Lancaster University Physicists Explore Noise Impact on Two-Qubit System Entanglement Evolution

Researchers from Lancaster University’s Department of Physics have studied the impact of local unitary noise on the entanglement evolution of a two-qubit system. Dominic Shea and Alessandro Romito used a stochastic Hamiltonian to identify optimal entanglement dynamics and develop a diagrammatic method for approximating average entanglement dynamics. The study found a non-monotonic relationship between concurrence and noise strength, indicating fluctuating, rather than consistent, increases or decreases. This research provides new insights into the behavior of quantum systems and the role of noise in these systems.

What is the Impact of Local Unitary Noise on the Entanglement Evolution of a Two-Qubit System?

The research conducted by Dominic Shea and Alessandro Romito from the Department of Physics at Lancaster University, UK, focuses on the effect of local unitary noise on the entanglement evolution of a two-qubit system. The two-qubit system is subject to local monitoring and interqubit coupling. The researchers constructed a stochastic Hamiltonian by incorporating the noise into the Chantasri-Dressel-Jordan path integral. This was used to identify the optimal entanglement dynamics and to develop a diagrammatic method for a closed-form approximation of the average entanglement dynamics with an analytical dependence on the noise and measurement intensity.

The study found that both the optimal trajectory and diagrammatic expansion capture the oscillations of entanglement at short times. A numerical investigation of long-time steady-state entanglement revealed a non-monotonic relationship between concurrence and noise strength. This means that the relationship between these two variables does not consistently increase or decrease but instead fluctuates.

How Does Quantum Entanglement Distinguish Quantum Systems from Classical Counterparts?

Quantum entanglement is a phenomenon that distinguishes quantum systems from their classical counterparts. It is a central resource in quantum information processing, enabling a variety of technological advances such as superdense coding, quantum teleportation, and quantum error correction. Entanglement is also key to understanding some properties of condensed matter systems, such as many-body localization.

Recently, entanglement has been exploited to identify out-of-equilibrium many-body states resulting from the stochastic dynamics of many-body systems subject to random unitary evolution and quantum monitoring. This has led to the emergence of entanglement scaling transitions from a volume to an area law in a many-body Zeno effect, along with a broader set of Measurement-induced Phase Transitions (MiPTs). These transitions appear when tracking the entanglement along individual quantum trajectories correlated with the measurement readout, as opposed to measurement-averaged dynamics.

What are the Nascent Features of Many-Body Competition in Entanglement Dynamics?

The nascent features of the many-body competition between unitary evolution and monitoring in the entanglement dynamics can be identified even in two-qubit systems. In these systems, different strategies to create, monitor, and maintain quantum entanglement can be implemented. The experiments reported have enabled the tracking of individual quantum trajectories for two entangled qubits. This development paves the way for the study of entanglement along trajectories in dual qubit systems.

While analytical expressions for the full probability distribution of steady states can be obtained only in particular cases, recent studies investigated the statistics of the entanglement properties for two qubits under half-parity Gaussian monitoring and the use of feedback control techniques to manipulate the purity and entanglement of dual qubit systems.

How Does the Monitored Unitary Dynamics Work in the Presence of a Stochastic Unitary Component?

In this work, the researchers studied the monitored unitary dynamics in the presence of a stochastic unitary component, which can have nontrivial effects in many-body MIPTs. They applied the Chantasri-Dressel-Jordan (CDJ) path integral to a two-qubit system subject to a driving Hamiltonian, two local Gaussian measurements, and external noise.

The CDJ path integral is a path-integral formulation explicitly developed for quantum systems subject to continuous Gaussian measurement and a driving Hamiltonian. It is especially advantageous for investigating rare events, providing a unique insight into quantum measurement dynamics. The researchers used these theoretical tools to develop a stochastic action and use a diagrammatic method to obtain a closed-form approximation for the average entanglement dynamics with an analytical dependence on the noise and measurement intensity.

What are the Findings of the Study on Two-Qubit Noisy Monitored Dynamics?

The paper considers a two-qubit system subject to unitary noisy dynamics and continuous quantum monitoring. The unitary dynamics in the system are generated by the Hamiltonian H, specified as H=H0+Hn. The system is further subject to continuous Gaussian monitoring on each qubit, which is described by the state update over an infinitesimal time δt as ψ(t+δt)=N1M1rM2wψ(t).

The researchers demonstrated numerically the existence of a non-monotonic dependence of the steady-state average entanglement, which is a unique feature of entanglement dynamics along quantum trajectories and would not be observable in the system’s average dynamics. This finding is significant as it provides new insights into the behavior of quantum systems and the role of noise in these systems.