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• W2093674341 abstract "It is known that, in an $(mensuremath{bigotimes}n)$-dimensional quantum system, the maximum dimension of a subspace that contains only entangled states is $(mensuremath{-}1)(nensuremath{-}1)$. We show that the exact same bound is tight if we require the stronger condition that every state with range in the subspace has non-positive partial transpose. As an immediate corollary of our result, we solve an open question that asks for the maximum number of negative eigenvalues of the partial transpose of a quantum state. In particular, we give an explicit method of construction of a bipartite state whose partial transpose has $(mensuremath{-}1)(nensuremath{-}1)$ negative eigenvalues, which is necessarily maximal, despite recent numerical evidence that suggested such states may not exist for large $m$ and $n$." @default.
• W2093674341 created "2016-06-24" @default.
• W2093674341 creator A5008998456 @default.
• W2093674341 date "2013-06-28" @default.
• W2093674341 modified "2023-10-14" @default.
• W2093674341 title "Non-positive-partial-transpose subspaces can be as large as any entangled subspace" @default.
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• W2093674341 doi "https://doi.org/10.1103/physreva.87.064302" @default.
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