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Dynamics of entanglement and decoherence in simple two-qubit systems

Carlos A. González-Gutiérrez, R. Román-Ancheyta, Diego Espitia

Published Apr 16, 2016• 0 citations
OpenAlex

Abstract

Using simple models of radiation-matter interaction we study the reduced dynamics of a quantum central system formed by two qubits under the spectator configuration. Purity and concurrence as measures of decoherence and entanglement are evaluated in analytical form. Interestingly in these systems, entanglement sudden death is found despite having less complex dynamics than models used in previous studies. Furthermore, we have analysed the associated local quantum operations generated by the dynamics and how their action on an initial Bell state is characterized in the concurrence-purity diagram.

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Using simple models of radiation-matter interaction we study the reduced dynamics of a quantum central system formed by two qubits under the spectator configuration. Purity and concurrence as measures of decoherence and entanglement are evaluated in analytical form. Interestingly in these systems, entanglement sudden death is found despite having less complex dynamics than models used in previous studies. Furthermore, we have analysed the associated local quantum operations generated by the dynamics and how their action on an initial Bell state is characterized in the concurrence-purity diagram.
Knowledge of the relationships among different features of quantumness, like entanglement and state purity, is important from both fundamental and practical viewpoints. Yet, this issue remains little explored in dynamical contexts for open quantum systems. We address this problem by studying the dynamics of entanglement and purity for two-qubit systems using paradigmatic models of radiation-matter interaction, with a qubit being isolated from the environment (spectator configuration). We show the effects of the corresponding local quantum channels on an initial two-qubit pure entangled state in the concurrence–purity diagram and find the conditions which enable dynamical closed formulas of concurrence, used to quantify entanglement, as a function of purity. We finally discuss the usefulness of these relations in assessing entanglement and purity thresholds which allow noisy quantum teleportation. Our results provide new insights about how different properties of composite open quantum systems behave and relate each other during quantum evolutions.
We study decoherence of one, two, and nnn non-interacting qubits. Decoherence, measured in terms of purity, is calculated in linear response approximation, making use of the spectator configuration. The environment and its interaction with the qubits are modelled by random matrices. For two qubits, numerical studies reveal a simple one to one correspondence between its decoherence and its internal entanglement decay. Using this relation we are able to give a formula for concurrence decay. For large environments the evolution induces a unital channel in the two qubits, providing a partial explanation for the relation above. Using a kicked Ising spin network, we study the exact evolution of two non-interacting qubits in the presence of a spin bath. We find that the entanglement (as measured by concurrence) of the two qubits has a close relation to the purity of the pair, and closely follows an analytic relation derived for Werner states. As a collateral result we find that an integrable environment causes quadratic decay of concurrence as well as of purity, while a chaotic environment causes linear decay. Both quantities display recurrences in some integrable environments. Good agreement with the results found using random matrix theory is obtained. Finally, we analyze decoherence of a quantum register in the absence of non-local operations. The problem is solved in terms of a sum rule which implies linear scaling in the number of qubits. Each term involves a single qubit and its entanglement with the remaining ones. Two conditions are essential: decoherence must be small and the coupling of different qubits must be uncorrelated in the interaction picture. We apply the result to the random matrix model, and illustrate its reach considering a GHZ state coupled to a spin bath.
The reduced dynamics of a single qubit or two qubits coupled to an interacting quantum spin bath modeled by an XXZXXZXXZ spin chain is investigated. By using the method of a time-dependent density matrix renormalization group (t-DMRG)(t\text{-DMRG})(t-DMRG), we go beyond the uniform coupling central spin model and nonperturbatively evaluate the induced decoherence and entanglement. It is shown that both the decoherence and the entanglement strongly depend on the phase of the underlying spin bath. We show that in general, spin baths can induce entanglement for an initially disentangled pair of qubits. Furthermore, when the spin bath is in the ferromagnetic phase because the qubits directly couple to the order parameter, the reduced dynamics shows an oscillatory type behavior. On the other hand, only for the paramagnetic and the antiferromagnetic phases do the initially entangled states suffer from an entanglement sudden death. By calculating the concurrence, the finite disentanglement time is mapped out for all of the phases in the phase diagram of the spin bath.
We examine the influence of environmental interactions on simple quantum systems by obtaining the exact reduced dynamics of a qubit coupled to a one-dimensional spin bath. In contrast to previous studies, both the qubit-bath coupling and the nearest-neighbor intrabath couplings are taken as the spin-flip XXXXXX type. We first study the Rabi oscillations of a single qubit with the spin bath prepared in a spin coherent state, finding that nonresonance and finite intrabath interactions have significant effects on the qubit dynamics. Then we discuss the bath-induced decoherence of the qubit when the bath is initially in the ground state and show that the decoherence properties depend on the internal phases of the spin bath. By considering two independent copies of the qubit-bath system, we finally probe the disentanglement dynamics of two noninteracting entangled qubits. We find that entanglement sudden death appears when the spin bath is in its critical phase. We show that the single-qubit decoherence factor is an upper bound for the two-qubit concurrence.
We investigate the entanglement dynamics of the bipartite quantum system between two qubits with the dissipative environment. We begin with the standard Markovian master equation in the Lindblad form and the initial state which is prepared in the extended Werner-like state: ρ Φ AB (0). We examine the conditions for entanglement sudden death (ESD) and calculate the corresponding ESD time by the Wootters concurrence. We observe that ESD is determined by the parameters such as the mean occupation number of the environment N , amount of initial entanglement α and the purity r . For N = 0, we get the analytical expressions of both ESD condition and ESD time. For N > 0 we give a theoretical analysis that ESD always occurs, and simulate the concurrence as a function of γ 0 t and one of the parameters N , α and r .