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arXiv:quant-ph/0703216 · Physical Review B

Disentanglement and decoherence in two-spin and three-spin systems under dephasing

Kevin Ann, Gregg S. Jaeger

Published Mar 9, 2007• 49 citations
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Abstract

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.

DOI
10.1103/physrevb.75.115307

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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.
We relate disentanglement and decoherence rates in a pair of three-level atoms subjected to multi-local and collective pure dephasing noise acting in a preferred basis. The bipartite entanglement decay rate, as bounded from above by the negativity, is found to be greater than or equal to the dephasing-decoherence rates characterized by the decay of off-diagonal elements in the corresponding full density matrix describing the system or the reduced density matrix describing either qutrit, extending previous results for qubit pairs subject to such noise.
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.
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.
By applying a modified conjugate gradient method in the evaluation of three-qubit residual entanglement, the disentanglement of three-qubit states in an amplitude-damping and dephasing environment is investigated numerically. It is found that the decay of tripartite entanglement is faster than bipartite entanglement in the same qubits-noise system, which indicates that multipartite entanglement is more fragile than bipartite entanglement in resisting quantum noises. Similar to the case of a two-qubit system, three-qubit entanglement subject to an open environment may also disappear abruptly (sudden death) or decrease asymptotically, which is dependent on the conditions of the initially entangled quantum state and the properties of quantum noise.
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.