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arXiv:2303.09238 · New Journal of Physics

The fastest generation of multipartite entanglement with natural interactions

Paweł Cieśliński, Waldemar Kłobus, Paweł Kurzyński, Tomasz Paterek, Wiesław Laskowski

Published Sep 1, 2023• 9 citations
arXivHTMLPDF

Abstract

Abstract Natural interactions among multiple quantum objects are fundamentally composed of two-body terms only. In contradistinction, single global unitaries that generate highly entangled states typically arise from Hamiltonians that couple multiple individual subsystems simultaneously. Here, we study the time to produce strongly nonclassical multipartite correlations with a single unitary generated by the natural interactions. We restrict the symmetry of two-body interactions to match the symmetry of the target states and focus on the fastest generation of multipartite entangled Greenberger–Horne–Zeilinger, W, Dicke and absolutely maximally entangled states for up to seven qubits. These results are obtained by constraining the energy in the system and accordingly can be seen as state-dependent quantum speed limits for symmetry-adjusted natural interactions. They give rise to a counter-intuitive effect where the creation of particular entangled states with an increasing number of particles does not require more time. The methods used rely on extensive numerical simulations and analytical estimations.

DOI
10.1088/1367-2630/acf953

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Abstract Natural interactions among multiple quantum objects are fundamentally composed of two-body terms only. In contradistinction, single global unitaries that generate highly entangled states typically arise from Hamiltonians that couple multiple individual subsystems simultaneously. Here, we study the time to produce strongly nonclassical multipartite correlations with a single unitary generated by the natural interactions. We restrict the symmetry of two-body interactions to match the symmetry of the target states and focus on the fastest generation of multipartite entangled Greenberger–Horne–Zeilinger, W, Dicke and absolutely maximally entangled states for up to seven qubits. These results are obtained by constraining the energy in the system and accordingly can be seen as state-dependent quantum speed limits for symmetry-adjusted natural interactions. They give rise to a counter-intuitive effect where the creation of particular entangled states with an increasing number of particles does not require more time. The methods used rely on extensive numerical simulations and analytical estimations.
We investigate the possibility to obtain higly multipartite-entangled states as non-degenerate eigenstates of Hamiltonians that involve only short-range and few-body interactions. We study small-size systems (with a number of qubits ranging from three to five) and search for Hamiltonians with a maximally multipartite entangled state (MMES) as a non-degenerate eigenstate. We then find conditions, including bounds on the number of coupled qubits, to build a Hamiltonian with a Greenberger–Horne–Zeilinger (GHZ) state as a non-degenerate eigenstate. We finally comment on possible applications.
The generation of genuine multipartite entangled states is challenging in practice. Here we explore an alternative route to this task, via autonomous entanglement engines which use only incoherent coupling to thermal baths and time-independent interactions. We present a general machine architecture, which allows for the generation of a broad range of multipartite entangled states in a heralded manner. Specifically, given a target multiple-qubit state, we give a sufficient condition ensuring that it can be generated by our machine. We discuss the cases of Greenberger-Horne-Zeilinger, Dicke, and cluster states in detail. These results demonstrate the potential of purely thermal resources for creating multipartite entangled states useful for quantum information processing.
The dynamics of quantum many-body systems in the chaotic regime are of particular interest due to the associated phenomena of information scrambling and entanglement generation within the system. While these systems are typically intractable using traditional numerical methods, an effective framework can be implemented based on dual-unitary circuits which have emerged as a minimal model for maximally chaotic dynamics. In this work, we investigate how individual two-body operators influence the global dynamics of circuits composed of dual-unitaries. We study their effect on entanglement generation while examining it from both bipartite and multipartite perspectives. Here we also highlight the significant role of local unitaries in the dynamics when paired with operators from the dual-unitary class, showing that systems with identical entangling power can exhibit a range of differing entanglement growth rates. Furthermore, we present calculations establishing time-step-dependent lower bounds, which depend on both the initial state and the entangling power of the constituent operators. Finally, we find that time-evolving an initial state composed of pair products generates a state with nearly maximal multipartite entanglement content, approaching the bounds established by Absolutely Maximally Entangled (AME) states.
Abstract The entanglement production is key for many applications in the realm of quantum information, but so is the identification of processes that allow to create entanglement in a fast and sustained way. Most of the advances in this direction have been circumscribed to bipartite systems only, and the rate of entanglement in multipartite system has been much less explored. Here we contribute to the identification of processes that favor the fastest and sustained generation of tripartite entanglement in a class of 3-qubit GHZ-type states. By considering a three-party interaction Hamiltonian, we analyze the dynamics of the 3-tangle and the entanglement rate to identify the optimal local operations that supplement the Hamiltonian evolution in order to speed-up the generation of three-way entanglement, and to prevent its decay below a predetermined threshold value. The appropriate local operation that maximizes the speed at which a highly-entangled state is reached has the advantage of requiring access to only one of the qubits, yet depends on the actual state of the system. Other universal (state-independent) local operations are found that conform schemes to maintain a sufficiently high amount of 3-tangle. Our results expand our understanding of entanglement rates to multipartite systems, and offer guidance regarding the strategies that improve the efficiency in various quantum information processing tasks.
We show that collective three-body interactions (3BIs), implementable with NNN atoms loaded inside an optical cavity, offer a significant advantage for preparing complex multipartite entangled states. Firstly, they enable a speedup of order ∼N\sim N∼N in preparing generalized Greenberger-Horne-Zeilinger (GHZ) states, outperforming conventional methods based on all-to-all two-body Ising interactions. Secondly, they saturate the Heisenberg bound in phase estimation tasks using a time-reversal protocol realized through simple rotations and followed by experimentally accessible collective spin measurements. Lastly, compared with two-body interactions (2BIs), in the presence of cavity losses and single particle decoherence, 3BIs feature a high gain in sensitivity for moderate atom numbers and in large ensembles a fast entanglement generation despite constraints in parameter regimes where they are implementable.
Characterizing entanglement of systems composed of multiple particles is a very complex problem that is attracting increasing attention across different disciplines related to quantum physics. The task becomes even more complex when the particles have many accessible levels, i.e., they are of high dimension, which leads to a potentially high-dimensional multipartite entangled state. These are important resources for an ever-increasing number of tasks, especially when a network of parties needs to share highly entangled states, e.g., for communicating more efficiently and securely. For these applications, as well as for purely theoretical arguments, it is important to be able to certify both the high-dimensional and the genuine multipartite nature of entangled states, possibly based on simple measurements. Here we derive a novel method that achieves this and improves over typical entanglement witnesses like the fidelity with respect to states of a Greenberger-Horne-Zeilinger (GHZ) form, without needing more complex measurements. We test our condition on paradigmatic classes of high-dimensional multipartite entangled states like imperfect GHZ states with random noise, as well as on purely randomly chosen ones and find that, in comparison with other available criteria our method provides a significant advantage and is often also simpler to evaluate.