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Entanglement groups
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abstract
We propose to define entanglement in terms of local unitary transformations acting on some parts of a system that can be undone by local unitary transformations acting on other parts. This leads to a characterization of entanglement in terms of groups. We refer to these as entanglement groups, and we refer to this notion as $g$-entanglement. We discuss the physical meaning of entanglement groups and contrast $g$-entanglement with other, more conventional definitions of entanglement. For pure states, entanglement groups are constructed as certain quotients of the stabilizer group and its subgroups. For mixed states, entanglement groups can be constructed from stabilizers of the purification. We analyze the structure of entanglement groups, show that they have properties which correspond to monogamy of entanglement, and explore the restrictions placed by separability. We show that $g$-entanglement underlies several well-known quantum tasks.
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Entanglement groups for mixed states
For mixed quantum states, entanglement can be characterized by a quotient group of local unitary stabilizers of the density matrix, and any nontriviality for separable states must come from multipartite entanglement w...
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