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We prove a decomposition theorem for generalized supermaps and describe the equivalence classes. The set of generalized supermaps having the same value on equivalent generalized channels is also characterized. Special cases include quantum combs and process positive operator valued measures (POVMs). ...
has no state constraints, the first-order optimality system is fulfilled without any further regularity assumptions. theorem 3.2 (first-order necessary optimality conditions) for given \(\rho >0\) and \(0\le \mu \in l^2(\omega )\) let \(({\bar{y}}_{\rho },{{\bar{u}}}_{\rho...
Then we prove that the Kreps–Yan theorem is valid for topological vector spaces in separating duality 〈 X , Y 〉, provided Y satisfies both a "completeness condition" and a "Lindelf-like condition". We apply this result to the characterization of the no-arbitrage assumption in a general ...
In this paper we formulate and study a minimax control problem for a class of parabolic systems with controlled Dirichlet boundary conditions and uncertain distributed perturbations under pointwise control and state constraints. We prove an existence theorem for minimax solutions and develop effective penal...
[1].Thecorrespondingasymmetries,inorder tobenon-zero,requiretwodifferentfinalstatesproducedbydifferentweak amplitudeswhichcangointoeachotherbyastronginteractionrescatter- ingandthereforedependonbothweakCKMphaseandstrongrescattering phaseprovidedbytheFSI.Thus,FSIdirectlyaffecttheasymmetriesand ∗ Invited...
The spectral duality axiom is introduced in the next subsection and used together with the atomic decomposition to give a geometric characterization of the dual ball of a JB ∗ -triple (Theorem 3.14). The final subsection applies the latter to give an operator space characterization of one-...
We prove a direct product theorem: if we're given two such problems, with optimal probabilities a and b, respectively, and the states in the first problem are pure, then the optimal probability for the joint bounded-error state identification problem is O(ab). Our proof is based on ...
is also commonly called the kantorovich–rubinstein distance and can be characterized by a useful duality formula (see, for instance, [ 23 ]) as follows $$\begin{aligned} d_1(m,m')=\sup \left\{ \int _{\mathbb {r}^d} f(x)\,dm(x)-\int _{\mathbb {r}^d} f(x)\,dm'(x)...
Thus, to prove Theorem 1, we only need to show that any (k,2k−1) protocol can be implemented using a weighted CVGS of infinite squeezing. Suppose that in a communication system with one dealer and 2k−1 players, a set of k players collaborate to reveal the secret. Since Eq. (12...