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AIP conference proceedings

Excitation and Entanglement Transfer Versus Spectral Gap

Michael J. Hartmann, M. E. Reuter, Martin Bodo Plenio

Published Jan 1, 2006• 0 citations
Publisher

Abstract

Condensed matter systems have recently been proposed as quantum channels for short distance communication. One characteristic of these systems is whether they feature a spectral gap between their ground and excited states. In this paper we study the transfer of excitations and entanglement between two ancillas, which are weakly coupled to a one dimensional chain at different sites. We find that the transfer is almost perfect but slow for large spectral gaps and fast but rather inefficient for small gaps.

DOI
10.1063/1.2400886

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Condensed matter systems have recently been proposed as quantum channels for short distance communication. One characteristic of these systems is whether they feature a spectral gap between their ground and excited states. In this paper we study the transfer of excitations and entanglement between two ancillas, which are weakly coupled to a one dimensional chain at different sites. We find that the transfer is almost perfect but slow for large spectral gaps and fast but rather inefficient for small gaps.
Recently, there has been growing interest in employing condensed matter systems such as quantum spin or harmonic chains as quantum channels for short distance communication. Many properties of such chains are determined by the spectral gap between their ground and excited states. In particular this gap vanishes at critical points of quantum phase transitions. In this article we study the relation between the transfer speed and quality of such a system and the size of its spectral gap. We find that the transfer is almost perfect but slow for large spectral gaps and fast but rather inefficient for small gaps.
We consider quantum many body systems as quantum channels and study the relation between the transfer quality and the size of the spectral gap between the system's ground and excited states. In our setup, two ancillas are weakly coupled to the quantum many body system at different sites, and we study the propagation of an excitation and quantum information from one ancilla to the other. We observe two different scenarios: a slow, but perfect transfer if the gap is large and a fast, but incomplete transfer otherwise. We provide a numerical and analytical approach as well as a simplified physical model explaining our findings. Our results relate the potential of spin chains acting as quantum channels to the concept of quantum phase transitions and offer a different approach to the characterization of these.
We study quantum chains whose Hamiltonians are perturbations by bounded interactions of short range of a Hamiltonian that does not couple the degrees of freedom located at different sites of the chain and has a strictly positive energy gap above its ground-state energy. We prove that, for small values of a coupling constant, the spectral gap of the perturbed Hamiltonian above its ground-state energy is bounded from below by a positive constant uniformly in the length of the chain. In our proof we use a novel method based on local Lie-Schwinger conjugations of the Hamiltonians associated with connected subsets of the chain.
This thesis covers open quantum systems and information transfer in the face of \ndissipation and disorder through numerical simulation. \nIn Chapter 3 we present work on an open quantum system comprising a two-level system, single bosonic mode and dissipative environment; we have included \nthe bosonic mode in the exact system treatment. This model allows us to gain an understanding of an environment’s role in small energy transfer systems. We observe \nhow the two-level system-mode coupling strength and the spectral density form characterising the environment interplay, affecting the system’s coherent behaviour. We \nfind strong coupling and a spectral density resonantly peaked on the two-level system oscillation frequency enhances the system’s coherent oscillatory dynamics. \nChapter 4 focusses on a physically motivated study of chain and ladder spin \ngeometries and their use for entanglement transfer between qubits. We consider a \nnitrogen vacancy centre qubit implementation with nitrogen impurity spin-channels \nand demonstrate how matrix product operator techniques can be used in simulations \nof this physical system. We investigate coupling parameters and environmental decay \nrates with respect to transfer efficiency effects. Then, in turn, we simulate the effects \nof missing channel spins and disorder in the spin-spin coupling. We conclude by \nhighlighting where our considered channel geometries outperform each other. \nThe work in Chapter 5 is an investigation into the feasibility of routing entanglement between distant qubits in 2D spin networks. We no longer consider a physical \nimplementation, but keep in mind the effects of dissipative environments on entanglement transfer systems. Starting with a single sending qubit-ancilla and multiple \naddressable receivers, we show it is possible to target a specific receiver and establish transferred entanglement between it and the sender’s ancilla through eigenstate tunnelling techniques. We proceed to show that eigenstate tunnelling-mediated entanglement transfer can be achieved simultaneously from two senders across one spin network.
We study the relationship between entanglement and spectral gap for local Hamiltonians in one dimension (1D). The area law for a 1D system states that for the ground state, the entanglement of any interval is upper bounded by a constant independent of the size of the interval. However, the possible dependence of the upper bound on the spectral gap Δ is not known, as the best known general upper bound is asymptotically much larger than the largest possible entropy of any model system previously constructed for small Δ. To help resolve this asymptotic behavior, we construct a family of 1D local systems for which some intervals have entanglement entropy, which is polynomial in 1/Δ, whereas previously studied systems, such as free fermion systems or systems described by conformal field theory, had the entropy of all intervals bounded by a constant time log(1/Δ).
We propose to use ferromagnetic systems for entanglement generation and distribution together with perfect state transfer between distant parties in a qubit chain. The scheme relies on an effective two-qubit dynamics, realized by leaving two empty sites in a uniformly filled chain. This allows long-range interacting qubit chains to serve as quantum channels for both tasks with optimal performances. Remarkably, the entanglement between sender and receiver sites is independent of both the transmission distance and the system size. This property opens new perspectives for short- and mid-range quantum communication with qubit chains.