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arXiv:0802.1596 · International Journal of Quantum Information

COHERENCE CONSERVATION OF A QUBIT COUPLED TO A DISSIPATING THERMAL ENVIRONMENT

ROBABEH RAHIMI, AKIRA SAITOH, MIKIO NAKAHARA

Published Jul 1, 2008• 0 citations
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Abstract

It is shown that quantum coherence is conserved in a principal system in the case that the system is coupled to a fast dissipating environment [arXiv:0709.0562]. The phenomenon is called the quantum wipe effect. Here, this effect is reviewed and the analytical proof for a model system consisting of a one-qubit system coupled to a fast dissipating environment is extended to an environment at a thermal equilibrium.

DOI
10.1142/s0219749908004109

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It is shown that quantum coherence is conserved in a principal system in the case that the system is coupled to a fast dissipating environment [arXiv:0709.0562]. The phenomenon is called the quantum wipe effect. Here, this effect is reviewed and the analytical proof for a model system consisting of a one-qubit system coupled to a fast dissipating environment is extended to an environment at a thermal equilibrium.
Quantum coherence conservation is shown to be achieved by a very high rate of dissipation of an environmental system coupled with a principal system. This effect is not in the list of previously-known strategies of noise suppression, such as Zeno effect, dynamical decoupling, quantum error correction code, and decoherence free subspace. An analytical solution is found for a simplified model of a single qubit coupled with an environmental single qubit dissipating rapidly. We also show examples of coherence conservation in a spin-boson linear coupling model with a numerical evaluation.
We consider a particularly simple exactly solvable model for a qubit coupled to sequentially nested environments. The purpose is to exemplify the coherence conserving effect of a central system, that has been reported as a result of increasing the coupling between near and far environment. The paradigmatic example is the Jaynes–Cummings Hamiltonian, which we introduce into a Kossakowski–Lindblad master equation using alternatively the lowering operator of the oscillator or its number operator as Lindblad operators. The harmonic oscillator is regarded as the near environment of the qubit, while effects of a far environment are accounted for by the two options for the dissipative part of the master equation. The exact solution allows us to cover the entire range of coupling strength from the perturbative regime to strong coupling analytically. The coherence conserving effect of the coupling to the far environment is confirmed throughout.
Cooperative effects in the loss (the amplitude damping) and decoherence (the phase damping) of the qubits (two-state quantum systems) due to the inevitable coupling to the same environment are investigated. It is found that the qubits undergo the dissipation coherently in this case. In particular, for a special kind of input states (called the coherence-preserving states), whose form depends on the type of the coupling, loss and decoherence in quantum memory are much reduced. Based on this phenomenon, a scheme by encoding the general input states of the qubits into the corresponding coherence-preserving states is proposed for reducing the cooperative loss and decoherence in quantum computation or communication.
The decoherence of entanglement of two-qubit states is investigated by means of the non-Markovian quantum master equation. It is assumed that the decoherence is caused by environmental systems in non-stationary states, which evolve from initial states into equilibrium states. In this case, the non-Markovian nature of the environmental systems is of essential importance. It is shown that the disentanglement time after which there is no qubit entanglement is determined by the non-Markovian effect and the thermal effect of the environmental systems.
In this paper, we provide an analytical investigation of the entanglement dynamics of moving qubits dissipating into a common and (in general) non-Markovian environment for both weak and strong coupling regimes. We first consider the case of two moving qubits in a common environment and then generalize it to an arbitrary number of moving qubits. Our results show that when the system evolves from an initial entangled state, the amount of initial entanglement decreases and finally disappears after a finite interval of time due to the environmental effects. Moreover, we observe that the movement of qubits has a constructive role in the protection of the initial entanglement. In a sense, in this case, we observe a Zeno-like effect due to the velocity of qubits. On the other hand, we demonstrate how a stationary state of entanglement may be achieved when we consider the case in which at least one of the moving qubits is initially in the ground state. Surprisingly, we observe that when we extend the number of moving qubits with the same velocity, the stationary state of the qubits does not depend on the velocity of qubits as well as on the environmental properties. This means that, in this condition, the stationary state of entanglement depends only on the number of moving qubits.
Decoherence induced by coupling a system with an environment may display universal features. We demonstrate that when the coupling to the system drives a quantum phase transition in the environment, the decay of quantum coherences in the system is Gaussian with a width independent of the system-environment coupling strength. We obtain analytical results for a class of solvable models, and present numerical evidence supporting the validity of our results in more general cases. This effect opens the way for a quantum simulation algorithm, where a single qubit is used to detect a quantum phase transition. We discuss possible implementations of such an algorithm and relate our results to available data on universal decoherence in NMR echo experiments.