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Physical review. B, Condensed matter

Qubit cross talk and entanglement decay

J. S. Pratt, Joseph H. Eberly

Published Oct 17, 2001• 31 citations
Publisher

Abstract

We study the decohering effect of qubit-qubit interactions on entanglement. Modeling such qubit cross talk by nearest-neighbor exchange interactions, we explore the Heisenberg spin chain as a system in which decoherence occurs dynamically, and we obtain an analytic description of the process. We find expressions for the short-time and long-time transfer and decay of entanglement in a long chain, and examine the role of entanglement propagation as a decoherence mechanism.

DOI
10.1103/physrevb.64.195314

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We study the decohering effect of qubit-qubit interactions on entanglement. Modeling such qubit cross talk by nearest-neighbor exchange interactions, we explore the Heisenberg spin chain as a system in which decoherence occurs dynamically, and we obtain an analytic description of the process. We find expressions for the short-time and long-time transfer and decay of entanglement in a long chain, and examine the role of entanglement propagation as a decoherence mechanism.
The interaction between entangled multi-particle systems with the environment leads to both local dynamics, associated with single-particle dissipation, diffusion, and decay, and to global dynamics, which may provoke the disappearance of entanglement at a finite time [1-6]. This phenomenon may occur even when single-particle decoherence is asymptotic in time, and constitutes yet another distinct trait of entanglement. It has been recently demonstrated, for two qubits under the action of independent environments, using an all-optical setup [7]. In this talk, some of the peculiarities of the dynamics of two-qubit entangled states undergoing decoherence will be reviewed, new features of the experiment realized at the Federal University of Rio de Janeiro [7] will be described, and the extension of these considerations to multi-particle entangled states will be discussed. Scaling laws for the decay of entanglement and its finite-time extinction in multi-particle systems will be discussed.
The phenomenon of quantum entanglement has a very important role in quantum mechanics. Particularly, the quantum spin chain provides a platform for theoretical and experimental investigation of many-body entanglement. In this paper, we investigate time evolution of entanglement in a four-qubit anisotropic Heisenberg XXZ chain with nearest neighboring (NN), the next nearest neighboring (NNN), and the Dzialoshinskii-Moriya (DM) interactions. Calculations of the entanglement evolution of the Werner state carried out in terms of concurrence for selected ranges of control parameters such as DM interaction, frustration, etc. The results show that for the Werner state, DM interaction and the frustration parameters play important roles. Furthermore, results show that the time evolution of the Werner state entanglement may be useful to capture the quantum phase transitions in quantum magnetic systems.
We study decoherence induced on a two-level system coupled to a one-dimensional quantum spin chain. We consider the cases where the dynamics of the chain is determined by the Ising, XYXYXY, or Heisenberg exchange Hamiltonian. This model of quantum baths can be of fundamental importance for the understanding of decoherence in open quantum systems, since it can be experimentally engineered by using atoms in optical lattices. As an example, here we show how to implement a pure dephasing model for a qubit system coupled to an interacting spin bath. We provide results that go beyond the case of a central spin coupled uniformly to all the spins of the bath, in particular showing what happens when the bath enters different phases, or becomes critical; we also study the dependence of the coherence loss on the number of bath spins to which the system is coupled and we describe a coupling-independent regime in which decoherence exhibits universal features, irrespective of the system-environment coupling strength. Finally, we establish a relation between decoherence and entanglement inside the bath. For the Ising and the XYXYXY models we are able to give an exact expression for the decay of coherences, while for the Heisenberg bath we resort to the numerical time-dependent density matrix renormalization group.
The aim of this topical review is a systematic and concise presentation of the results of a series of theoretical works on the quantum dynamics of two-spin-qubit systems towards the elaboration of a physical mechanism of the quantum information transfer between two spin-qubits. For this purpose the main attention is paid to exactly solvable models of two-spin-qubit systems, since the analytical expressions of the elements of their reduced density matrices explicitly exhibit the mutual dependence of the quantum information encoded into the spin-qubits. The treatment of their decoherence due to the interaction with the environment is performed in the Markovian approximation. Rate equations for axially symmetric systems of two coupled spin-qubits non-interacting, as well as interacting, with the environment are exactly solved. It is shown how the solutions of rate equations demonstrate the physical mechanism of the quantum information exchange between the spin-qubits. This mechanism holds also in all two-spin-qubit systems whose rate equations can be solved only by means of numerical calculations. Exact solutions of rate equations for two uncoupled spin-qubits interacting with two separate environments reveal an interesting physical phenomenon in the time evolution of the qubit-qubit entanglement generated by their interaction with the environments: the entanglement sudden death and revival. A two-spin-qubit system with an asymptotically decoherence free subspace was also explicitly constructed. The presented calculations and reasonings can be extended for application to the study of spin-qubit chains or networks.
We study the time evolution of decoherence factor of two spin qubits and qutrits coupled to an XYXYXY spin chain with Dzyaloshinsky-Moriya (DM) interaction environment. The dynamical process of the decoherence is numerically and analytically investigated. We find that the DM interaction can enhance slightly the decay of the decoherence factor in the weak-coupling region. However, in the strong-coupling region, the decoherence factor is very sensitive to the DM interaction.