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arXiv:1811.01808 · Physical Review A

Reexamination of the decoherence of spin registers

Jan Tuziemski, Aniello Lampo, Maciej Lewenstein, Jarosław K. Korbicz

Published Feb 21, 2019• 17 citations
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Abstract

We revisit the decoherence process of a multiqubit register interacting with a thermal bosonic bath. We generalize the previous studies by considering not only the register's behavior but also a part of its environment. In particular, we are interested in information flow from the register to the environment, which we describe using recently introduced multipartite quantum state structures called spectrum broadcast structures. Working in two specific cases of (i) two-qubit register and (ii) collective decoherence, we identify the regimes where the environment acquires almost complete information about the register state. We also study in more detail the interesting causal aspects related to the finite propagation time of the field disturbances between the qubits. Finally, we describe quantum state structures which appear due to the presence of protected spaces.

DOI
10.1103/physreva.99.022122

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•Jan 1, 2019•0 citations
We revisit the decoherence process of a multiqubit register interacting with a thermal bosonic bath. We generalize the previous studies by considering not only the register's behavior but also a part of its environment. In particular, we are interested in information flow from the register to the environment, which we describe using recently introduced multipartite quantum state structures called spectrum broadcast structures. Working in two specific cases of (i) two-qubit register and (ii) collective decoherence, we identify the regimes where the environment acquires almost complete information about the register state. We also study in more detail the interesting causal aspects related to the finite propagation time of the field disturbances between the qubits. Finally, we describe quantum state structures which appear due to the presence of protected spaces.
We study in detail the decoherence process of a quantum register, coupled to a composite environment. We use recently developed methods of information transfer study in open quantum systems to analyze information flow between the register and its environment. We show that there are regimes when not only the register decoheres effectively to a classical bit string, but this bit string is redundantly encoded in the environment, making it available to multiple observers. This process is more subtle and in general qualitatively different than in the case of a single qubit due to the presence of various protected subspaces: decoherence-free subspaces and so-called orthogonalization-free subspaces. We show that this leads to a rich structure of coherence loss or protection in the asymptotic state of the register and a part of its environment. We formulate a series of examples illustrating these structures.
The dynamical evolution of a quantum register of arbitrary length coupled to an environment of arbitrary coherence length is predicted within a relevant model of decoherence. The results are reported for quantum bits (qubits) coupling individually to different environments (``independent decoherence'') and qubits interacting collectively with the same reservoir (``collective decoherence''). In both cases, explicit decoherence functions are derived for any number of qubits. The decay of the coherences of the register is shown to strongly depend on the input states: We show that this sensitivity is a characteristic of both types of coupling (collective and independent) and not only of the collective coupling, as has been reported previously. A nontrivial behavior (``recoherence'') is found in the decay of the off-diagonal elements of the reduced density matrix in the specific situation of independent decoherence. Our results lead to the identification of decoherence-free states in the collective decoherence limit. These states belong to subspaces of the system's Hilbert space that do not get entangled with the environment, making them ideal elements for the engineering of ``noiseless'' quantum codes. We also discuss the relations between decoherence of the quantum register and computational complexity based on the dynamical results obtained for the register density matrix.
We analyze decoherence and objectivization processes in spin-spin models for arbitrary spins without interactions between different spins in the environment. We first derive the most general analytic form of the decoherence factor in the measurement limit, where the interaction Hamiltonian dominates the rest. We then analyze thermal environments and derive exact, analytic formulas for both the decoherence factor and the state fidelity of postinteraction environment states, conditioned on different states of the system. This allows us to analyze the objectivization process of the state of the central spin during the interaction. We do so using so-called spectrum broadcast structures (SBS), which are specific multipartite quantum states encoding a certain operation notion of objectivity. We analyze analytically (for short times) and numerically how higher spin influences the efficiency of decoherence and objectivization processes. As expected, the higher the spin of the environment, the more efficient decoherence and objectivization become. This work is a generalization of previous studies, limited to spin-1/21/21/2 systems only, and we hope will be useful in future objectivity experiments.
A model for a quantum register dissipatively coupled with a bosonic thermal bath is studied. The register consists of NNN quantum bits (qubits) the bath is described by Nb{N}_{b}Nb​ bosonic modes. The register-bath coupling is chosen in such a way that the total number of excitations is conserved. The Hilbert space splits, allowing the study of the dynamics separately in each sector. Assuming that the coupling with the bath is the same for all qubits, the excitation sectors have a further decomposition according the irreducible representations of the su(2) spin algebra. The stability against environment-generated noise of the information encoded in a quantum state of the register depends on its SU(2) symmetry content. At zero temperature we find that states belonging to the vacuum symmetry sector have, for long time, vanishing fidelity, whereas each lowest spin vector is decoupled from the bath and therefore is decoherence free. Numerical results are shown in the one-excitation space in the case of qubit-dependent bath-system coupling.
We investigate the decoherence process for a quantum register composed of NNN qubits coupled to an environment. We consider an environment composed of one common phonon bath and several electronic baths. This environment is relevant to the implementation of a charge based solid-state quantum computer. We explicitly compute the time evolution of all off-diagonal terms of the register's reduced density matrix. We find that in realistic configurations, ``superdecoherence'' and ``decoherence-free subspaces'' do not exist for an NNN-qubit system. This means that all off-diagonal terms decay, but not faster than ${e}^{\ensuremath{-}q(t)N}$, where q(t)q(t)q(t) is of the same order as the decay function of a single qubit.
We present a theoretical discussion of various aspects of the dynamics of information in quantum systems of qubits. We begin by reviewing ideas about entanglement and information in systems of qubits, different models for realistic qubits coupled to an external environment, how this causes the loss of information stored in qubits, and some practical designs for qubits that have been created. Then we study how the state of many-body systems can be decomposed in terms of its different subsystems and derived a hierarchy of equations describing the motion of these different parts. We show that in a qubit system, the central objects in this hierarchy are correlators between different components of different qubits. Systems where the environment coupled to a central qubit is a "spin bath'' of environmental qubits are then considered in detail and we find that information lost by the central qubit is transferred via a cascade to higher and higher order correlations with the environment. We discuses this process in the realistic example of an "Fe₈'' magnetic molecule qubit. Finally we discuss simple models of the dynamics of many entangled qubits.