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Journal of Physics Conference Series

A study of two qubits system with Quantum operator formalism

S Thammasuwan, A. Limphirat, C C Chen, Yiying Yan

Published Dec 1, 2018• 0 citations
Publisher

Abstract

An open system consists of the decay of the excited states of two two-level atoms due to the stimulated emission of photons is studied in a quantum operator formalism, the approach of Kraus operators.We have constructed in the work the Kraus operators which will be applied to derive the time evolution of the density matrix for analyzing the stability of the entanglement of two qubits system.

DOI
10.1088/1742-6596/1144/1/012037

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An open system consists of the decay of the excited states of two two-level atoms due to the stimulated emission of photons is studied in a quantum operator formalism, the approach of Kraus operators.We have constructed in the work the Kraus operators which will be applied to derive the time evolution of the density matrix for analyzing the stability of the entanglement of two qubits system.
The necessity and utility of considering the interaction of a quantum system with its environment when describing its time evolution have been recognized in several branches of physics and of other sciences. The Kraus' representation is a general and succinct approach to describe such open system dynamics in a wide range of relevant physical scenarios. In this article, by abdicating from the generality of the formalism of quantum operations and with this avoiding its associated complications, we show in a simple manner how we can obtain the Kraus' representation using basically the closed system (system plus environment) unitary dynamics and the partial trace function. The example of a two-level atom interacting with the vacuum of the electromagnetic field is regarded for the sake of instantiating this formalism, which is then applied to study the time evolution of the atom's quantum coherence.
We propose a way to understand the evolution of an open quantum system using a description that dispenses a continuous evolution in time, by discrete operators entangled states, in its most direct and fundamental way. We show that the successive application of these operators in very small time intervals reproduce continuous evolution. It describes and compares the temporal evolution of an open quantum system of three levels, for which the Lindblad equation is solved to obtain the density matrix function of time, a method is developed to find Kraus operators time dependent and also finds constant Kraus operators differentials operate computationally $ n $ times evolving in discrete-time $ Δt = τ= t / n $. It is seen in the example of atom cavity inside a reservoir that by calculating the distance and the relative error we define is a relationship with the evolution of discrete steps and physical variables as $ ω$ which presuppose a natural discretization found time.
We study the entanglement dynamics of multi-qubit systems coupled to a common dissipative environment, focusing on systems with one or two initially excited qubits. Using the Lindblad master equation, we derive the time evolution of the density matrix and analyze the entanglement between qubit pairs via the concurrence measure. The solution method involves applying the Lindblad super-operator to the initial density matrix, generating a subspace of non-duplicate states. We extend our analysis to nnn-qubit systems, including three-qubit and four-qubit configurations, and explore the effects of thermal noise on entanglement dynamics. Our results demonstrate how initial conditions, system size, and environmental interactions shape entanglement, providing valuable insights for quantum information processing applications.
For a system of two spatially separated qubits (two-level atoms) coupled to a one-dimensional waveguide we have described the time evolution of singly or doubly excited states of the atomic subsystem. When the interatomic distance lll takes special (``resonant'' or ``antiresonant'') values, the singly excited system of resonant atoms can form metastable (dark) states. If lll slightly deviates from one of the special values or the atomic frequencies do not coincide, the dark states slowly decay and we have calculated the decay rate. Also, we have found that the doubly excited state of two resonant atoms located at the special positions does not completely decay but, with a finite probability, can evolve (with the emission of a single photon) to one of the metastable singly excited states. Metastable states of pairs of qubits may find applications (e.g., as memory elements) in information processing or as detectors sensitive to external perturbations.
We set up the fermionic thermal entangled state approach to address Fermi operator master equations for the amplitude- and phase-decay processes and find the explicit Kraus operator-sum representations (KOSR) describing time-evolution of Fermi systems. As an application of KOSR, the evolution law of the two-level atomic system interacting with a photon field in these two decay processes is analytically derived, which shows that the interaction system has a quantum jump as a result of dissipation, but it always remains unchanged in the phase-decay process.