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The present paper studies an operator norm that captures the distinguishability of quantum strategies in the same sense that the trace norm captures the distinguishability of quantum states or the diamond norm captures the distinguishability of quantum channels. Characterizations of its unit ball and dual norm are established via strong duality of a semidefinite optimization problem. A full, formal proof of strong duality is presented for the semidefinite optimization problem in question. This norm and its properties are employed to generalize a state discrimination result of Ref. [GW05]. The generalized result states that for any two convex sets S,T of strategies there exists a fixed interactive measurement scheme that successfully distinguishes any choice of s in S from any choice of t in T with bias proportional to the minimal distance between the sets S and T as measured by this norm. A similar discrimination result for channels then follows as a special case.
Especially investigated in recent years, the Gaussian discord can be quantified by a distance between a given two-mode Gaussian state and the set of all the zero-discord two-mode Gaussian states. However, as this set consists only of product states,
We initiate the study of quantum races, games where two or more quantum computers compete to solve a computational problem. While the problem of dueling algorithms has been studied for classical deterministic algorithms, the quantum case presents add
We evaluate a Gaussian entanglement measure for a symmetric two-mode Gaussian state of the quantum electromagnetic field in terms of its Bures distance to the set of all separable Gaussian states. The required minimization procedure was considerably
We discuss some properties of the quantum discord based on the geometric distance advanced by Dakic, Vedral, and Brukner [Phys. Rev. Lett. {bf 105}, 190502 (2010)], with emphasis on Werner- and MEM-states. We ascertain just how good the measure is in
We introduce a new semi-relativistic quantum operator for the length of the worldline a particle traces out as it moves. In this article the operator is constructed in a heuristic way and some of its elementary properties are explored. The operator e