Entanglement production by statistical operators

V. I. Yukalov, E. P. Yukalova, V. A. Yurovsky

Research output: Contribution to journalArticlepeer-review


In the problem of entanglement there exist two different notions. One is the entanglement of a quantum state, characterizing the state structure. The other is entanglement production by quantum operators, describing the action of operators in the given Hilbert space. Entanglement production by statistical operators, or density operators, is an important notion arising in quantum measurements and quantum information processing. The operational meaning of the entangling power of any operator, including statistical operators, is the property of the operators to entangle wave functions of the Hilbert space they are defined on. The measure of entanglement production by statistical operators is described and illustrated by entangled quantum states, equilibrium Gibbs states, as well as by the state of a complex multiparticle spinor system. It is shown that this measure is in intimate relation to other notions of quantum information theory, such as the purity of quantum states, linear entropy, or impurity, inverse participation ratio, quadratic Rényi entropy, the correlation function of composite measurements, and decoherence phenomenon. This measure can be introduced for a set of statistical operators characterizing a system after quantum measurements. The explicit value of the measure depends on the type of the Hilbert space partitioning. For a general multiparticle spinor system, it is possible to accomplish the particle-particle partitioning or spin-spatial partitioning. Conditions are defined showing when entanglement production is maximal and when it is zero. The study on entanglement production by statistical operators is important because, depending on whether such an operator is entangling or not, it generates qualitatively different probability measures, which is principal for quantum measurements and quantum information processing.

Original languageEnglish
Article number065502
JournalLaser Physics
Issue number6
StatePublished - 16 Apr 2019


  • Hilbert space partitioning
  • entanglement production
  • spinor atoms
  • statistical operators


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