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Physical Review A

Robustness of optimal transport in one-dimensional particle quantum networks

C. Javaherian, Jason Twamley

Published Oct 10, 2014• 3 citations
Publisher

Abstract

We study the robustness of quantum transport in four-site one-dimensional (1D) particle quantum networks irreversibly connected to a target site in the presence of environmental dephasing noise. Under conditions of Markovian decoherence we define a quantity---which we denote as geometrical robustness---to quantify the robustness of transport with regard to the geometrical arrangement of the spin network. We examine the behavior of this geometrical robustness for both nearest and non-nearest site interactions and show that for some values of dephasing noise and other network parameters the robustness undergoes revivals, i.e., the robustness periodically increases with dephasing. In addition, we find that for high amounts of dephasing noise, the pattern of optimal network configurations changes noticeably from central symmetric configurations to laterally gathered ones, and we show that this change of pattern seems to occur for any number of network sites in the 1D chain.

DOI
10.1103/physreva.90.042313

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We study the robustness of quantum transport in four-site one-dimensional (1D) particle quantum networks irreversibly connected to a target site in the presence of environmental dephasing noise. Under conditions of Markovian decoherence we define a quantity---which we denote as geometrical robustness---to quantify the robustness of transport with regard to the geometrical arrangement of the spin network. We examine the behavior of this geometrical robustness for both nearest and non-nearest site interactions and show that for some values of dephasing noise and other network parameters the robustness undergoes revivals, i.e., the robustness periodically increases with dephasing. In addition, we find that for high amounts of dephasing noise, the pattern of optimal network configurations changes noticeably from central symmetric configurations to laterally gathered ones, and we show that this change of pattern seems to occur for any number of network sites in the 1D chain.
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Abstract Optimal energy transport is one of the primary goals for designing efficient quantum networks. In this work, the maximum energy transport is investigated for three-dimensional quantum networks with Platonic geometries affected by dephasing and dissipative Markovian noise. The network and the environmental characteristics corresponding the optimal design are obtained and investigated for five Platonic networks with 4, 6, 8, 12, and 20 number of sites that one of the sites is connected to a sink site through a Markovian dissipative process. Such optimal designs could have various applications like switching and multiplexing in quantum circuits.
Quantum transport in disordered systems poses intriguing fundamental questions about the interplay of disorder, interactions, and decoherence, with important implications for nanoscale energy transfer and quantum information transfer. Here, we investigate the emergence of multiple transport timescales in the dissipative dynamics of a spin impurity coupled to a small, spatially disordered network of spins. Using a two-dimensional tight-binding model with dipolar interactions and local dephasing, we demonstrate that geometric heterogeneity leads to hierarchical coupling strengths and pronounced separation of dynamical timescales. By analyzing different metrics for dynamics, we identify distinct relaxation timescales associated with cluster-level equilibration and global equilibration. A minimal three-site model reveals the physical origin of the longest timescale: strong internal hybridization generates an effective detuning that suppresses transfer to other weakly coupled sites, yielding a parametrically enhanced relaxation time in the weak-dephasing regime. We corroborate this picture with nonequilibrium steady-state transport calculations and simulations of disordered spin configurations, demonstrating orders-of-magnitude slowing of relaxation when hierarchical couplings are present. Our results highlight the central role of geometry and connectivity in spin networks and open quantum systems in general, and provide experimentally relevant predictions for relaxation times in small spin baths.
We study the environment-assisted enhancement of the excitation-transport efficiency across a network of interacting quantum particles or sites. Our study reveals a crucial influence of the network configuration - and especially its degree of connectivity - on the amount of environment-supported enhancement. In particular, we find a significant interplay of direct and indirect connections between excitation sending and receiving sites. On the other hand, the non-Markovianity induced by memory-bearing, finite sized environments does not seem to provide a critical resource for the enhanced excitation-transport mechanism.
Environmental noise can enhance transport, an effect known as environmental noise-assisted quantum transport. Most theoretical studies focus on optimizing system parameters under spatially uniform system-environment coupling. Here, instead, we optimize the environmental noise itself by allowing for site-dependent dephasing. We investigate steady-state transport in one-dimensional lattices with either ramped or disordered energy landscapes, considering both short- and long-range coherent tunneling. In the absence of environmental effects, in the thermodynamic limit these systems can exhibit localization, and thus suppressed transport, arising from destructive interference. Using a Lindblad master equation framework, we implement local dephasing optimized to maximize steady-state population flux. We find that for ramp potentials, short-range tunneling favors selective dephasing on alternating sites, whereas long-range tunneling benefits from a dephasing profile that increases with distance from the injection site. In energetically disordered systems, strongly detuned sites require enhanced local dephasing under short-range tunneling to facilitate transport. In all cases, we find that site-optimized dephasing allows higher transport efficiency than uniform dephasing, and it is accompanied by increased spatial delocalization of the steady state. Our results provide microscopic insight into the interplay between coherent dynamics and environmental noise. Dephasing broadens energy levels locally, helping to overcome detuning and destructive interference. More generally, we establish spatially-structured environmental noise as a strategy for controlling both quantum transport and state coherence in open systems.
Quantum networks are promising venues for quantum information processing. This motivates the study of the entanglement properties of the particular multipartite quantum states that underpin these structures. In particular, it has been recently shown that when the links are noisy two drastically different behaviors can occur regarding the global entanglement properties of the network. While in certain configurations the network displays genuine multipartite entanglement (GME) for any system size provided the noise level is below a certain threshold, in others GME is washed out if the system size is big enough for any fixed non-zero level of noise. However, this difference has only been established considering the two extreme cases of maximally and minimally connected networks (i.e. complete graphs versus trees, respectively). In this article we investigate this question much more in depth and relate this behavior to the growth of several graph theoretic parameters that measure the connectivity of the graph sequence that codifies the structure of the network as the number of parties increases. The strongest conditions are obtained when considering the degree growth. Our main results are that a sufficiently fast degree growth (i.e. Ω ( N ) , where N is the size of the network) is sufficient for asymptotic robustness of GME, while if it is sufficiently slow (i.e. o ( log ⁡ N ) ) then the network becomes asymptotically biseparable. We also present several explicit constructions related to the optimality of these results.