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International Journal of Pure and Apllied Mathematics

DECOHERENCE-FREE SUBSPACES FOR OPEN QUANTUM RANDOM WALKS ON GRAPHS

Julián Agredo

Published Oct 9, 2016• 2 citations
Publisher

Abstract

We study decoherence-free subspaces in a type of Quantum Markov Semigroups called continuous-time open quantum random walks on graphs.We measure the temporary changes of quantum correlations using geometric quantum discord with bures distance under some assumptions about the semigroup.In particular, we characterize the decay of correlations to zero, showing that turns out to be closely related with the structure of decoherence-free subspace.

DOI
10.12732/ijpam.v109i4.16

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We study decoherence-free subspaces in a type of Quantum Markov Semigroups called continuous-time open quantum random walks on graphs.We measure the temporary changes of quantum correlations using geometric quantum discord with bures distance under some assumptions about the semigroup.In particular, we characterize the decay of correlations to zero, showing that turns out to be closely related with the structure of decoherence-free subspace.
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In the present paper, we study the continuous-time quantum walk on quotient graphs. On such graphs, there is a straightforward reduction of the problem to a subspace that can be considerably smaller than the original one. Along the lines of reductions, by using the idea of calculation of the probability amplitudes for continuous-time quantum walk in terms of the spectral distribution associated with the adjacency matrix of graphs [Jafarizadeh and Salimi (Ann. Phys.322 (2007))], we show that the continuous-time quantum walk on original graph Γ induces a continuous-time quantum walk on quotient graph ΓH. Finally, for example, we investigate the continuous-time quantum walk on some quotient Cayley graphs.
We establish the structure of uniformly continuous quantum Markov semigroups with atomic decoherence-free subalgebra and apply the result to derive a natural decomposition of a Markovian open quantum system into its noiseless (decoherence-free) and irreducible (ergodic) components. We deduce the structure of invariant states and a method for finding decoherence-free subsystems and subspaces. The relationship between environment induced decoherence and the decoherence-free subalgebra is also discussed.
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In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we address the quantification of general non-classical correlations in Gaussian states of continuous variable systems from a geometric perspective. We give a description of the Gaussian geometric discord by using the Hellinger distance as a measure for quantum correlations between two non-interacting non-resonant bosonic modes embedded in a thermal environment. We evaluate the Gaussian geometric discord by taking two-mode squeezed thermal states as initial states of the system and show that it has finite values between 0 and 1 and that it decays asymptotically to zero in time under the effect of the thermal bath.