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arXiv:quant-ph/0702244 · Physical Review A

Multiparticle decoherence-free subspaces in extended systems

Raisa I. Karasik, Karl-Peter Marzlin, Barry C. Sanders, K. Birgitta Whaley

Published Jul 27, 2007• 19 citations
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Abstract

We develop a method to determine spatial configurations to realize decoherence-free subspaces for spatially extended multiparticle systems. We have assumed normal reservoir behavior including translational invariance of the reservoir and preparation in stationary states or mixture thereof and weak Markovian system-reservoir coupling that requires energy transfer. One important outcome of our method is a proof that there does not exist a multiparticle decoherence-free subspace in such systems except in the limit that the spatial extent of the system becomes infinitesimal.

DOI
10.1103/physreva.76.012331

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We develop a method to determine spatial configurations to realize decoherence-free subspaces for spatially extended multiparticle systems. We have assumed normal reservoir behavior including translational invariance of the reservoir and preparation in stationary states or mixture thereof and weak Markovian system-reservoir coupling that requires energy transfer. One important outcome of our method is a proof that there does not exist a multiparticle decoherence-free subspace in such systems except in the limit that the spatial extent of the system becomes infinitesimal.
Coherence in an open quantum system is degraded through its interaction with a bath. This decoherence can be avoided by restricting the dynamics of the system to special decoherence-free subspaces. These subspaces are usually constructed under the assumption of spatially symmetric system-bath coupling. Here we show that decoherence-free subspaces may appear without spatial symmetry. Instead, we consider a model of system-bath interactions in which to first order only multiple-qubit coupling to the bath is present, with single-qubit system-bath coupling absent. We derive necessary and sufficient conditions for the appearance of decoherence-free states in this model, and give a number of examples. In a sequel paper we show how to perform universal and fault tolerant quantum computation on the decoherence-free subspaces considered in this paper.
We introduce a generalized theory of decoherence-free subspaces and subsystems (DFSs), which do not require accurate initialization. We derive a set of conditions for the existence of DFSs within this generalized framework. By relaxing the initialization requirement we show that a DFS can tolerate arbitrarily large preparation errors. This has potentially significant implications for experiments involving DFSs, in particular for the experimental implementation, over DFSs, of the large class of quantum algorithms which can function with arbitrary input states.
Decoherence free subspaces (DFS) is a theoretical tool towards experimental implementation of quantum information storage and processing. However, they represent an experimental challenge, since conditions for their existence are very stringent. This work explores the situation in which a system of NNN oscillators coupled to a bath of harmonic oscillators is close to satisfy the conditions for the existence of DFS. We show, in the Born-Markov limit and for small deviations from separability and degeneracy conditions, that there are {\emph{weak decoherence subspaces}} which resemble the original notion of DFS.
Analyzing the S matrices associated with a host of relaxation processes allows one, using extra ``chaperon'' states, to construct a decoherence-free subspace (DFS) that is immune to the effects of relaxation. The method does not require knowledge of the system-bath Hamiltonian, which is rarely known. Thus, a DFS can be constructed directly from experimentally determined relaxation and dephasing rates of the relevant decoherence processes. Although the method requires resetting the coefficients of the chaperon states at various times, this resetting does not require determining the coefficients of the states belonging to the DFS that one uses for control, computations, or information storage.