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Limit formulas for norms of tensor power operators and entanglement annihilating maps

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QIAW02 - New trends at the intersection of quantum information theory, quantum groups and operator algebras

Given an operator between Banach spaces X and Y, we consider its tensor powers as operators from the k-fold injective tensor product of X to the k-fold projective tensor product of Y. We show that after taking the kth root, the operator norms of these tensor power operators converge to the 2-dominated norm (one of the standard operator ideal norms) of the original operator. We discuss applications of this result to the problem of finding entanglement annihilating maps that are not entanglement breaking between pairs of proper cones, a problem related to a major open problem in quantum information theory. Joint work with Guillaume Aubrun. For more information see: arxiv:2410.23063   

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