⚛️ quantum physics

Chiral Transfer and Entanglement Generation of Even-Parity Bell States with Engineered Two-Photon Loss

This paper demonstrates that a two-qubit system with engineered two-photon loss and coherent driving can achieve direction-dependent chiral transfer between even-parity Bell states and generate strong entanglement from separable states by adiabatically encircling a second-order exceptional point, utilizing a hybrid-Liouvillian framework to validate the robustness of these effects against quantum jumps.

Original authors: Lin Xiao, Jian Li, Mu Zhou, Bin Wei, Qing-Xu Li, Jia-Ji Zhu

Published 2026-09-28

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CC BY 4.0

Original authors: Lin Xiao, Jian Li, Mu Zhou, Bin Wei, Qing-Xu Li, Jia-Ji Zhu

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the quiet, controlled world of quantum physics, scientists have long treated the environment as an enemy. To keep delicate quantum states alive, the standard approach has been to isolate them completely, shielding them from the outside world to prevent the loss of information. However, a newer perspective suggests that this isolation is not the only path. Instead, researchers are learning to design the environment itself, turning the very act of energy loss into a tool for building and shaping quantum states. This approach relies on a concept known as an exceptional point, a special condition where the rules of energy and decay merge in a way that makes the system behave differently depending on the direction from which it is approached. By carefully guiding a system around this point, scientists can create a one-way street for quantum information, forcing it to move in a specific direction regardless of how it started.

Building on this idea, a team of researchers has now demonstrated a method to control and create a specific type of powerful connection between two particles, known as an even-parity Bell state. These states are unique because they link the particles in a way that involves both the complete absence of energy and the presence of two energy units simultaneously, a delicate balance that is notoriously difficult to maintain. The researchers worked with a system of two interacting quantum bits, or qubits, and applied a specific type of rhythmic driving force while engineering a controlled leak of energy. This setup created a scenario where the system could be steered around an exceptional point. When they guided the system in a counter-clockwise direction around this point, the two particles reliably switched from one specific linked state to another. When they guided it in the opposite direction, the switch was effectively blocked. This directional control, known as chiral transfer, was achieved with high precision, showing that the system could be made to follow a chosen path with a success rate of nearly ninety-nine percent when the process was carefully monitored.

The study also revealed that this same mechanism could be used to create entanglement from scratch. By starting the system in a simple, unconnected state and running it through the same directional loop, the researchers found that the process naturally generated a strong, linked state between the two particles. This means that a single experimental setup could serve two purposes: transferring existing quantum information and creating new quantum connections. The team simulated these processes to see how they would hold up against real-world imperfections, such as random noise or unintended energy loss. They found that the method is remarkably robust. Even when the system was subjected to significant disturbances, the directional control remained effective, and the generated connections stayed strong. This resilience is partly because the specific way the energy was engineered to leak out kept the system within a protected zone, preventing the particles from falling into states where the connection could not be recovered.

To understand how these results would look in a real laboratory, the researchers translated their theoretical numbers into the language of superconducting circuits, a common platform for building quantum computers. They determined that the required driving forces and timing intervals are well within the reach of current technology. The entire process would take place in just a few microseconds, a blink of an eye in human terms but a long duration for quantum events. The simulations suggest that with the best available equipment, the unwanted noise from the environment would be so small compared to the engineered control that it would barely disturb the outcome. This indicates that the method is not just a theoretical curiosity but a practical recipe for future quantum devices.

The work highlights a fundamental shift in how quantum states can be managed. Rather than fighting against the environment to preserve a state, the researchers showed how to harness the flow of energy to build and move states with purpose. By using a loop of control parameters that encircles a special point of instability, they created a system where the direction of travel dictates the final result. This discovery extends the ability to control quantum states beyond simple scenarios, proving that complex, two-particle connections can be manipulated and generated using engineered dissipation. It offers a clear path forward for creating and moving the specific types of quantum links that are essential for advanced computing and communication, all while working with the natural tendency of systems to lose energy rather than fighting against it.

Technical Summary: Chiral Transfer and Entanglement Generation of Even-Parity Bell States with Engineered Two-Photon Loss

Problem Statement
While chiral state transfer (CST) via the adiabatic encircling of exceptional points (EPs) has been demonstrated for odd-parity Bell states ( $|\Psi^\pm\rangle$ ) within the single-excitation manifold, extending this control to even-parity Bell states ( $|\Phi^\pm\rangle = (|00\rangle \pm |11\rangle)/\sqrt{2}$ ) presents distinct physical challenges. Unlike odd-parity states, even-parity states require coherence between the zero- and two-excitation sectors. Consequently, their generation and control cannot rely on single-excitation-conserving dynamics; they necessitate a specific dissipative architecture based on two-photon processes. The central question addressed is whether EP-induced chiral transfer and dissipative entanglement generation are feasible in this even-parity setting and how their dynamical features are modified by the presence of quantum jumps.

Methodology
The authors propose a two-qubit system driven by a coherent two-photon field and subject to engineered two-photon loss. The system Hamiltonian includes a two-photon driving term with strength $\Omega$ and phase $\phi$ , while the dissipation is modeled by a jump operator $L = \sqrt{\kappa}\sigma^{(1)}_-\sigma^{(2)}_-$ , describing the decay from $|11\rangle$ to $|00\rangle$ .

To analyze the dynamics across different monitoring regimes, the authors develop a hybrid-Liouvillian description governed by a control parameter $q \in [0, 1]$ :
$\dot{\rho} = \mathcal{L}[q]\rho = -i(H_{\text{eff}}\rho - \rho H_{\text{eff}}^\dagger) + q \sum_k L_k \rho L_k^\dagger$

$q=0$ : Represents conditional "no-jump" dynamics (post-selected trajectories).
$q=1$ : Represents unconditional Lindblad evolution (full master equation).
$0 < q < 1$ : Models imperfect monitoring followed by post-selection, where a fraction of jump events are discarded.

The protocol involves adiabatically encircling a second-order exceptional point (EP) in the parameter space of the two-photon detuning ( $\Delta_p$ ) and driving strength ( $\Omega$ ). The study investigates two scenarios:

Chiral Transfer: Starting from an even-parity Bell state ( $|\Phi^+\rangle$ ) and targeting the orthogonal state ( $|\Phi^-\rangle$ ).
Entanglement Generation: Starting from the separable state $|00\rangle$ and evolving along the same loop.

Key Results

Chiral State Transfer:
- Encircling the EP induces direction-dependent transfer between $|\Phi^+\rangle$ and $|\Phi^-\rangle$ .
- In the post-selected limit ( $q=0$ ), counter-clockwise (CCW) encircling achieves near-perfect transfer fidelity ( $F \approx 0.9976$ ), while clockwise (CW) encircling suppresses transfer ( $F \approx 0.0002$ ).
- The mechanism is governed by a time-integrated low-loss branch-selection process. While the EP encircling determines the geometric branch exchange, the chiral asymmetry is dominated by the selection of the low-loss eigenstate branch during the evolution.
- Under full Lindblad dynamics ( $q=1$ ), the chiral contrast decreases but remains significant ( $\Delta F \approx 0.77$ ), demonstrating robustness against quantum jumps.
Entanglement Generation:
- Initializing the same EP-encircling loop in the separable state $|00\rangle$ directly generates strong even-parity entanglement.
- The separable state enters the loop as a superposition of the two eigenstate branches; the branch-selection mechanism drives the system toward the low-loss branch, which corresponds to a Bell state.
- For $q=0$ , the protocol generates near-maximal concurrence. Even for $q=1$ , the final concurrence remains high ( $C \approx 0.827$ ), indicating that the protocol retains substantial entanglement-generation capability despite dissipation.
Robustness and Comparison:
- The even-parity scheme exhibits superior robustness against parasitic single-photon loss compared to previous odd-parity schemes. In the even-parity manifold, parasitic loss recycles population back into the protected subspace (specifically to $|00\rangle$ ), whereas in odd-parity schemes, it removes population from the single-excitation manifold entirely.
- The protocol identifies an intermediate operating window (driving period $T \in [11, 20]\kappa^{-1}$ ) that balances non-Hermitian adiabaticity, transfer fidelity, and post-selection success probability.

Significance and Claims
The paper claims to extend dissipative Bell-state control beyond the single-excitation manifold to the even-parity sector. The authors emphasize three structural distinctions that define their work:

Manifold Protection: The even-parity subspace is strictly decoupled by parity, requiring parametric two-photon driving and engineered two-photon loss, which are qualitatively different resources from those used for odd-parity states.
In-Manifold Jumps: The engineered jump operator acts entirely within the target manifold. This structural protection ensures that quantum jumps degrade but never depopulate the target subspace, allowing for high-fidelity chiral contrast and concurrence even in the unconditional limit ( $q=1$ ).
Unified Protocol: A single EP-encircling loop serves a dual purpose: it enables chiral transfer between Bell states and generates entanglement from a separable state within one engineered platform.

The authors assert that these results demonstrate that exceptional-point-based protocols can unify chiral state transfer and entanglement generation. They suggest the scheme is experimentally feasible in superconducting circuits, where the required two-photon driving and engineered dissipation have already been demonstrated, and where parasitic decoherence rates are sufficiently low to preserve the chiral dynamics.

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