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Re ection symmetries for multiqubit density operators Claudio Alta ni

Summary: Re ection symmetries for multiqubit density operators
Claudio Alta ni
International School for Advanced Studies
via Beirut 2-4, 34014 Trieste, Italy
Timothy F. Havel
Dept. of Nuclear Eng.
MIT, 150 Albany St.
Cambridge, MA 02139-4307
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 classi able as re ection
symmetries, i.e., orientation changing rotations. While one-qubit 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 well-posed
only for suĂciently 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 suĂciently
mixed states.
PACS numbers: 03.65.Ud, 03.67.Mn, 03.67.-a
The Wigner Theorem aĂrms that unitary and antiuni-


Source: Altafini, Claudio - Functional Analysis Sector, Scuola Internazionale Superiore di Studi Avanzati (SISSA)


Collections: Engineering; Mathematics