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arXiv:2511.04110

Controllable Non-Hermitianity in Continuous-Variable Qubits

Ke-Xiong Yan, Zhi-Cheng Shi, Ye-Hong Chen, Yan Xia

quant-phSubmitted Nov 6, 2025• Announced Nov 7, 2025• 0 citations
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Abstract

Pure dephasing is the dominant leak mechanism in photonic cat qubits because its phase errors disrupt the parity protection, rendering the qubit vulnerable to energy relaxation. In this manuscript, we reveal that this dephasing mechanism conceals an interesting physical phenomenon: it induces \textit{asymmetric leakage} from the cat-state subspace, where even- and odd-parity cat states decay at different rates. This leak asymmetry enables the dynamics of the system to be described by a non-Hermitian Hamiltonian, thereby transforming the cat qubit into a platform with controllable gain and loss for probing non-Hermitian physics. Within this platform, we demonstrate the possibility to control the parity-time symmetry phase transition in a single cat qubit by adjusting its amplitude. Moreover, we couple two cat qubits to realize an entanglement phase transition induced by the exceptional point. Our work constructs a controllable non-Hermitian system simulator, overturning the conventional paradigm that treats dephasing as harmful noise.

Comments
7 pages, 4 figures, welcome to comments

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Pure dephasing is the dominant leak mechanism in photonic cat qubits because its phase errors disrupt the parity protection, rendering the qubit vulnerable to energy relaxation. In this manuscript, we reveal that this dephasing mechanism conceals an interesting physical phenomenon: it induces \textit{asymmetric leakage} from the cat-state subspace, where even- and odd-parity cat states decay at different rates. This leak asymmetry enables the dynamics of the system to be described by a non-Hermitian Hamiltonian, thereby transforming the cat qubit into a platform with controllable gain and loss for probing non-Hermitian physics. Within this platform, we demonstrate the possibility to control the parity-time symmetry phase transition in a single cat qubit by adjusting its amplitude. Moreover, we couple two cat qubits to realize an entanglement phase transition induced by the exceptional point. Our work constructs a controllable non-Hermitian system simulator, overturning the conventional paradigm that treats dephasing as harmful noise.
Exceptional points in non-Hermitian quantum systems give rise to novel genuine quantum phenomena. Recent explorations of exceptional-point-induced quantum phase transitions have extended from discrete-variable to continuous-variable-encoded quantum systems. However, quantum phase transitions driven by Liouvillian exceptional points (LEPs) in continuous-variable platforms remain largely unexplored. Here, we construct and investigate a Liouvillian exceptional structure based on a driven-dissipative Kerr-cat qubit. Through numerical simulations, we reveal a quantum phase transition occurring at the LEP characterized by a sudden change in dynamical behavior from underdamped oscillations to overdamped relaxations as visualized via Wigner functions and Bloch sphere trajectories. Notably the negativity of the Wigner function serves as a direct signature of genuine quantum coherence unattainable in conventional single-qubit non-Hermitian systems. Furthermore, we introduce the phase difference between the off-diagonal elements of the Liouvillian eigenmatrices as a novel parameter to quantify the transition. Our results establish the Kerr-cat qubit as a novel continuous-variable setting for exploring dissipative quantum criticality and intrinsic non-Hermitian physics.
Dissipatively stabilized cat qubits are promising for fault-tolerant quantum information processing, yet their non-Hermitian (NH) spectral topology remains largely unexplored. We uncover rich Liouvillian exceptional structures in a cat-qubit mode stabilized by two-photon drive (TPD) and engineered two-photon loss, in the presence of single-photon drive (SPD) and single-photon loss. In the parameter space spanned by SPD strength and detuning, we identify both second- and third-order Liouvillian exceptional points (LEP2s and LEP3s). Remarkably, we show that the phase θθθ of TPD provides coherent control over these exceptional points: the LEP3 diverges and vanishes at θ=π/2θ=π/2θ=π/2, while remaining stable and tunable elsewhere. We introduce a topological invariant based on the winding number of a resultant vector, which robustly identifies LEP3s with unit topological charge. Full master-equation simulations confirm that the system dynamics remains confined to the logical subspace with near-unity fidelity. Our results bridge dissipative stabilization, phase-coherent control, and NH topology, demonstrating controllable higher-order LEPs in open quantum systems.
Abstract Exceptional points in non-Hermitian quantum systems give rise to genuine quantum phenomena. Recent explorations of exceptional-point-induced phase transitions have extended from discrete-variable to continuous-variable-encoded quantum systems. However, phase transitions driven by Liouvillian exceptional points (LEPs) in continuous-variable platforms remain largely unexplored. Here, we construct and investigate a Liouvillian exceptional structure based on a driven-dissipative Kerr-cat qubit. Through numerical simulations, we numerically reveal a non-Hermitian phase transition occurring at the LEP characterized by a sudden change in dynamical behavior from underdamped oscillations to overdamped relaxations as visualized via Wigner functions and Bloch sphere trajectories. The dynamical pattern of Wigner interference fringes provides a phase-space signature of the LEP-induced phase transition, while Wigner negativity certifies the genuine quantum nonclassicality of the system. Our results establish the Kerr-cat qubit as a continuous-variable setting for exploring dissipative quantum criticality and intrinsic non-Hermitian physics.
The intriguing physical phenomena associated with exceptional points have established non-Hermitian physics as a frontier of modern research. Recent investigations have extended non-Hermitian physics into the fully quantum domain. However, existing studies predominantly concentrate on discrete-variable quantum systems, while non-Hermitian quantum effects in continuous-variable encoded systems remain largely unexplored. In this work, we investigate the exceptional structure for a driven-dissipative Kerr-cat qubit, realized with a Kerr nonlinear resonator. We find that the dissipation leads to a bidirectional jump between the two basis states of the cat qubit, which is in distinct contrast with the unidirectional jump associated with normal two-level systems. The competition between this jump and a single-photon drive gives arise to the emergence of third-order Liouvillian exceptional points (LEP3s), each corresponds to a crossing point of two lines of LEP2s. We further show that the LEP3 can exhibit the topological character of the Hamiltonian EP3s, which cannot be realized with a single qubit. Our work opens the possibility of realizing non-Hermitian phenomena with continuous-variable quantum systems.
Parity-time (PT ) symmetric systems are gain-loss systems whose dynamics are governed by non-Hermitian Hamiltonians with degeneracies at exceptional-points (EPs) and has been studied in various photonic, electrical, mechanical systems, and so on. However, it is still an open question how to capture PT symmetry phase transition in electronic system where the transport properties of electron will be dramatically effected. Fortunately, the hybridization between photon and electron offers a novel way not only to control but also probe material properties. Here, we investigate a cavity coupled to a non-Hermitian Su-Schrieffer-Heeger (SSH) chain within mean-field ansatzs. We find that Squeezed Displaced Schrodinger cat (SDSc) will emerge with high fidelity in cavity ground state when PT -symmetry is broken and the fidelity will experience a sharp drop from almost 1 to 0 as PT symmetry recovers. Additionally, in semiclassical limit, we find that there exists local extrema at two sides of x=0x=0x=0 in semiclassical photon Hamiltonian Heff(x,p)H_{\rm eff}(x, p)Heff​(x,p), a clear signature of the emergence of SDSc state in cavity ground state. Thus, the appearance of SDSc state can be used to capture PT-symmetry phase transition which can not be modified by cavity mode. Besides, we exploit the cavity ground state to estimate the phase in the optical interferometer, and show that the quantum Fisher information and nonclassicality will sharply decline at EPs. This reveals that PT-symmetry breaking in electronic materials can also be captured by the quantum Fisher information and nonclassicality in phase estimation.
Exceptional-point (EP) sensing has attracted considerable interest because of its anomalous response scaling. However, recent studies have shown that the enhanced response near an EP is inevitably accompanied by amplified quantum noise, fundamentally limiting the achievable signalto-noise ratio (SNR). Here, we propose a fundamentally different route toward non-Hermitian quantum sensing based on symmetry-protected noise suppression rather than response amplification. We develop a fully quantum continuous-variable model that unifies parity-time (PT) and anti-paritytime(APT) symmetries within a single framework. Exploiting the incompatibility between these two symmetries, we uncover a non-Hermitian Dirac eigenspectrum and reveal a hidden symmetryprotected phase transition embedded in the Hamiltonian spectrum. Remarkably, this hidden phasetransition simultaneously constitutes a symmetry-protected vacuum-noise fixed point, where collective three-mode quadratures exhibit suppressed quantum fluctuations despite the absence of any anomalous spectral response. As a consequence, quantum sensing is enhanced through the suppression of excess quantum noise while maintaining a finite response sensitivity, establishing a sensing mechanism fundamentally different from conventional EP-based approaches. These results reveal an unexpected connection between hidden symmetry, quantum fluctuations, and non-Hermitian quantum metrology, and establish noise suppression as an alternative paradigm for non-Hermitian quantum sensing.