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arXiv:2407.08525

Using PT-symmetric Qubits to Break the Tradeoff Between Fidelity and the Degree of Quantum Entanglement

Benxin Liu, Shi‐Lei Su, Yi Zuo, Qiongyi He, Gang Chen, Franco Nori, Hui Jing

Published Jul 11, 2024• 2 citations
arXivHTMLPDF

Abstract

A noteworthy discovery is that the minimal evolution time is smaller for parity-time ($\mathcal{PT}$) 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 $\mathcal{PT}$-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 $\mathcal{PT}$-devices as a powerful tool for creating and engineering diverse quantum resources for applications in quantum information technology

DOI
10.48550/arxiv.2407.08525

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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
Breaking the entanglement-fidelity tradeoff in PT{\mathscr{ \mathcal P \mathcal T }}PT-symmetric quantum systems
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 an exceptional point (EP), or spectral coalescence, within such a system. Nevertheless, an important problem often overlooked for quantum EP-based devices is their fidelity, greatly affected by the process of dissipation. We identify an inherent trade-off relation between the degree of entanglement and fidelity, and demonstrate 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 and coupling strength errors. Two- to six-partite entanglement is prepared as the concrete example to show (i) how to break this inherent fidelity-entanglement trade-off even with non-balanced gain and loss, and its resilience against non-resonant errors, in contrast to passive PT{\mathcal{PT}}PT -symmetric dynamics; (ii) achieving speedups of many orders of magnitude, in contrast to conventional Hermitian dynamics. We use this approach to prepare 10-qubit entanglement to show the generality of this method. These findings highlight the potential of truly PT{\mathcal{PT}}PT -symmetric devices as a versatile platform for generating and manipulating diverse quantum resources, with implications for advancing quantum information technologies.
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In the past years, many efforts have been made to study various noteworthy phenomena in both parity-time (PT)(\mathcal{PT})(PT) and anti-parity-time (APT)(\mathcal{APT})(APT) symmetric systems. However, entanglement dynamics in APT\mathcal{APT}APT-symmetric systems has not previously been investigated in both theory and experiments. Here, we investigate the entanglement evolution of two qubits in an APT\mathcal{APT}APT-symmetric system. In the APT\mathcal{APT}APT-symmetric unbroken regime, our theoretical simulations demonstrate the periodic oscillations of entanglement when each qubit evolves identically, while the nonperiodic oscillations of entanglement when each qubit evolves differently. In particular, when each qubit evolves near the exceptional point in the APT\mathcal{APT}APT-symmetric unbroken regime, there exist entanglement sudden vanishing and revival. Moreover, our simulations demonstrate rapid decay and delayed death of entanglement provided one qubit evolves in the APT\mathcal{APT}APT-symmetric broken regime. In this work, we also perform an experiment with a linear optical setup. The experimental results agree well with our theoretical simulation results. Our findings reveal novel phenomena of entanglement evolution in the APT\mathcal{APT}APT-symmetric system and opens a new direction for future studies on the dynamics of quantum entanglement in multiqubit APT\mathcal{APT}APT-symmetric systems or other non-Hermitian quantum systems.
Abstract Parity‐time (PT) symmetric systems with gain‐loss balanced structures can have entirely real eigenenergy spectra despite their non‐Hermitian nature, leading to peculiar discoveries such as single‐mode lasers, wireless power transfer, and non‐reciprocal light propagation. Recently, the study of PT‐symmetry has extended to the quantum realm, inspiring a search for PT‐symmetric quantum effects as well as their unique applications. Here, quantum entanglement and sensing with a PT‐symmetric system of two qubits are studied with Ising‐type interaction. It is shown that exceptional points (EPs) can induce exceptional entanglement phenomena such as collapse‐revival and steady‐state entanglement on the two sides of EPs. The entanglement in the PT‐symmetric system is also found to be generated more quickly than that in the Hermitian counterpart. In addition, a scheme for realizing EP‐enhanced quantum sensing is proposed by calculating the quantum Fisher information to estimate the parameters of the system. The work provides new insights into EP‐engineered quantum effects and can benefit a wide range of applications based on non‐Hermitian quantum devices.
Entanglement generation is a cornerstone of quantum information science, yet its speed in Hermitian systems is fundamentally constrained by the coupling strength, a restriction known as the quantum speed limit. Here we demonstrate that this bound can be beaten by exploiting the unique topology of non-Hermitian systems near exceptional points (EPs). Using a pair of trapped ions, we engineer a parity-time symmetric Hamiltonian where the coalescence of eigenstates near the EP distorts the Hilbert space geometry, providing a shortcut for quantum state evolution. We observe that, as the system approaches the EP, the time required to generate a maximally entangled state is markedly reduced with respect to the limits imposed by the equivalent Hermitian interaction. We further uncover a fundamental physical trade-off whereby the acceleration of entanglement is intrinsically coupled to a reduction in the success probability, revealing the information cost of non-Hermitian speedup. Our results suggest that tailored dissipation, rather than being a source of decoherence, can serve as a powerful resource for accelerating quantum dynamics, offering a new paradigm for designing high-speed quantum gates and sensors in hardware-constrained platforms.
Abstract Open quantum systems are susceptible to losses in information, energy, and particles due to their surrounding environment. One novel strategy to mitigate these losses is to transform them into advantages for quantum technologies through tailored non-Hermitian quantum systems. In this work, we theoretically propose a fast generation of multipartite entanglement in non-Hermitian qubits. Our findings reveal that weakly coupled non-Hermitian qubits can accelerate multiparty entanglement generation by thousands of times compared to Hermitian qubits, in particular when approaching the 2 n -th order exceptional points of n qubits in the P T − symmetric regime. Furthermore, we show that Hermitian qubits can generate GHZ states with a high fidelity more than 0.9995 in a timescale comparable to that of non-Hermitian qubits, but at the expense of intense driving and large coupling constant. Our approach is scalable to a large number of qubits, presenting a promising pathway for advancing quantum technologies through the non-Hermiticity and higher-order exceptional points in many-body quantum systems.