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Journal of Modern Physics

Study of Decoherence of Entangled States Made up of Two Basic States in a Linear Chain of Three Qubits

Gustavo López Velázquez, Gustavo Montes Cabrera

Published Jan 1, 2015• 0 citations
Publisher

Abstract

Using Lindblad approach to study decoherence of quantum systems, we study the decoherence and decay of entangled states, formed by two basic states of a chain of thee qubits. We look on these states for a possible regular dependence on their decay as a function of their energy separation between the basic states under different types of environments. We didn’t find regular or significant dependence on this energy separation for the type of environment considered.

DOI
10.4236/jmp.2015.611172

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Using Lindblad approach to study decoherence of quantum systems, we study the decoherence and decay of entangled states, formed by two basic states of a chain of thee qubits. We look on these states for a possible regular dependence on their decay as a function of their energy separation between the basic states under different types of environments. We didn’t find regular or significant dependence on this energy separation for the type of environment considered.
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We study the phenomenon of decoherence during the operation of one qubit transformation, controlled-not (CNOT) and controlled-controlled-not (C2NOT) quantum gates in a quantum computer model formed by a linear chain of three nuclear spins system. We make this study with different type of environments, and we determine the associated decoherence time as a function of the dissipative parameter. We found that the dissipation parameter to get a well defined quantum gates (without significant decoherence) must be within the range of . We also study the behavior of the purity parameter for these gates and different environments and found linear or quadratic decays of this parameter depending on the type of environments.
The study is focused on the thermal entanglement of spin chains. Chains consisting of two and three qubits are considered. These chains are considered open because they are coupled to bosonic baths at different temperatures. The baths represent the environment. The dynamics of these open systems are examined as are the effects of different parameters - such as bath temperature - on the entanglement of the spins. The measure of entanglement used in these cases is the concurrence. Comparisons are made between a model that assumes a strong spinspin interaction and one that assumes a weak one. In all these cases, analytical solutions for the system dynamics are presented. It is found that at large times, all systems converge to a state that depends only on bath temperature. It is also found that increases in bath temperatures diminish the entanglement between spins and that at high enough temperatures the entanglement vanishes altogether. The time and temperature dependence of the entanglement is different for the two models that are studied.
We study decoherence of two non-interacting qubits. The environment and its interaction with the qubits are modelled by random matrices. Decoherence, measured in terms of purity, is calculated in linear response approximation. Monte Carlo simulations illustrate the validity of this approximation and of its extension by exponentiation. The results up to this point are also used to study one-qubit decoherence. Purity decay of entangled and product states are qualitatively similar though for the latter case it is slower. Numerical studies for a Bell pair as initial state reveal a one to one correspondence between its decoherence and its internal entanglement decay. For strong and intermediate coupling to the environment this correspondence agrees with the one for Werner states. In the limit of a large environment the evolution induces a unital channel in the two qubits, providing a partial explanation for the above relation.
We study decoherence of two non-interacting qubits. The environment and its interaction with the qubits are modelled by random matrices. Decoherence, measured in terms of purity, is calculated in linear response approximation. Monte Carlo simulations illustrate the validity of this approximation and of its extension by exponentiation. The results up to this point are also used to study one qubit decoherence. Purity decay of entangled and product states are qualitatively similar though for the latter case it is slower. Numerical studies for a Bell pair as initial state reveal a one to one correspondence between its decoherence and its internal entanglement decay. For strong and intermediate coupling to the environment this correspondence agrees with the one for Werner states. In the limit of a large environment the evolution induces a unital channel in the two qubits, providing a partial explanation for the relation above.