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Five Open Problems in Quantum Information Theory
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DOI：10.1103/PRXQuantum.3.010101.png)
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Abstract
En 中文
We identify five selected open problems in the theory of quantum information, which are rather simple to formulate, are 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, measurements saturating multiparameter Cramer-Rao bound and bound entangled states with negative partial transpose. The fifth problem requires checking whether a certain state of a two-ququart system is two-copy distillable.
Keywords:
MUTUALLY UNBIASED BASES
COMPLEX HADAMARD-MATRICES
ENTANGLED STATES
MAXIMUM NUMBER
LATIN SQUARES
DISTILLATION
SEPARABILITY
CRYPTOGRAPHY