Bloch vectors for qudits

By Reinhold A. Bertlmann, Philipp Krammer. 2008

415 citations recorded by the source corpus.

We present three different matrix bases that can be used to decompose density matrices of d-dimensional quantum systems, so-called qudits: the generalized Gell–Mann matrix basis, the polarization operator basis and the Weyl operator basis. Such a decomposition can be identified with a vector—the Bloch vector, i.e. a generalization of the well-known qubit case—and is a convenient expression for comparison with measurable quantities and for explicit calculations avoiding the handling of large matrices. We present a new method to decompose density matrices via so-called standard matrices, consider the important case of an isotropic two-qudit state and decompose it according to each basis. In the case of qutrits we show a representation of an entanglement witness in terms of expectation values of spin-1 measurements, which is appropriate for an experimental realization.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/ee0b0ee3476c4c919eb7e081604bdd0788b7fe02

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In Artificial Intelligence

1. Mehul Malik
2. Giuseppe Vitagliano
3. Marcus Huber
4. Nicolai Friis

In Atomic and Molecular Physics, and Optics

1. Mehul Malik
2. Giuseppe Vitagliano
3. Marcus Huber
4. Nicolai Friis

Citations in the corpus

• Entanglement certification from theory to experiment (2018, background): “[114] Reinhold A.”