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Five open problems in quantum information
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We identify five selected open problems in the theory of quantum information, which are rather simple to formulate, were well-studied in the literature, but are technically not easy. As these problems enjoy diverse mathematical connections, they offer a huge breakthrough potential. The first four concern existence of certain objects relevant for quantum information, namely a family of symmetric informationally complete generalized measurements in an infinite sequence of dimensions, mutually unbiased bases in dimension six, absolutely maximally entangled states for four subsystems with six levels each and bound entangled states with negative partial transpose. The fifth problem requires checking whether a certain state of a two-ququart system is 2-copy distillable. An award for solving each of them is announced.
Forward citations
Cited by 2 Pith papers
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On the two-copy distillability of Werner states and a new partial trace inequality
Werner states ρ(d,α) are two-copy undistillable exactly when α≥−1/2, so ρ(4,−1/2) is not two-copy distillable.
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Entanglement Distillation of some Rank-Five Symmetric NPT States in Two-Qutrit Systems
The previously open interval of the eigenvalue parameter for a rank-five symmetric NPT two-qutrit state family is proven 1-undistillable, and a structural obstruction to 2-distillability is identified.
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