Phys. 54, 122203, (2013), and Wilde, Winter, Yang, Commun. Math. Phys. 331, (2014), have an
Heisenbergs uncertainty principle has recently led to general measurement uncertainty relations for quantum systems: incompatible observables can be measured jointly or in sequence only with some unavoidable approximation, which can be quantified in