Heisenberg-Weyl Observables: Bloch vectors in phase space
arXiv:1512.05640 · doi:10.1103/PhysRevA.94.010301
Abstract
We introduce a Hermitian generalization of Pauli matrices to higher dimensions which is based on Heisenberg-Weyl operators. The complete set of Heisenberg-Weyl observables allows us to identify a real-valued Bloch vector for an arbitrary density operator in discrete phase space, with a smooth transition to infinite dimensions. Furthermore, we derive bounds on the sum of expectation values of any set of anti-commuting observables. Such bounds can be used in entanglement detection and we show that Heisenberg-Weyl observables provide a first non-trivial example beyond the dichotomic case.
10 pages, 1 figure. Closed to the published version
References in corpus (16)
- Entanglement detection
- Contextuality supplies the magic for quantum computation
- Bloch vectors for qudits
- Detecting Genuine Multipartite Entanglement with Two Local Measurements
- Entanglement Detection in the Stabilizer Formalism
- Entangled Bloch Spheres: Bloch Matrix and Two Qubit State Space
- Observation of quantum interference between separated mechanical oscillator wavepackets
- Entangled Singularity patterns of Photons in Ince-Gauss modes
- Further results on entanglement detection and quantification from the correlation matrix criterion
- Characterizing multipartite entanglement without shared reference frames
- Entropic uncertainty from effective anti-commutators
- Permutation Symmetry Determines the Discrete Wigner Function
- A composite parameterization of unitary groups, density matrices and subspaces
- Genuine Multipartite Entanglement without Multipartite Correlations
- Contextuality in phase space
- Discrete Fourier-based Correlations for Entanglement Detection
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