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arXiv:0908.0958 · Physical Review A

Decoherence suppression via environment preparation

Olivier Landon-Cardinal, R. MacKenzie

Published Dec 9, 2009• 1 citation
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Abstract

To protect a quantum system from decoherence due to interaction with its environment, we investigate the existence of initial states of the environment allowing for decoherence-free evolution of the system. For a class of models in which a two-state system and a dynamical environment interact through a Hamiltonian restricted to be a tensor product, we prove that such states exist if and only if the interaction and self-evolution Hamiltonians of the environment share an eigenstate. If decoherence by state preparation is not possible, we show that initial states minimizing decoherence result from a delicate compromise between the environment and interaction dynamics.

DOI
10.1103/physreva.80.062319

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To protect a quantum system from decoherence due to interaction with its environment, we investigate the existence of initial states of the environment allowing for decoherence-free evolution of the system. For a class of models in which a two-state system and a dynamical environment interact through a Hamiltonian restricted to be a tensor product, we prove that such states exist if and only if the interaction and self-evolution Hamiltonians of the environment share an eigenstate. If decoherence by state preparation is not possible, we show that initial states minimizing decoherence result from a delicate compromise between the environment and interaction dynamics.
To protect a quantum system from decoherence due to interaction with its environment, we investigate the existence of initial states of the environment allowing for decoherence-free evolution of the system. For a class of models in which a two-state system and a dynamical environment interact through a Hamiltonian restricted to be a tensor product, we prove that such states exist if and only if the interaction and self-evolution Hamiltonians of the environment share an eigenstate. If decoherence by state preparation is not possible, we show that initial states minimizing decoherence result from a delicate compromise between the environment and interaction dynamics.
We investigate the conditions which can lead to the occurrence of "decoherence" (i.e., of "environment-induced superselection"), in a quantum system interacting with another, infinite quantum system (an apparatus, environment, etc.), in the context of the nonrelativistic quantum mechanics. We are particularly concerned with: a kind of interaction, its relative strength, initial state of the apparatus (environment), and compatibility of the self-Hamiltonian and the interaction Hamiltonian of the composite system, "system plus apparatus", including time dependent interactions. As necessary conditions concerning occurrence of decoherence appear the two requirements: (i) That the interaction Hamiltonian is of the separable kind , and (ii) That the complete Hamiltonian, Ĥ u satisfies commutator relation [Ĥ u ( t ), Ĥ u ( t ')] = 0 ( t and t ' arbitrary instants). Since non-separable interaction cannot produce the same, we conclude that occurrence of decoherence is neither a rule (as it is sometimes assumed in the context of the "environment theory"), nor an exceptional consequence of the dynamics of a system interacting with its environment (as it is sometimes claimed in the criticism of the environment theory). Exhaustiveness and generality of our analysis extend applicability of related results (which are independent on a particular model of (infinite) environment), at least as a qualitative test and/or quantitative estimation of the results of the calculations obtained by the use of the different methods (semiclassical methods, path-integration technique, etc.) in quantum many-particle physics.
We study the decoherence process induced by a spin chain environment on a central spin consisting of R spins and we apply it on the dynamics of quantum correlations (QCs) of three interacting qubits. In order to see the impact of the initial prepared state of the spin chain environment on the decoherence process, we assume the spin chain environment prepared in two main ways, namely, either the ground state or the vacuum state in the momentum space. We develop a general heuristic analysis when the spin chain environment in prepared in these states, in order to understand the decoherence process against the physical parameters. We show that the decoherence process is mainly determined by the choice of the initial prepared state, the number of spin of the chain, the coupling strength, the anisotropy parameter and the position from the quantum critical point. In fact, in the strong coupling regime, the decoherence process does not appear for the environment prepared in the vacuum state and it behaves oscillatory in the case of evolution from ground state. On the other hand, in the weak coupling regime and far from the quantum critical point, decoherence induced by the ground state is weaker than that of the vacuum state. Finally, we show that, QCs are completely shielded from decoherence in the case of evolution from the W state and obey the same dynamics as the decoherence factors for the GHZ state.
The dynamics of a decohering two-level system driven by a suitable control Hamiltonian is studied. The control procedure is implemented as a sequence of radio-frequency pulses that repetitively flip the state of the system, a technique that can be termed quantum ``bang-bang'' control after its classical analog. Decoherence introduced by the system's interaction with a quantum environment is shown to be washed out completely in the limit of continuous flipping and greatly suppressed provided the interval between the pulses is made comparable to the correlation time of the environment. The model suggests a strategy to fight against decoherence that complements existing quantum error-correction techniques.
Decoherence of qubits is one main limitation in quantum information processing, where the qubits themselves can be mixed because of decoherence and additional decoherence may generated through interactions with a bath. Here, we present a complete study of qubit-environment entanglement in the case of interactions that lead to pure dephasing of the qubit by allowing the initial state of the qubit to be mixed, exceeding previous restrictions. We find that the criteria for separability that hold for pure initial states of the qubit are reduced to witness status. Yet, the evolution of the witnesses reflects the array of features that entanglement can exhibit in the mixed case but are forbidden in the pure-qubit case. Most notably, this includes sudden birth of entanglement as the initial phase of the evolution is typically separable. Moreover, there is a stark numerical advantage to the study of entanglement for large environments when using the witness rather than the traditional measures available. We include the study of entanglement generated between a spin qubit and a sparse spin environment to illustrate the peculiarities of the evolution of entanglement in this case, as well as to emphasize the level of reliability of the entanglement witness.