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Symmetry

The Bipartite and Tripartite Entanglement in PT-Symmetric System

Vinh Le Duc, Mateusz Nowotarski, Joanna K. Kalaga

Published Jan 27, 2021• 4 citations
Publisher

Abstract

We consider a PT-symmetric system that involves three optical resonant elements coupled together. We investigate the quantum correlations between subsystems by calculating bipartite and tripartite entanglement. We show that when PT-symmetry is maintained, the correlations between subsystems strongly depend on the parameters describing the interaction between them and characterizing the gain and loss of energy in the system’s active and passive elements. We estimate the range of interaction parameter values for which the strongest bipartite and tripartite entanglement can be produced. Additionally, we show that the discussed system can be a source of stable entangled states.

DOI
10.3390/sym13020203

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We consider a PT-symmetric system that involves three optical resonant elements coupled together. We investigate the quantum correlations between subsystems by calculating bipartite and tripartite entanglement. We show that when PT-symmetry is maintained, the correlations between subsystems strongly depend on the parameters describing the interaction between them and characterizing the gain and loss of energy in the system’s active and passive elements. We estimate the range of interaction parameter values for which the strongest bipartite and tripartite entanglement can be produced. Additionally, we show that the discussed system can be a source of stable entangled states.
A noteworthy discovery is that the minimal evolution time is smaller for parity-time (PT\mathcal{PT}PT) symmetric systems compared to Hermitian setups. Moreover, there is a significant acceleration of two-qubit quantum entanglement preparation near the exceptional point (EP), or spectral coalescence, within such system. Nevertheless, an important problem often overlooked for quantum EP-based devices is their fidelity, greatly affected by the process of dissipation or post-selection, creating an inherent trade-off relation between the degree of entanglement and fidelity. Our study demonstrates that this limitation can be effectively overcome by harnessing an active PT\mathcal{PT}PT-symmetric system, which possesses balanced gain and loss, enabling maximal entanglement with rapid speed, high fidelity, and greater resilience to non-resonant errors. This new approach can efficiently prepare multi-qubit entanglement and use not only bipartite but also tripartite entanglement, as illustrative examples, even when the precise gain-loss balance is not strictly maintained. Our analytical findings are in excellent agreement with numerical simulations, confirming the potential of truly PT\mathcal{PT}PT-devices as a powerful tool for creating and engineering diverse quantum resources for applications in quantum information technology
Non-Hermitian quantum systems have attracted significant interest in recent years due to the presence of unique spectral singularities in which eigenvalues and eigenvectors coalesce. Those singularities are known as exceptional points (EPs). The drastic changes of the non-Hermitian systems around their EPs have led to unique entanglement dynamics, which remained elusive until quite recently. In this work, we theoretically investigate the robustness of multipartite entanglement induced by EPs of the passive PT -symmetric non-Hermitian superconducting qubits, both in stand-alone configurations and hybrid setups with Hermitian qubits. In particular, we consider the qubits with both all-to-all and nearest-neighbor couplings under uniform and nonuniform coupling strengths. Our results reveal that non-Hermitian qubits with all-to-all coupling generate GHZ states, while those with nearest-neighbor interactions produce W states. These entangled states are resilient to nonuniform couplings, off-resonant driving fields, and decoherence effects. Moreover, the hybrid configurations combining Hermitian and non-Hermitian qubits indicate the necessity of EPs for rapidly generating and maintaining genuine multipartite entanglement. Additionally, driving the PT -symmetric qubits with a strong Rabi frequency can help sustain the entanglement over time by countering losses, while strong interqubit coupling favors the entangled states in the low dissipation regime. We also demonstrate that increasing the number of non-Hermitian qubits speeds up multipartite entanglement generation due to enhanced collective interactions. These findings reveal that exploiting non-Hermitian systems and their associated EPs is beneficial for generating robust and genuine entangled states which are useful for both fundamental studies and quantum technologies.
We study steady-state continuous-variable entanglement in a three-mode optomechanical system consisting of an active optical cavity (gain) coupled to a passive optical cavity (loss) supporting a mechanical mode. For a driving laser which is blue-detuned, we show that coupling between optical and mechanical modes is enhanced in the unbroken-PT\mathcal{PT}PT-symmetry regime. We analyze the stability and this shows that steady-state solutions are more stable in the gain and loss systems. We use these stable solutions to generate distant entanglement between the mechanical mode and the optical field inside the gain cavity. It results in a giant enhancement of entanglement compared to what is generated in the single lossy cavity. This work offers the prospect of exploring quantum state engineering and quantum information in such systems. Furthermore, such entanglement opens up an interesting possibility to study spatially separated quantum objects.
Abstract In this work, we investigate effect of parity-time ( PT ) symmetric operation on the dynamic behavior of entanglement for two qubits system in Markovian and non-Markovian regimes with the resonant and off-resonant cases. First we derive the explicit expressions of concurrence quantifying entanglement for an exactly solving model consisting of two qubits interacting with independent structured reservoir. Then, we give two schemes, i.e. pre- and post- PT symmetric operations, to show the performance of PT symmetric operation on entanglement dynamics of two qubits. By investigation, we find that the lower the absolute value of the PT operation strength, the better the enhancement of entanglement. In addition, we show that the entanglement can be obviously enhanced by means of the pre- PT symmetric operation in different regimes.
The dynamics of tripartite entanglement and intramolecular energy for one harmonic- and two anharmonic-vibrational modes in a symmetric trimer molecule is studied for various initial states, where the entanglement is quantified in terms of concurrence and the interacting energy among three modes is calculated to establish a link between entanglement and energy. It is shown that the concurrence and the interacting energy behave dominantly positive correlation for the localized state in the anharmonic-vibrational mode, while they are dominantly anti-correlated for the localized state in the harmonic-vibrational mode. The relation between bipartite entanglement and the energy in a subsystem is discussed as well. Those are useful for quantum computing and quantum information in high dimensional states prepared in polyatomic molecules.