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We define a new divergence of von Neumann algebras using a variational expression that is similar in nature to Kosakis formula for the relative entropy. Our divergence satisfies the usual desirable properties, upper bounds the sandwiched Renyi entropy and reduces to the fidelity in a limit. As an illustration, we use the formula in quantum field theory to compute our divergence between the vacuum in a bipartite system and an orbifolded -- in the sense of conditional expectation -- system in terms of the Jones index. We take the opportunity to point out entropic certainty relation for arbitrary von Neumann subalgebras of a factor related to the relative entropy. This certainty relation has an equivalent formulation in terms of error correcting codes.
We initiate the study of relative operator entropies and Tsallis relative operator entropies in the setting of JB-algebras. We establish their basic properties and extend the operator inequalities on relative operator entropies and Tsallis relative o
We provide lower and upper bounds on the information transmission capacity of one single use of a classical-quantum channel. The lower bound is expressed in terms of the Hoeffding capacity, that we define similarly to the Holevo capacity, but replaci
A prepotential approach to constructing the quantum systems with dynamical symmetry is proposed. As applications, we derive generalizations of the hydrogen atom and harmonic oscillator, which can be regarded as the systems with position-dependent mas
In this work, we investigate the possibility of compressing a quantum system to one of smaller dimension in a way that preserves the measurement statistics of a given set of observables. In this process, we allow for an arbitrary amount of classical
We prove decomposition rules for quantum Renyi mutual information, generalising the relation $I(A:B) = H(A) - H(A|B)$ to inequalities between Renyi mutual information and Renyi entropy of different orders. The proof uses Beigis generalisation of Reis