arXiv subjects

Jun Jing

Publications and source records attributed to Jun Jing.

At least 19 recordsLinked to original sources

arXiv2026

Biorthogonal universal quantum control

As a paradigm for describing open-quantum-system dynamics, the non-Hermitian Schrödinger equation generally modifies state norms, complicating coherent control over the system's Hilbert space. With a general instantaneous frame spanned by biorthogonal ancillary bases, we develop a biorthogonal quantum-control theory for discrete-variable systems governed by time-dependent non-Hermitian Hamiltonian. In particular, we derive a necessary and sufficient condition for extracting the transitionless pathways that transport parallel in ket and bra states. When this condition is satisfied by a set of projectors constructed with biorthogonal basis states, the non-Hermitian Hamiltonian becomes diagonal in the relevant biorthogonal subspace, enabling arbitrary initial state to evolve as a superposition of controlled transitionless passages. We further identify the parametric constraints under which the transformation linking the initial and final states becomes unitary. As a result, the final system state is automatically normalized even though the transitional dynamics is nonunitary. Our theory is justified by the bidirectional population transfer and a holomonic quantum gate implemented by a non-Hermitian three-level system in $Λ$ type. For the population transfer, controlled gain and loss reduce the required coherent pulse area, enabling shorter transfer times than the Hermitian benchmark with the same average Rabi frequency. Our work integrates the universal quantum control (UQC) into the biorthogonal representation, displaying full-rank passage engineering with coherent operations in non-Hermitian systems.

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arXiv2026

Noise-Assisted Quantum Entanglement: Memory-Enhanced Coherence in Stochastic Jaynes-Cummings Dynamics

We investigate qubit entanglement dynamics in a two-qubit cavity system with stochastically fluctuating coupling strength, comparing white noise (Markovian) and Ornstein-Uhlenbeck noise (non-Markovian) processes. We analytically solve the system dynamics for both Fock and coherent cavity states and systematically characterize how initial qubit configurations affect entanglement generation and preservation. Our results reveal distinct dynamical regimes: in the Fock-state cavity, initial states in the single-excitation subspace generate robust qubit entanglement in decoherence-free subspaces, while initially entangled states in the double-excitation subspace exhibit inevitable decay without protective symmetries. For coherent cavities, we identify a critical photon-number threshold in the intermediate coherent-state amplitude regime where dynamics transition from low-frequency to high-frequency entanglement oscillations, while universal entanglement loss occurs at large amplitudes. Remarkable resilience against entanglement sudden death emerges under strong non-Markovian noise with long correlation times, where repeated revivals occur. These findings establish cavity photon statistics and environmental memory time as key control parameters for engineering qubit entanglement dynamics in qubit-cavity systems, revealing how system-environment correlations govern quantum information preservation.

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arXiv2026

From Liouville equation to universal quantum control: A study of generating ultra highly squeezed states

We find that the seemingly disparate control approaches for classical and quantum continuous-variable systems can be unified via differential manifolds of the ancillary representations. For classical systems, the ancillary representation is defined by the time-dependent ancillary canonical variables resulting from symplectic transformation over the original canonical variables. Under the Hamilton-Jacobi theory, the ancillary canonical variables act as dynamical invariants to guide the system nonadiabatically through the entire phase space. The second quantization of the Liouville equation for the dynamical invariants leads to the Heisenberg equation for the relevant ancillary operators, which is found to be a sufficient condition to activate nonadiabatic passages towards arbitrary target states in both Hermitian and non-Hermitian systems and yield constrained exact solutions of the time-dependent Schroedinger equation. Using the non-Hermitian Hamiltonian rigorously derived from the Lindblad master equation, our theory is exemplified by the generation of single-mode squeezed states with a squeezing level about 29.3 dB and double-mode squeezed states with 20.6 dB, respectively.

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arXiv2026

Precision limit under weak coupling with an ancillary qubit

We propose a measurement-based quantum metrology protocol in a composite model, where the probe system (a spin ensemble) is coupled to an ancillary two-level system (qubit) with a general Heisenberg XXZ interaction. With optimized probe-ancilla coupling strengths and duration of joint evolution, the two parallel evolution paths of the probe system induced by the unconditional measurement on qubit can transform an eigenstate of the collective angular momentum operator of spin ensemble into a two-component state with a large distance in eigenspace. The quantum Fisher information about the phase encoded in the probe system of polarized states or their superposition, that could be relaxed to mixed states, can therefore manifest an exact or asymptotic quadratic scaling with respect to the probe size (spin number) $N$. The quadratic scaling behavior is found to be insensitive to the imperfect encoding operator, polarized direction of probe, and coupling strength. The phase sensitivity can approach the Heisenberg limit by virtue of the parity detection on either ancillary qubit or probe system. This work justifies that the unconditional measurement on a weakly coupled qubit could be an efficient resource to replace Greenberger-Horne-Zeilinger-type states and squeezing Hamiltonian for exceeding the standard quantum limit in metrology precision.

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arXiv2026

Generating Fock state exceeding 10000 excitations with near unit fidelity by adaptive generalized-parity measurement

Fock states are fundamental quantum states with a precisely defined integer number of excitations, serving as the core basis for describing bosonic modes. Large Fock states provide irreplaceable non-classical resources for quantum information processing and quantum metrology. The deterministic generation of macroscopic photon-number Fock states has long been a difficult problem in the field of quantum optics. We propose an adaptive generalized parity measurement (GPM) protocol for generating Fock states with more than $10000$ excitations, avoiding low success probability subject to postselection and high cost under complex coherent controls. For general discrete-spectrum systems, e.g., a bosonic mode coupled to an ancillary qubit, we derive a construction rule in which the intervals between repeated measurements on qubit are updated adaptively based on the last outcome. It means that our protocol does not discard any measurement trajectory, dramatically different from the probabilistic protocols that retain only one prescribed trajectory of postselection. In the resonant Jaynes-Cummings model, a large coherent state can be almost deterministically transformed to a large Fock state of $n_t=\mathcal{O}(10^4)$ excitations by $10$ rounds of measurements, the average fidelity of which is about $87\%$. The success probability for obtaining $|20000-\sqrt{20000}\leq n_t\leq20000+\sqrt{20000}\rangle$ with a fidelity above $99\%$ is about $35\%$ with respect to the ensemble sampling. Our protocol is fault-tolerant in the presence of moderate measurement error and parametric imperfection. Also it remains effective when the system is prepared as displaced thermal states, showing reliable performance regardless of initial state.

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arXiv2026

Criterion for qubit-assisted quantum metrology approaching Heisenberg scaling

We study in this work the metrology precision of a probe system coupled to an ancillary qubit. Restricting the probe-qubit coupling along only one or two directions is found to be a sufficient criterion for the effective dynamical generator to achieve the Heisenberg limit in precision. Under the criterion, the quantum Fisher information (QFI) about the to-be-estimated parameter becomes the expectation value of mean square of the effective generator with respect to the initial state of the composite system. Our criterion is justified in two distinct systems. For a bosonic probe, QFI about the displacement estimation is found to be proportional to the mean excitation number of probe. It renders a counterintuitive result that quantum metrology sensitivity can be enhanced by increasing the temperature of the probe system. For a spin-ensemble probe, QFI about both rotation-phase and magnetic-field estimation exhibit a quadratic dependence on the probe-spin number. It is found that even when the spin-ensemble is prepared as a finite-temperature state, faraway from the so-called resource states, e.g., the squeezed state or the Greenberger-Horne-Zeilinger state, QFI can still manifest a Heisenberg scaling behavior.

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arXiv2026

Deterministic generation of cat states with more than $100$ photons under dissipation

Large-size cat states are especially meaningful and fundamental for exploring the quantum-to-classical transition, as well as promising resources for quantum metrology and fault-tolerant quantum computation. However, amplifying the magnitude of cat states remains challenging because of the growing fragility under decoherence. We propose to generate large cat states by using the dynamical invariant of hybrid qubit-bosonic systems under Hermitian or non-Hermitian time-dependent Hamiltonian. It is a study with the universal quantum control (UQC) theory, in which the system dynamics is analyzed in the ancillary picture via a unitary transformation conditional on the qubit state. The controllable dynamics that can be encoded in the evolution of the dynamical invariant is presented by the Heisenberg equation, which imposes constrains on the Hamiltonian. When the qubit is prepared in a balanced superposed state, the bosonic mode can evolve deterministically from the vacuum state to the cat state of a mean photon number over $120$. In the Hermitian case, the generation is perfect; and in the non-Hermitian case, the fidelity is over $0.962$. Our protocol can also be applied to the generation of the intrinsic cat states and the four-component cat states of large size. Through the preparation of macroscopic quantum states, our work essentially advances UQC to hybrid discrete-continuous variable systems.

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arXiv2026

Universal quantum control over non-Hermitian continuous-variable systems

Current studies about the continuous-variable systems in non-Hermitian quantum mechanics heavily revolved around the singularities in the eigenspectrum by mimicking their discrete-variable counterparts. Discussions over the nonunitary features in time evolution are growing and yet limited in scalability and controllability. We develop here a general theory to control an arbitrary number of bosonic modes under time-dependent non-Hermitian Hamiltonian. Far beyond the subspace of few excitations, our control theory operates in the Heisenberg picture and exploits the gauge potential underlying the instantaneous frames rather than the eigenspectrum. In particular, instantaneous frames are defined by time-dependent ancillary operators as linear combinations of the laboratory-frame operators, while the gauge potential arises from the unitary transformation between the time-dependent and stationary ancillary frames. We find that upper triangularization condition of the non-Hermitian Hamiltonian's coefficient matrix in the stationary ancillary frame yields two nonadiabatic passages in both bra and ket spaces and also the exact solutions of the time-dependent Schrödinger equation. At the end of these passages, probability conservation of wave function is automatically restored without brute-force normalization. Our theory is exemplified by perfect and nonreciprocal state transfers in a cavity magnonic system under non-Hermitian Hamiltonian rigorously derived from the Lindblad master equation with all quantum-jump terms retained. Under certain conditions, perfect state transfer holds for arbitrary initial states and is irrelevant to both parity-time symmetry of coefficient matrix and exceptional points of eigenspectrum. The nonreciprocal transfer is consistent with coherent perfect absorption, providing a first-principles route to coherent control of non-Hermitian continuous-variable systems.

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arXiv2026

Efficient nonclassical state preparation via generalized parity measurement

Nonclassical states of bosonic modes, especially the large number states, are valuable resources for quantum information processing and quantum metrology. It is however intricate to generate a desired Fock state of bosonic systems by unitary protocols due to their uniform energy spectrum. We here propose a nonunitary protocol that is based on the resonant Jaynes-Cummings interaction of the bosonic mode with an ancillary two-level atom and sequential projective measurements on the atom. Using the generalized parity-measurement operator constructed by several rounds of free evolution with stepwise halved intervals and measurement, we can efficiently filter out the unwanted population and push the target resonator conditionally toward the desired Fock state. In the ideal situation, a Fock state $|n_t\approx2000\rangle$ can be prepared with a fidelity over $98\%$ using only eight rounds of measurements. Under qubit dissipation and dephasing and cavity decay in the current circuit-QED platforms, a Fock state $|n_t\approx100\rangle$ can be prepared with a fidelity of about $80\%$ by six measurements. It is found that the number of measurement rounds for preparing a large Fock state $|n_t\rangle$ scales roughly as $\log_2\sqrt{n_t}$, which is similar to the number of ancillary qubits required in the state preparation via the quantum phase estimation algorithm and yet costs much less in gate operations. Our protocol can also be used to prepare a large Dicke state $|J\simeq1000,0\rangle$ of a spin ensemble with a sufficiently high fidelity by less than six measurements. It is qualified by the quantum Fisher information approaching the Heisenberg scaling in sensing the rotation phase along the $x$ axis.

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arXiv2026

Universal quantum control over bosonic network

Perfect transfer of {\em unknown} states across distinct nodes is a basic function in bosonic quantum networks. Here we develop a general theory to construct an $N$-node bosonic network governed by the time-dependent Hamiltonian, as the universal quantum control theory for continuous-variable systems. In particular, we can activate nonadiabatic passages superposed of initial and target modes by the commutation condition about the Hamiltonian's coefficient matrix and projection operator in the representation of time-independent ancillary modes, which serves as the necessary and sufficient condition to solve the time-dependent Schrödinger equation of the full Hamiltonian. To exemplify the versatility of our theory on the Heisenberg-picture passages, we perform arbitrary state exchange between two nodes, chiral entanglement transfer among three bosonic nodes, and chiral Fock-state transfer among three of four bosonic nodes. Our work provides a promising avenue toward the universal control of any pair of nodes or modes as well as the entire bosonic network.

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arXiv2025

Universal quantum control over Majorana zero modes

Majorana zero mode (MZM) exhibits inherent resilience to local parametric fluctuations, due to the topological protection mechanism in the non-Abelian braiding statistics of the anyonic quasiparticles. In this paper, we construct the braiding operations between an arbitrary pair in three MZMs under the theoretical framework of universal quantum control. Largely detuned driving fields on the mediator, a local defect of lattice, enable indirect and tunable exchange interaction between arbitrary two MZMs. The braiding operations can then emerge through the time evolution along the universal nonadiabatic passages, whose robustness against driving-field errors and quasiparticle poisoning can be substantially enhanced by the rapid modulation over the passage-dependent global phase. Moreover, a chiral transfer for population on MZMs along the universal passage can be perfectly demonstrated in both clockwise and counterclockwise manners without eliminating the mediator defect. Our protocol is linear scalable and provides an avenue towards the universal quantum control over MZMs, which is fundamental and essential for topological quantum computation.

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arXiv2025

Achieving the Heisenberg limit of metrology via measurement on an ancillary qubit

In the scenario of the probe-ancilla interaction, we propose a quantum metrology protocol by the unconditional measurement on the ancillary qubit after an optimized period of joint evolution from product state. Its key element is the construction of two parallel evolution paths by the measurement that can transform the probe system (a spin ensemble) from an eigenstate of a collective angular momentum operator $|j,m\rangle$ to a superposed state $(|j,m\rangle+|j,-m\rangle)/\sqrt2$. With synchronous parametric encoding and qubit measurement, the quantum Fisher information about the phase encoded in the probe system with optimized initial states can exactly attain the Heisenberg scaling $N^2$ with respect to the probe size (spin number) $N$. The quadratic scaling behavior is not sensitive to the imprecise control over the joint evolution time, the time delay between encoding and measurement, and the coherence in the probe ensemble or the ancillary system that would be degraded by local dephasing. The classical Fisher information of the spin ensemble is found to saturate with its quantum counterpart, irrespective of the idle joint evolution after the parametric encoding. We suggest that both Greenberger-Horne-Zeilinger (GHZ)-like states and nonlinear Hamiltonian are {\em not} necessary resources for exceeding the standard quantum limit in metrology precision since in our protocol even thermal states can hold an asymptotic quadratic scaling.

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arXiv2025

Dissipative qutrit-mediated stable charging

In this work, we propose a stable charging scheme mediated by a three-level system (qutrit), which renders a unidirectional energy flow from an external power source to an $(N+1)$-dimensional quantum battery. By virtue of the qutrit dissipation, the battery avoids the spontaneous discharging induced by the time-reversal symmetry of any unitary-charging scheme. Irrespective of the initial state, the battery can be eventually stabilized at the maximal-ergotropy state as long as the charger-battery interaction is present. We use a Dyson series of Lindbladian superoperator to obtain an effective master equation for the battery, which is found to be equivalent to the high-order Fermi's golden rule adapted to the non-Hermitian Hamiltonian and spontaneous decay. We extract the optimization condition for charging efficiency and justify it in the finite-size battery with uniform energy splitting, the large spin battery, and the truncated harmonic-oscillator battery.

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arXiv2025

Universal quantum control by non-Hermitian Hamiltonian

Conventional manipulations over quantum systems for such as coherent population trapping and unidirectional transfer focus on Hamiltonian engineering while regarding the system's manifold geometry and constraint equation as secondary causes. Here we treat them on equal footing in controlling a finite-dimensional quantum system under a time-dependent non-Hermitian Hamiltonian, which is inspired by the D'Alembert principle of regarding active force, constraint force, and inertial force in an unbiased way. Under the biorthogonal condition, the non-Hermitian Hamiltonian could be triangularized in a constraint picture spanned by a set of completed and orthonormal basis states, which is found to be a sufficient condition to construct at least one universal nonadiabatic passage in both bra and ket spaces. The passage ends up with a desired target state that is automatically normalized without artificial normalization in the existing treatments for non-Hermitian quantum systems. Moreover, the passage is found to be robust against the parametric deviation when the real part of its global phase is rapidly varying with time. Our protocol is explicitly verified for the perfect population transfer in the two-level system and the chiral population transfer in the three-level system. It generalizes our framework of universal quantum control to the field of the biorthogonal quantum mechanics.

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arXiv2025

Universal quantum control with dynamical correction

Error correction is generally demanded in large-scale quantum information processing and quantum computation. We provide here a universal and realtime control strategy to dynamically correct the arbitrary type of errors in the system Hamiltonian. It yields multiple error-resilient paths for the interested system which are activated by the von Neumann equation for ancillary projection operators. With no extra control fields and precise designs, the path-dependent global phase alone suffices to mitigate the error-induced transitions among distinct paths as long as it varies faster than the other parameters. The corrected paths can also be regarded as the approximate solutions to the time-dependent Schrödinger equation perturbed by errors. Our dynamical-correction strategy is practiced with the cyclic transfer of populations in a three-level system, showing a superior error resilience to the parallel-transport condition. It provides a promising idea for advancing control methodologies in imprecise quantum systems.

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arXiv2025

Preparing Greenberger-Horne-Zeilinger state on ground levels of neutral atoms

We propose a scalable protocol in the Rydberg atomic system to generate the Greenberger-Horne-Zeilinger (GHZ) states, where the qubits are encoded on the hyperfine ground levels. Our system is featured with off-resonant driving fields rather than strong Rydberg interaction sufficient for blockade. Closely it can follow the desired nonadiabatic passage during the time evolution and avoid the unwanted transition by imposing the passage-dependent and fast-varying global phase, that serves as an error correction to the universal quantum control. In our protocol, an $N$-qubit GHZ state is prepared in $N-1$ steps, which is found to be robust against both environmental noise and systematic deviation. Our protocol therefore provides an avenue toward large-scale entanglement, which is essential for quantum information processing and computation based on neutral atoms.

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arXiv2025

Entangling distant systems via universal nonadiabatic passage

In this paper, we derive universal nonadiabatic passages in a general $M+N$-dimensional discrete system, where $M$ and $N$ denote the degrees of freedom for the assistant and working subspaces, respectively, that could be separated by rotation or energy and coupled through driving. A systematic method is provided to construct parametric ancillary bases by the von Neumann equation with the time-dependent system Hamiltonian. The resulting universal passages set up connections between arbitrary initial and target states. In applications, a transitionless dynamics can be formulated to entangle distant qubits, as a crucial prerequisite for practical quantum networks. Using tunable longitudinal interaction between distant qubits and driving frequency, the superconducting qubits can be prepared from the ground state to the single-excitation Bell state with a fidelity as high as $\mathcal{F}=0.997$ and be further converted to the double-excitation Bell state with $\mathcal{F}=0.982$. Moreover, our protocol is extended to generate the Greenberger-Horne-Zeilinger state for an $N$-qubit system with $N$ steps. Our work develops a full-fledged theory for nonadiabatic state engineering, which is flexible in target selection and robust against both external noises and systematic errors in quantum information processing.

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arXiv2025

Realizing a mechanical dynamical Casimir effect with a low-frequency oscillator

We propose to realize a mechanical dynamical Casimir effect (MDCE) in a hybrid optomechanical system consisting of a cavity mode, a low-frequency mechanical oscillator, and a two-level atomic system. Described by the effective Hamiltonian, the mechanical energy is directly converted to the photons through a three-wave-mixing mechanism. It is not a quantum simulation of a parametric DCE such as in superconducting circuits. Using a master-equation approach, we analyze the system dynamics in various regimes with respect to the ratio of the effective coupling strength and the loss rate of the system. The dynamics under the strong-coupling regime confirms various three-wave-mixing processes for creating photons by annihilation of mechanical and atomic excitations. Under the weak-coupling regime, a continuous production of photons can be demonstrated by driving both the mechanical oscillator and atom. By virtue of an atom of tunable frequency, our method avoids using the high-frequency mechanical oscillator, which is required for the conventional DCE in optomechanical systems under the double-photon resonance yet is out of reach of experiment. It is found that the mechanical frequency can be about two orders smaller than the cavity mode in yielding a remarkable flux of DCE photons.

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