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arXiv:2511.00323 · Entropy

Optimal Transfer of Entanglement in Oscillator Chains in Non-Markovian Open Systems

Da-Wei Luo, Edward T. Yu, Ting Yu

Published Dec 8, 2025• 0 citations
arXivHTMLPDF

Abstract

We consider the transfer of continuous-variable entangled states in coupled oscillator chains embedded in a generic environment. We demonstrate high-fidelity transfer via optimal control in two configurations-a linear chain and an X-shaped chain. More specifically, we use the Krotov optimization algorithm to design control fields that achieve the desired state transfer. Under environmental memory effects, the Krotov algorithm needs to be modified, since the dissipative terms in non-Markovian dynamics are generally governed by the time-dependent system Hamiltonian. Remarkably, we can achieve high-fidelity transfer by simply tuning the frequencies of the oscillators while keeping the coupling strength constant, even in the presence of open-system effects. For the system under consideration, we find that quantum memory effects can aid in the transfer of entanglement and show improvement over the memoryless case. In addition, it is possible to target a range of entangled states, making it unnecessary to know the parameters of the initial state beforehand.

DOI
10.3390/e27121239

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We consider the transfer of continuous-variable entangled states in coupled oscillator chains embedded in a generic environment. We demonstrate high-fidelity transfer via optimal control in two configurations-a linear chain and an X-shaped chain. More specifically, we use the Krotov optimization algorithm to design control fields that achieve the desired state transfer. Under environmental memory effects, the Krotov algorithm needs to be modified, since the dissipative terms in non-Markovian dynamics are generally governed by the time-dependent system Hamiltonian. Remarkably, we can achieve high-fidelity transfer by simply tuning the frequencies of the oscillators while keeping the coupling strength constant, even in the presence of open-system effects. For the system under consideration, we find that quantum memory effects can aid in the transfer of entanglement and show improvement over the memoryless case. In addition, it is possible to target a range of entangled states, making it unnecessary to know the parameters of the initial state beforehand.
An efficient optimal-control theory based on the Krotov method is introduced for a non-Markovian open quantum system with a time-nonlocal master equation in which the control parameter and the bath correlation function are correlated. This optimal-control method is developed via a quantum dissipation formulation that transforms the time-nonlocal master equation to a set of coupled linear time-local equations of motion in an extended auxiliary Liouville space. As an illustration, the optimal-control method is applied to find the control sequences for high-fidelity ZZZ gates and identity gates of a qubit embedded in a non-Markovian bath. ZZZ gates and identity gates with errors less than ${10}^{\ensuremath{-}5}$ for a wide range of bath decoherence parameters can be achieved for the non-Markovian open qubit system with control over only the ${\ensuremath{\sigma}}_{z}$ term. The control-dissipation correlation and the memory effect of the bath are crucial in achieving the high-fidelity gates.
We investigate the optimal control of a continuous variable system, focusing on entanglement generation in an optomechanical system without utilizing Fock basis cutoffs. Using the Krotov algorithm to optimize the dynamics of the covariance matrix, we illustrate how to design a control objective function to manipulate the dynamics of the system to generate a desirable target state. We show that entanglement between the macroscopic mechanical mirror and the quantum optical cavity can be reliably generated through imposing the control on the detuning of the external laser field. It has been shown that the control may still be achieved when imposing spectral constraints on the external field to restrict it to low-frequency components. In addition, we systematically study the effects of quantum control on non-Markovian open system dynamics. We observe that memory effects can play a beneficial role in mitigating detrimental impacts of environmental noises. Specifically, the generated entanglement shows a reduced decay rate in the presence of these memory effects.
The realization of high-fidelity quantum control is crucial for quantum information processing, particularly in noisy environments where control strategies must simultaneously achieve precise manipulation and effective noise suppression. Conventional optimal control designs typically require numerical calculations of the system dynamics. Recent studies have demonstrated that long short-term memory neural networks (LSTM) can accurately predict the time evolution of open quantum systems. Based on LSTM predicted dynamics, we propose an optimal control framework for rapid and efficient optimal control design in open quantum systems. As illustrative examples, we apply the proposed framework to design optimal control for adiabatic speedup in a two-level system and for quantum state transfer in a spin chain, both under non-Markovian environments. For adiabatic speedup, our optimization procedure involves two steps: driving trajectory optimization and zero-area pulse optimization. Fidelity improvements for both steps have been obtained, demonstrating the effectiveness of the scheme. Furthermore, this effectiveness is validated for quantum state transfer in a spin chain, which is a high dimensional control problem. Our optimal control design scheme utilizes predicted dynamics to generate optimized controls, offering broad application potential in quantum computing, communication, and sensing.
We consider the quantum state control of a multi-state system which evolves an initial state into a target state. We explicitly demonstrate the control method in an interesting case involving the transfer and rotation of a Schr\"{o}dinger cat state through a coupled harmonic oscillator chain at a predetermined time TTT. We use the gradient-based Krotov's method to design the time-dependent parameters of the coupled chain to find an optimal control shape that will evolve the system into a target state. We show that the prescribed quantum state control can be achieved with high fidelity, and the robustness of the control against generic environment noises is explored. Our findings will be of interest for the optimal control of a many-body open quantum system in the presence of environmental noise.
We investigate the non-Markovian effects on the entanglement transfer to the distant non-interacting atom qubits, which are embedded in a coupled superconducting resonator. The master equation governing the dynamics of the system is derived by the non-Markovian quantum state diffusion (NMQSD) method. Based on the solution, we show that the memory effect of the environment can lead to higher entanglement revival and make the entanglement last for a longer time. That is to say, the non-Markovian environment can enhance the entanglement transfer. It is also found that the maximum entanglement transferred to distant atoms can be modified by appropriately selecting the frequency of the modulated inter-cavity coupling. Moreover, with the initial anti-correlated state, the entanglement between the cavity fields can be almost completely transferred to the separated atoms. Lastly, we show that the memory effect has a significant impact on the generation of entanglement from the initial non-entangled states.
Abstract We contribute further to recent theoretical studies of entanglement dynamics in open quantum systems to include a continuous variable N-harmonic oscillator ring system bathed in Ornstein–Uhlenbeck noise. Despite the fact that harmonic oscillator systems are one of the most studied systems in physics, we believe that our work here is unique and sheds a new perspective in terms of a potential application. We present two sets of differential equations that govern the dynamics of N harmonic oscillators derived from first principles, one for a Markovian environment and the other for non-Markovian one. With these two sets, we are able to compare their entanglement dynamics between environments given an initial state of our oscillators. Across several system and environmental parameters, we show that the entanglement dynamics between oscillator pairs in a non-Markovian environment may be significantly enhanced in both magnitude and duration when compared to its Markovian approximation. We showcase this by numerically simulating a specific solution, i.e., we choose N = 4 oscillators, where two harmonic oscillators are initialized as a two-mode squeezed state while the remaining oscillators are vacuum states. By leveraging our N = 4 results, we consider a slightly larger number of oscillators, i.e., N = 6, and show how we can generate a hidden quantum network, in the absence of direct coupling, that may allow multiple parties to secretly and passively entangle oscillators in their possession. This is accomplished by exploiting the environmental memory effect and maintaining resonance with other oscillators or the central frequency in a shared non-Markovian bath, which may allow for autonomous entanglement distribution over a network of oscillators and aid in future quantum technologies.