## Reflection symmetries for multiqubit densities

### Claudio Altafini and Timothy F. Havel

*Journal of Mathematical Physics *, 47, 032104, 2006.

For multiqubit density operators in a suitable tensorial basis, we show that a number of nonunitary oper
ations used in the detection and synthesis of entanglement are classifiable as reflection symmetries, i.
e., orientation changing rotations.
While one-qubit reflections correspond to antiunitary symmetries, as is known for example from the parti
al transposition criterion, reflections on the joint density of two or more qubits are not accounted for
by the Wigner Theorem and are well-posed only for sufficiently mixed states.
One example of such nonlocal reflections is the unconditional NOT operation on a multiparty density, i.e
., an operation yelding another density and such that the sum of the two is the identity operator. This
nonphysical operation is admissible only for sufficiently mixed states.

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