 
Summary: Re
ection symmetries for multiqubit density operators
Claudio Altani
SISSAISAS
International School for Advanced Studies
via Beirut 24, 34014 Trieste, Italy
Timothy F. Havel
Dept. of Nuclear Eng.
MIT, 150 Albany St.
Cambridge, MA 021394307
For multiqubit density operators in a suitable tensorial basis, we show that a number of nonuni
tary operations used in the detection and synthesis of entanglement are classiable as re
ection
symmetries, i.e., orientation changing rotations. While onequbit re
ections correspond to antiuni
tary symmetries, as is known for example from the partial transposition criterion, re
ections on the
joint density of two or more qubits are not accounted for by the Wigner Theorem and are wellposed
only for suÆciently mixed states. One example of such nonlocal re
ections 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 suÆciently
mixed states.
PACS numbers: 03.65.Ud, 03.67.Mn, 03.67.a
The Wigner Theorem aÆrms that unitary and antiuni
