Geometric phase as a determinant of a qubit--environment coupling

We investigate the qubit geometric phase and its properties in dependence on the mechanism for decoherence of a qubit weakly coupled to its environment. We consider two sources of decoherence: dephasing coupling (without exchange of energy with environment) and dissipative coupling (with exchange of energy). Reduced dynamics of the qubit is studied in terms of the rigorous Davies Markovian quantum master equation, both at zero and non--zero temperature. For pure dephasing coupling, the geometric phase varies monotonically with respect to the polar angle (in the Bloch sphere representation) parameterizing an initial state of the qubit. Moreover, it is antisymmetric about some points on the geometric phase-polar angle plane. This is in distinct contrast to the case of dissipative coupling for which the variation of the geometric phase with respect to the polar angle typically is non-monotonic, displaying local extrema and is not antisymmetric. Sensitivity of the geometric phase to details of the decoherence source can make it a tool for testing the nature of the qubit--environment interaction.Comment: accepted for publication in Quantum Information Processin

Exact solution of the Schrodinger equation with the spin-boson Hamiltonian

We address the problem of obtaining the exact reduced dynamics of the spin-half (qubit) immersed within the bosonic bath (enviroment). An exact solution of the Schrodinger equation with the paradigmatic spin-boson Hamiltonian is obtained. We believe that this result is a major step ahead and may ultimately contribute to the complete resolution of the problem in question. We also construct the constant of motion for the spin-boson system. In contrast to the standard techniques available within the framework of the open quantum systems theory, our analysis is based on the theory of block operator matrices.Comment: 9 pages, LaTeX, to appear in Journal of Physics A: Mathematical and Theoretica

Temperature-independent teleportation of qubits in Davies environments

A quantum channel teleporting qubits from Alice to Bob is considered in which the bipartite resource state shared by Alice and Bob is affected by bilocal thermal noise treated in rigorous Davis approximation. Specific conditions are identified where the fidelity of the teleportation channel can be either independent of temperature or even enhanced by the temperature of the environment

Quantum cloning disturbed by thermal Davies environment

A network of quantum gates designed to implement universal quantum cloning machine is studied.We analyze how thermal environment coupled to auxiliary qubits, ‘blank paper’ and ‘toner’ required at the preparation stage of copying, modifies an output fidelity of the cloner. Thermal environment is described in terms of the Markovian Davies theory. We show that such a cloning machine is not universal any more but its output is independent of at least a part of parameters of the environment. As a case study, we consider cloning of states in a six-state cryptography’s protocol. We also briefly discuss cloning of arbitrary input states

Quantum two player game in thermal environment

A two-player quantum game is considered in the presence of thermal decoherence. It is shown how the thermal environment modeled in terms of rigorous Davies approach affects payoffs of the players. The conditions for either beneficial or pernicious effect of decoherence are identified. The general considerations are exemplified by the quantum version of Prisoner Dilemm

Payoffs and coherence of a quantum two-player game in a thermal environment

A two-player quantum game is considered in the presence of a thermal decoherence modeled in terms of a rigorous Davies approach. It is shown how the energy dissipation and pure decoherence affect the payoffs of the players of the (quantum version) of prisoner dilemma. The impact of the thermal environment on a coherence of game, as a quantum system, is also presented

Faint trace of a particle in a noisy Vaidman three-path interferometer

We study weak traces of particle passing Vaidman’s nested Mach–Zehnder interferometer. We investigate an effect of decoherence caused by an environment coupled to internal degree of freedom (a spin) of a travelling particle. We consider two models: pure decoherence leading to exact results and weak coupling Davies approximation allowing to include dissipative effects. We show that potentially anomalous discontinuity of particle paths survives an effect of decoherence unless it affects internal part of the nested interferometer

Łamanie nierówności Leggetta-Garga w otwartych układach kwantowych

Pełny tekst artykułu nr 3, dołączonego do rozprawy, dostępny jest lokalnie w sieci bibliotek Uniwersytetu Śląskiego: http://www.bc.us.edu.pl/publication/16367This dissertation concerns an analysis of obtained theoretical values of temporal correlation functions in open quantum systems in the context of Leggett-Garg inequalities. The violation of these inequalities indicates that a system reveals non-classical correlations. A special case of the temporal correlations, analysed in this work, are used to tests of macrorealism, likewise as an indicator of the “quantumness” of a system or in order to perform the quantum information protocols. Despite of the well grounded results on the temporal quantum correlations in isolated systems, the open systems are still barely explored. The main motivation to study this subject is a possibility to obtain better models of real physical systems and to develop new methods to control the amount of the non-classical correlations. The main research objective is to establish an influence on the amount of the non-classical correlations in the measured subsystem by a coupling with the environment. In this work, four distinct physical models of open quantum systems are presented. In the first one there is revealed a violation of Leggett-Garg inequality in the system weakly coupled to thermal environment where especially is discussed the process of decoherence and dissipation. The main result is an observation that, under some conditions, the violation of the inequality is independent of environment properties like temperature. The second model concerns an analysis of temporal quantum correlations in the systems that dynamics is governed by the angular momentum operators and driven by classical white noise. In this case strict analytical results reveal an exponential dumping of the non-classical correlations as well as a property that such dumping can be less effective for systems with larger state space. The last but not least two models for which is calculated the Leggett-Garg correlator are the systems which interact with the environment due to the spin-spin coupling. In this context, a physical model of atoms from the first group of the periodic table and a model of quantum-classical hybrids, for which is discussed the semi-classical approach, is proposed. In both examples it is proven that for “more macroscopic” systems as well as for “classical environments”, it is possible to observe higher violation of the Leggett-Garg inequality