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Tensor representation of spin States.

O Giraud1, D Braun2, D Baguette3

  • 1LPTMS, CNRS and Université Paris-Sud, UMR 8626, Bâtiment 100, 91405 Orsay, France.

Physical Review Letters
|March 14, 2015
PubMed
Summary

We introduce a new tensor representation for arbitrary spin states, generalizing the Bloch sphere. This method simplifies handling spin density matrices and offers a criterion for anticoherence relevant to quantum optics.

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Area of Science:

  • Quantum mechanics
  • Quantum information theory
  • Tensor analysis

Background:

  • The Bloch sphere is a standard representation for single-qubit states.
  • Generalizing this representation to arbitrary spin states and density matrices is challenging.
  • Existing methods may lack compactness or straightforward transformation properties.

Purpose of the Study:

  • To generalize the Bloch sphere representation for arbitrary spin states.
  • To develop a compact and elegant tensor-based representation for spin density matrices.
  • To establish a criterion for anticoherence applicable to quantum polarization of light.

Main Methods:

  • Utilizing covariant matrices from quantum field theory (Weinberg).
  • Developing a tensor representation that mimics Bloch vector properties.
  • Applying the representation to parametrize coherent spin states and transform density matrices.

Main Results:

  • A generalized Bloch sphere representation using tensors for arbitrary spin states.
  • The tensor representation shares key properties with Bloch vectors.
  • A straightforward method for transforming density matrices under local unitary and partial tracing operations.
  • A criterion for anticoherence derived from the new representation.

Conclusions:

  • The proposed tensor representation offers a powerful tool for analyzing arbitrary spin states.
  • This generalization simplifies complex quantum spin manipulations.
  • The anticoherence criterion has implications for quantum polarization phenomena.