Classification of quantum channels of information transfer

Classification of states of quantum channels of information transfer is built on the basis of unreducible representations of qubit state space group of symmetry and properties of density matrix spectrum. It is shown that pure disentangled states form two-dimensional surface, and the reason of state disentanglement is in degeneration of non-zero density matrix eigenvalues. 1 Group of symmetry of Quantum Information Group of symmetry in quantum information theory Q is the group of unitary transformations of qubit state space U(2) (see [1, 2]). In reality important is Lie algebra of quantum information AQ = u(2) generated by operators J3,J+,J−: [J−J+] = 2J3; [J3J±] = ±J±. (1) The report deals with physically substantial consequences of existence of group of symmetry of quantum information. In problems of quantum information one applies term qubit to arbitrary two-level quantum system. Qubit pure state is characterized by state vector – normalized vector |ψ〉: |ψ〉 = cos θ 2 |0〉+ e sin θ 2 |1〉 . (2) Set of state vectors forms a sphere – Poincare sphere in quantum optics, or Bloch sphere in laser physics. Group of unitary transformations U(2) is the group of symmetry of qubit sphere. 2 Information transfer channels Information is obtained through comparison of results of measurements to expected results [4, 5]. In the case of given probability distribution pk for each of k variants of expected results of measurement, value 1 ar X iv :0 71 1. 02 17 v1 [ qu an tph ] 1 N ov 2 00 7