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Embedded Spin Disentanglement and Decoherence via Dephasing

Ting Yu, Joseph H. Eberly

Published May 14, 2003• 0 citations
OpenAlex

Abstract

It has been demonstrated in various ways, if not rigorously proven, that when a quantum system and an environment interact they become entangled extremely rapidly and are essentially impossible to disentangle. Another interesting matter has received little attention, namely whether non-local entanglement between small systems is more or less susceptible to rapid decay than local measures of system coherence. An instance of potential importance for solid state quantum computing arises if embedded qubit spins are exposed to both global and local noise at the same time. Here we show that phase-noisy channels affect local and non-local measures of system coherence differently. A consequence is that the time for entanglement decay can be significantly shorter than the time for complete local dephasing for two qubits.

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It has been demonstrated in various ways, if not rigorously proven, that when a quantum system and an environment interact they become entangled extremely rapidly and are essentially impossible to disentangle. Another interesting matter has received little attention, namely whether non-local entanglement between small systems is more or less susceptible to rapid decay than local measures of system coherence. An instance of potential importance for solid state quantum computing arises if embedded qubit spins are exposed to both global and local noise at the same time. Here we show that phase-noisy channels affect local and non-local measures of system coherence differently. A consequence is that the time for entanglement decay can be significantly shorter than the time for complete local dephasing for two qubits.
We consider whether quantum coherence in the form of mutual entanglement between a pair of qubits is susceptible to decay that may be more rapid than the decay of the coherence of either qubit individually. An instance of potential importance for solid-state quantum computing arises if embedded qubits (spins, quantum dots, Cooper pair boxes, etc.) are exposed to global and local noise at the same time. Here we allow separate phase-noisy channels to affect local and nonlocal measures of system coherence. We find that the time for decay of the qubit entanglement can be significantly shorter than the time for local dephasing of the individual qubits.
One of the main obstacles toward building efficient quantum computing systems is decoherence, where the inevitable interaction between the qubits and the surrounding environment leads to a vanishing entanglement. We consider a system of two interacting asymmetric two-level atoms (qubits) in the presence of pure and correlated dephasing environments. We study the dynamics of entanglement while varying the interaction strength between the two qubits, their relative frequencies, and their coupling strength to the environment starting from different initial states of practical interest. The impact of the asymmetry of the two qubits, reflected in their different frequencies and coupling strengths to the environment, varies significantly depending on the initial state of the system and its degree of anisotropy. For an initial disentangled, or a Werner, state, as the difference between the frequencies increases, the entanglement decay rate increases, with more persistence at the higher degrees of anisotropy in the former state. However, for an initial anti-correlated Bell state, the entanglement decays more rapidly in the symmetric case compared with the asymmetric one. The difference in the coupling strengths of the two qubits to the pure (uncorrelated) dephasing environment leads to higher entanglement decay in the different initial state cases, though the rate varies depending on the degree of anisotropy and the initial state. Interestingly, the correlated dephasing environment, within a certain range, was found to enhance the entanglement dynamics starting from certain initial states, such as the disentangled, anti-correlated Bell, and Werner, whereas it exhibits a decaying effect in other cases such as the initial correlated Bell state.
We study the time evolution of two two-state systems (two qubits) initially in the pure entangled states or the maximally entangled mixed states interacting with the individual environmental noise. It is shown that due to environment noise, all quantum entangled states are very fragile and become a classical mixed state in a short-time limit. But the environment can affect entanglement in very different ways. The type of decoherence process for certain entangled states belongs to amplitude damping, while the others belong to dephasing decoherence.
We compare disentanglement and decoherence rates within two-spin and three-spin entangled systems subjected to all possible combinations of local and collective pure dephasing noise combinations. In all cases, the bipartite entanglement decay rate is found to be greater than or equal to the dephasing-decoherence rates and often significantly greater. This sharpens previous results for two-spin systems [T. Yu and J. H. Ebenly Phys. Rev. B 68, 165322 (2003)] and extends them to the three-spin context.
Decoherence and disentanglement are phenomena central to quantum mechanics. Here, we consider the relative rates of decoherence and disentanglement in two‐qubit, three‐qubit, and two‐qutrit systems when subject to pure dephasing noise alone, and a very recent result for d×d systems. Of particular interest is the specific counterintuitive effect related to the nonadditivity of such weak noises, known as Entanglement Sudden Death (ESD), in which the entanglement of a composite quantum system goes abruptly to zero in finite time, coherence only exponentially decaying. We discuss these results in the context of the foundations of quantum mechanics.
We study the robustness and fragility of entanglement of open quantum systems in some exactly solvable models in which the decoherence is caused by a pure dephasing process. In particular, for the toy models presented in this paper, we identify two different time scales, one is responsible for local dephasing, while the other is for entanglement decay. For a class of fragile entangled states defined in this paper, we find that the entanglement of two qubits, as measured by concurrence, decays faster asymptotically than the quantum dephasing of an individual qubit.