Generalized Kraus operators for the one-qubit depolarizing quantum channel

Microscopic Hamiltonian models of the composite system "open system + environment" typically do not provide the operator-sum Kraus form of the open system's dynamical map. With the use of a recently de- veloped method [16], we derive the Kraus operators starting from the mi- croscopic Hamiltonian model, i.e. from the proper master equation, of the one-qubit depolarizing channel. Those Kraus operators generalize the stan- dard counterparts, which are widely used in the literature. Comparison of the standard and the here obtained Kraus operators is performed via inves- tigating dynamical change of the Bloch sphere volume, entropy production and the open system's state trace distance. We find that the standard depo- larizing channel is more deteriorating than the generalized one.Comment: 17 pages, 6 figures, aaccepted for publication in Brazilian Journal of Physics, in pres

Complete positivity on the subsystems level

We consider complete positivity of dynamics regarding subsystems of an open composite quantum system, which is subject of a completely positive dynamics. By "completely positive dynamics", we assume the dynamical maps called the completely positive and trace preserving maps, with the constraint that domain of the map is the whole Banach space of the system's density matrices. We provide a technically simple and conceptually clear proof for the subsystems' completely positive dynamics. Actually, we prove that every subsystem of a composite open system can be subject of a completely positive dynamics if and only if the initial state of the composite open system is tensor-product of the initial states of the subsystems. An algorithm for obtaining the Kraus form for the subsystem's dynamical map is provided. As an illustrative example we consider a pair of mutually interacting qubits. The presentation is performed such that a student with the proper basic knowledge in quantum mechanics should be able to reproduce all the steps of the calculations.Comment: revised ms, improved presentation, 18 pages, no tables or figure

Kraus operators for a pair of interacting qubits: a case study

The Kraus form of the completely positive dynamical maps is appealing from the mathematical and the point of the diverse applications of the open quantum systems theory. Unfortunately, the Kraus operators are poorly known for the two-qubit processes. In this paper, we derive the Kraus operators for a pair of interacting qubit, while the strength of the interaction is arbitrary. One of the qubits is subjected to the x-projection spin measurement. The obtained results are applied to calculate the dynamics of the initial entanglement in the qubits system. We obtain the loss of the correlations in the finite time interval; the stronger the inter-qubit interaction, the longer lasting entanglement in the system.Comment: 13 pages, 2 figure