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arXiv:0905.3399 · Journal of Physics B Atomic Molecular and Optical Physics

Decoherence effects in interacting qubits under the influence of various environments

Sumanta Das, G. S. Agarwal

Published Oct 7, 2009• 47 citations
arXivHTMLPDF

Abstract

We study competition between the dissipative and coherent effects in the entanglement dynamics of two qubits. The coherent interactions are needed for designing logic gate operations with systems such as ion traps, semiconductor quantum dots and atoms. We show that the interactions lead to a phenomenon of periodic disentanglement and entanglement between the qubits. The disentanglement is primarily caused by environmental perturbations. The qubits are seen to remain disentangled for a finite time before getting entangled again. We find that the phenomenon is generic and occurs for a wide variety of models of the environment. We present analytical results for the time dependence of concurrence for all the models. The periodic disentanglement and entanglement behaviour is seen to be a precursor to the sudden death of entanglement (ESD) and can happen for environments which do not show ESD for non-interacting qubits. Further we also find that this phenomenon can even lead to delayed death of entanglement for correlated environments.

DOI
10.1088/0953-4075/42/20/205502

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We study competition between the dissipative and coherent effects in the entanglement dynamics of two qubits. The coherent interactions are needed for designing logic gate operations with systems such as ion traps, semiconductor quantum dots and atoms. We show that the interactions lead to a phenomenon of periodic disentanglement and entanglement between the qubits. The disentanglement is primarily caused by environmental perturbations. The qubits are seen to remain disentangled for a finite time before getting entangled again. We find that the phenomenon is generic and occurs for a wide variety of models of the environment. We present analytical results for the time dependence of concurrence for all the models. The periodic disentanglement and entanglement behaviour is seen to be a precursor to the sudden death of entanglement (ESD) and can happen for environments which do not show ESD for non-interacting qubits. Further we also find that this phenomenon can even lead to delayed death of entanglement for correlated environments.
Interaction among the qubits are basis to many quantum logic operations. We report how such inter-qubit interactions can lead to new features, in the form of bright and dark periods in the entanglement dynamics of two qubits subject to environmental perturbations. These features are seen to be precursors to the well known phenomenon of sudden death of entanglement [Yu $&$ Eberly, Phys. Rev. Lett. {\bf 93}, 140404 (2004)] for noninteracting qubits. Further we find that the generation of bright and dark periods are generic and occur for wide varieties of the models of environment. We present explicit results for two popular models.
Interaction among the qubits are basis to many quantum logic operations. We report how such inter-qubit interactions can lead to new features, in the form of bright and dark periods in the entanglement dynamics of two qubits subject to environmental perturbations. These features are seen to be precursors to the well known phenomenon of sudden death of entanglement [Yu $&$ Eberly, Phys. Rev. Lett. {\bf 93}, 140404 (2004)] for noninteracting qubits. Further we find that the generation of bright and dark periods are generic and occur for wide varieties of the models of environment. We present explicit results for two popular models.
We investigate the entanglement dynamics of two interacting qubits in a common vacuum environment. The inevitable environment interaction leads to entanglement sudden death (ESD) in a two qubit entangled state system. The entanglement dynamics can be modified by the use of local unitary operations (quantum gates), applied on the system during its evolution. We show that these operations not only delays or avoids the ESD but also advances the entanglement revival with high concurrence value depending on the time of operation. We have analytically found out different time windows for switching with different quantum gates so that the ESD can be completely avoided in the subsequent evolution of the system. Our result offers practical applications in the field of quantum information processing where the entanglement is a necessary resource.
This thesis is a theoretical study of entanglement dynamics and its control of qubit-qubit and qubit-qutrit systems. In particular, we focus on the decay of entanglement of quantum states interacting with dissipative environments. Qubit-qubit entanglement may vanish suddenly while interacting with statistically independent vacuum reservoirs. Such finite-time disentanglement is called sudden death of entanglement(ESD). We investigate entanglement sudden death of qubit-qubit and qubit-qutrit systems interacting with statistically independent reservoirs at zero- and finite-temperature. It is shown that for zero-temperature reservoirs, some entangled states exhibit sudden death while others lose their entanglement only after infinite time. Thus, there are two possible routes of entanglement decay, namely sudden death and asymptotic decay. We demonstrate that starting with an initial condition which leads to finite-time disentanglement, we can alter the future course of entanglement by local unitary actions. In other words, it is possible to put the quantum states on other track of decay once they are on a particular route of decay. We show that one can accelerate or delay sudden death. However, there is a critical time such that if local actions are taken before that critical time then sudden death can be delayed to infinity. Any local unitary action taken after that critical time can only accelerate or delay sudden death. In finite-temparature reservoirs, we demonstrate that a whole class of entangled states exhibit sudden death. This conclusion is valid if at least one of the reservoirs is at finite-temperature. However, we show that we can still hasten or delay sudden death by local unitary transformations up to some finite time. We also study sudden death for qubit-qutrit systems. Similar to qubit-qubit systems, some states exhibit sudden death while others do not. However, the process of disentanglement can be effected due to existence of quantum interference between excited levels of qutrit. We show that it is possible to hasten, delay, or avoid sudden death by local unitary actions taken later in time.
environment on the entanglement dynamics in non-Markov process. Our results show that the entanglement degree is strongly related with the initial quantum state and the coupling between the qubits and the environment. The interaction between the qubits and the environment suppresses the decay of the entanglement. The sudden death of entanglement (ESD) can be prevented only by using and controlling targeted the interaction model between the different qubits and the environment. We also find the dissipation phenomenon always exists when the qubits system is initially in the maximally entangled mixed states.