In this paper we propose a scheme for quasi-perfect state transfer in a network of dissipative harmonic oscillators. We consider ideal sender and receiver oscillators connected by a chain of nonideal transmitter oscillators coupled by nearest-neighbor resonances. From the algebraic properties of the dynamical quantities describing the evolution of the network state, we derive a criterion, fixing the coupling strengths between all the oscillators, apart from their natural frequencies, enabling perfect state transfer in the particular case of ideal transmitter oscillators. Our criterion provides an easily manipulated formula enabling perfect state transfer in the special case where the network nonidealities are disregarded. By adjusting the common frequency of the sender and the receiver oscillators to be out of resonance with that of the transmitters, we demonstrate that the sender's state tunnels to the receiver oscillator by virtually exciting the nonideal transmitter chain. This virtual process makes negligible the decay rate associated with the transmitter line on the expenses of delaying the time interval for the state transfer process. Apart from our analytical results, numerical computations are presented to illustrate our protocol.

In this paper we analyze the double Caldeira-Leggett model: the path integral approach to two interacting dissipative harmonic oscillators. Assuming a general form of the interaction between the oscillators, we consider two different situations: i) when each oscillator is coupled to its own reservoir, and ii) when both oscillators are coupled to a common reservoir. After deriving and solving the master equation for each case, we analyze the decoherence process of particular entanglements in the positional space of both oscillators. To analyze the decoherence mechanism we have derived a general decay function for the off-diagonal peaks of the density matrix, which applies both to a common and separate reservoirs. We have also identified the expected interaction between the two dissipative oscillators induced by their common reservoir. Such reservoir-induced interaction, which gives rise to interesting collective damping effects, such as the emergence of relaxation-and decoherence-free subspaces, is shown to be blurred by the high-temperature regime considered in this study. However, we find that different interactions between the dissipative oscillators, described by rotating or counter-rotating terms, result in different decay rates for the interference terms of the density matrix.At the beginning of the 1980s, the work of Zurek [1], Caldeira and Leggett (CL) [2], and Zeh and Joos [3] played a decisive role in the understanding of the still unsolved phenomenon of quantum measurement; more specifically, the collapse of the wave function and the associated decoherence of superposition states [4]. Taking the reservoir into account explicitly as a quantum ingredient, and analyzing its effect on the evolution of an initial pure state into a statistical mixture, these papers shed light on the shadowy interface between microscopic and macroscopic domains. Although the wave function collapse remains an obscure process, despite striking contributions also dating from the eighties [5], much is known today about the mechanisms leading to decoherence. In the last few decades we have analyzed this phenomenon exhaustively, enabling the proposition of a plethora of protocols to circumvent it, ranging from quantum error correction codes QECC [6] and engineered reservoirs [7] to dynamical decoupling [8] and relaxation-and decoherence-free subspaces (R-DFSs) [9,10].More recently, it was demonstrated that entanglement shows scaling behavior in the vicinity of the transition point [11]. This connection between the theories of critical phenomena and quantum information, together with the search for R-DFSs -which encompasses dissipative coupled systems -has triggered the study of fundamental quantum processes in the domain of many-body physics. Apart from the crucial role played by entanglements in the understanding of quantum phase transitions [12], the study of the complex dynamics of coherence and decoherence of superposition states in networks of dissipative quantum systems has also produced interesting results for quantum informa...

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We present a technique to build, within a dissipative bosonic network, decoherence-free channels (DFCs): a group of normal-mode oscillators with null effective damping rates. We verify that the states protected within the DFC define the well-known decoherence-free subspaces (DFSs) when mapped back into the natural network oscillators. Therefore, our technique to build protected normal-mode channels turns out to be an alternative way to build DFSs, which offers advantages over the conventional method. It enables the computation of all the network-protected states at once, as well as leading naturally to the concept of the decoherence quasi-free subspace (DQFS), inside which a superposition state is quasi-completely protected against decoherence. The concept of the DQFS, weaker than that of the DFS, may provide a more manageable mechanism to control decoherence. Finally, as an application of the DQFSs, we show how to build them for quasi-perfect state transfer in networks of coupled quantum dissipative oscillators.