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arXiv:quant-ph/0506208 · Physical Review A

Spin gases as microscopic models for non-Markovian decoherence

Ludwig Hartmann, John Calsamiglia, Wolfgang Dür, Hans J. Briegel

Published Nov 10, 2005• 17 citations
arXivHTMLPDF

Abstract

We analyze a microscopic decoherence model in which the total system is described as a spin gas. A spin gas consists of $N$ classically moving particles with additional, interacting quantum degrees of freedom (e.g., spins). For various multipartite entangled probe states, we analyze the decoherence induced by interactions between the probe and environmental spins in such spin gases. We can treat mesoscopic environments ($\ensuremath{\approx}{10}^{5}$ particles). We present results for a lattice gas, which could be realized by neutral atoms hopping in an optical lattice, and show the effects of non-Markovian and correlated noise, as well as finite-size effects.

DOI
10.1103/physreva.72.052107

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We analyze a microscopic decoherence model in which the total system is described as a spin gas. A spin gas consists of NNN classically moving particles with additional, interacting quantum degrees of freedom (e.g., spins). For various multipartite entangled probe states, we analyze the decoherence induced by interactions between the probe and environmental spins in such spin gases. We can treat mesoscopic environments (\ensuremath≈105\ensuremath{\approx}{10}^{5}\ensuremath≈105 particles). We present results for a lattice gas, which could be realized by neutral atoms hopping in an optical lattice, and show the effects of non-Markovian and correlated noise, as well as finite-size effects.
We study the dynamics of entanglement in spin gases. A spin gas consists of a (large) number of interacting particles whose random motion is described classically while their internal degrees of freedom are described quantum-mechanically. We determine the entanglement that occurs naturally in such systems for specific types of quantum interactions. At the same time, these systems provide microscopic models for non–Markovian decoherence: the interaction of a group of particles with other particles belonging to a background gas are treated exactly, and differences between collective and non–collective decoherence processes are studied. We give quantitative results for the Boltzmann gas and also for a lattice gas, which could be realized by neutral atoms hopping in an optical lattice. These models can be simulated efficiently for systems of mesoscopic sizes (N ~ 105).
We study a spin-gas model, where NS{N}_{S}NS​ system qubits are interacting with NB{N}_{B}NB​ bath qubits via many-body interactions. We consider multipartite Ising interactions and show how the effect of decoherence depends on the specific coupling between the system and its environment. For instance, we analyze the influence of decoherence induced by kkk-body interactions for different values of kkk. Moreover, we study how the effect of decoherence depends on the correlation between bath qubits that are coupled to different individual system qubits and compare Markovian with non-Markovian scenarios. We derive a useful canonical form of a completely positive map that describes a class of system environment interactions with a finite size of environment correlations. As examples we consider specific quantum many-body states and investigate their evolution under different decoherence models. As a complementary investigation, we study how the coupling to the environment can be employed to generate a desired multipartite state.
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A spin gas is a natural extension of a classical gas. It consists of a large number of particles whose (random) motion is described classically, but, in addition, have internal (quantum mechanical) degrees of freedom that interact during collisions. For specific types of quantum interactions we determine the entanglement that occurs naturally in such systems. We analyze how the evolution of the quantum state is determined by the underlying classical kinematics of the gas. For the Boltzmann gas, we calculate the rate at which entanglement is produced and characterize the entanglement properties of the equilibrium state.
Weighted graph states naturally arise when spin systems interact via an Ising-type interaction. First, we abstractly define the class of weighted graph states and demonstrate its computational accessibility. We show how reduced density matrices of a small number of spins (≈10) can be computed from arbitrarily large systems using weighted graph techniques and projected entangled pair techniques, and we discuss various entanglement measures accessible from these reduced density matrices. Second, we apply these findings to spin chains and lattices with long-range interactions and analytically derive area laws for the scaling of block-wise entanglement. Then, we turn to disordered spin systems, spin gases, which are connected to random weighted graph states and which share their entanglement properties. Finally, we use a spin gas as a bath that introduces decoherence in single as well as multipartite spin systems. The microscopic, exact decoherence model we obtain can operate in different regimes and exhibit non-Markovian features as well as spatially correlated noise effects.
During the last decade the field of quantum information has seen considerable progress both theoretically and experimentally. The building block of this theory is the so-called qubit, the quantum counterpart of the classical bit. It turns out that spin degrees of freedom of quantum particles are among the most promising candidates for quantum information processing and computation. Thus, a deep understanding of the different processes that govern the dynamics of these objects is of fundamental importance. For instance, the decoherence process, caused the coupling of the qubits to their surrounding environment, is the main obstacle to quantum information processing: it leads them to lose their quantum coherence and thus behave classically. In addition, quantum systems exhibit correlations that have no classical counterpart. This phenomenon is called entanglement and is the vital resource for quantum teleportation and quantum computing. Decoherence and entanglement dynamics were extensively studied within the framework of the Markovian approximation using the master equation approach. However, due to the non-commuting character of quantum observables, only few models are known to be exactly solvable. Moreover, many spin systems display a strongly non-Markovian behavior. This thesis is devoted to the development of new techniques for deriving the exact dynamics of spin qubits, coupled through Heisenberg and/or Ising interactions to spin environments that have internal dynamics. The basic idea behind these techniques is to use the underlying symmetries exhibited by the Hamitonian operators of the composite systems. This allows for the study of problems related to decoherence and entanglement.