Reflection Symmetries for Multiqubit Density Operators
arXiv:quant-ph/0405123 · doi:10.1063/1.2181827
Abstract
For multiqubit density operators in a suitable tensorial basis, we show that a number of nonunitary operations 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 partial 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.
9 pages
References in corpus (7)
- The Bloch Vector for N-Level Systems
- Characterization of the Positivity of the Density Matrix in Terms of the Coherence Vector Representation
- Controllability properties for finite dimensional quantum Markovian master equations
- Entanglement, Mixedness, and Spin-Flip Symmetry in Multiple-Qubit Systems
- A multi-photon Stokes-parameter invariant for entangled states
- Tensor of coherences parameterization of multiqubit density operators for entanglement characterization
- Representing multiqubit unitary evolutions: spin coherences and infinitesimal coherences