In the domain of quantum key distribution (QKD), the establishment of secure communication channels relies on the comprehensive analysis of the secure bounds. However, the impact of nonuniform random numbers in privacy amplification on secure bounds has rarely been discussed. This work proposes a more comprehensive analysis method for the secure bounds of practical QKD systems with imperfect random numbers in privacy amplification (PA) . We expand the quantum leftover hash lemma to the case of nonuniform random numbers and prove its security based on the min-entropy. Following this, we derive a revised secure bound for practical QKD systems. Using the two-decoy-state BB84 protocol as an example, we simulate the impact of imperfect random numbers in privacy amplification on the secure bounds of a QKD system. The simulation results indicate that the secure bound will be seriously affected when the average min-entropy of random numbers is below 0.95. These findings theoretically validate the necessity of using distilled uniform random numbers in PA, providing practical guidance for mitigating potential loopholes in practical QKD systems caused by imperfect random numbers.

We study relativistic twisted (orbital-angular-momentum) states of a massive charged particle propagating through an axially symmetric, longitudinally inhomogeneous solenoid field and a codirected accelerating or decelerating electric field. Starting from the Dirac equation and using controlled spinless and paraxial approximations, we show that the transverse envelope obeys an effective nonstationary Schrödinger equation governed by a Caldirola-Kanai Hamiltonian. The longitudinal energy gain or loss encoded in $f\left(z\right)={[E_0-V\left(z\right)]}^2-m^2$ generates an effective gain or damping rate $\tilde{\gamma }\left(z\right)={\partial }_{z}f\left(z\right)/\left[2f\left(z\right)\right]$ and a $z$-dependent oscillator frequency $\tilde{\omega }\left(z\right)=p_0\mathrm{\Omega }\left(z\right)/\sqrt{f\left(z\right)}$. Exploiting the Ermakov mapping (unitary equivalence of Caldirola-Kanai systems), we obtain a closed-form propagated twisted wave function by transforming the stationary Landau basis. The transverse evolution is controlled by a single scaling function $b\left(z\right)$ that satisfies a generalized Ermakov-Pinney equation with coefficients determined by $E_z\left(z\right)$ and $B_z\left(z\right)$. In the limiting cases of uniform acceleration with $B_z=0$ and of solenoid focusing with negligible acceleration, our solution reduces to previously known analytic results, providing a direct bridge to established models.

Decoherence which describes the disappearance or absence of certain superpositions of quantum states can be employed as an essential tool in diverse quantum technologies. Following this line of thought, we propose a protocol aimed at enhancing the estimation precision of an unknown coupling strength in the quantum Wheatstone bridge in this paper. We consider the setup consisting of two interface spins, two outer spins, and two baths of different temperatures at each extremity. There are coherent interactions between nearest-neighboring spins, and a dissipative coupling between the two interface spins via an engineered shared reservoir. We identify the balance of the quantum Wheatstone bridge as the steady state of the system. When the controllable coupling approaches the unknown coupling, the population of the antisymmetric Bell state shows a sharp dip due to destructive interference, resulting in the state of the interface spins being highly sensitive to changes in the unknown coupling strength. Compared with the previous quantum Wheatstone bridge, the introduction of dissipative coupling significantly enhances the estimation precision of the unknown coupling strength. This work would open a different avenue for enhancing the precision through reservoir engineering and find applications in many fields, including precise measurement and quantum information science.

We present a manifestly covariant route to designing exact Dirac solutions from geometric data. Given the spinor density $\rho$, four-velocity $v^{\mu }$, spin $s^{\mu }$, Yvon-Takabayashi (YT) angle ${\beta }_s$, and the local Lorentz rotor, covariant relativistic dynamical inversion (CRDI) returns a real four-potential $A_{\mu }$ for which the prescribed spinor is a solution to the Dirac equation. We investigate the relationship between the parameters of the spinor and the electromagnetic potentials that satisfy the corresponding Dirac equation. Specifically, we examine the impact of a nontrivial variation of the YT angle and the boost matrix embedded within the spinor on the distortion of electromagnetic fields, and seek analytically tractable null-sphere solutions on the hypersurfaces $u=ct-r$. We show how this approach facilitates a generalized parametrization of established solutions, providing a pathway to generate novel, physically meaningful configurations.

Decision diagrams (DDs) have emerged as an efficient tool for simulating quantum circuits due to their capacity to exploit data redundancies in quantum states and quantum operations, enabling the efficient computation of probability amplitudes. However, their application in quantum machine learning (QML) has remained unexplored. This paper introduces variational decision diagrams (VDDs), an alternative graph structure that combines the structural benefits of DDs with the adaptability of variational methods for efficiently representing quantum states. We investigate the trainability of VDDs by applying them to the ground-state estimation problem for transverse-field Ising and Heisenberg Hamiltonians. Analysis of gradient variance suggests that training VDDs is possible, as no signs of vanishing gradients—also known as barren plateaus—are observed. This work provides insights into the use of decision diagrams in QML as an alternative to design and train variational Ansätze.

While the structure of entangled quantum states is relatively well understood, the characterization of entangled measurements, especially in multipartite and high-dimensional settings, remains far less developed. In this work we introduce a general approach to construct highly symmetric, locally encodable orthonormal measurement bases, as orbits of a single fiducial state under tensor-product actions of Pauli subgroups. This framework recovers the elegant joint measurement—a two-qubit measurement whose local marginals form a regular tetrahedron on the Bloch sphere—as a special case, and we extend the construction to both more systems and higher dimensions. We analyze the entanglement cost required to implement these measurements locally via the Clifford hierarchy and use this criterion to classify them. We show how the symmetry of our constructions allows us to characterize their localizability, which is generally a challenging problem, and to identify certain classes of measurement bases that are efficiently localizable. Our approach offers a systematic toolkit for designing entangled measurements with rich symmetry and implementability properties.

Nonadiabatic two-qubit gate proposals for trapped-ion systems offer superior performance and flexibility over adiabatic schemes at the cost of increased laser control requirements. Existing fast gate schemes are limited by single-qubit transition errors, which constrain the total number of pulses in high-fidelity solutions. We introduce an improved gate search scheme that enables both local and nonlocal two-qubit gates in chains containing tens of ions. These protocols use a multiobjective machine design approach that incorporates dominant sources of error in the design to ensure the solutions are compatible with existing fast laser controls. We also generalize previous schemes by allowing for unpaired pulses during the gate evolution. By imposing symmetries on the pulse sequences, we eliminate susceptibility to laser phase noise and further simplify the multimode control over the state-dependent motion of the ion crystal. We perform a comprehensive analysis of expected gate performance in the presence of random and systematic experimental errors to demonstrate the feasibility of performing microsecond two-qubit gates between arbitrary ion pairs in current linear ion-trap processors of up to 40 ions with fidelities approaching $99.9\%$.

Describing dynamics of a quantum system coupled to a complex many-body environment is a ubiquitous problem in quantum science. General non-Markovian environments are characterized by their influence matrix (IM)—a multitime tensor arising from repeated interactions between the system and environment. While complexity of the most generic IM grows exponentially with the evolution time, recent works argued that for many instances of physical many-body environments, the IM is significantly less complex. This is thanks to area-law scaling of temporal entanglement, which quantifies the correlations between the past and the future states of the system. However, efficient classical algorithms for computing IM are only available for noninteracting environments or certain interacting one-dimensional (1D) environments. Here, we study a learning algorithm for reconstructing IMs of large many-body environments simulated on a quantum processor. This hybrid algorithm involves experimentally collecting quantum measurement results of auxiliary qubits which are repeatedly coupled to the many-body environment, followed by a classical machine-learning construction of a matrix-product representation of the IM. Using the example of 1D spin-chain environments, with a classically generated training dataset, we demonstrate that the algorithm allows scalable reconstruction of IMs for long evolution times. The reconstructed IM can be used to efficiently model quantum transport through an impurity, including cases with multiple leads and time-dependent controls. These results indicate the feasibility of characterizing long-time dynamics of complex environments using a limited number of measurements, under the assumption of a moderate temporal entanglement.

Moiré systems have recently become an important way to explore two-dimensional exotic strongly correlated physics, in which flat bands, generated from twist leading large periodic supercell structures, play a crucial role. Here we propose a valid and feasible scheme for implementing topological flat bands with ultracold atoms trapped in an optical lattice. Instead of introducing a twist, via a spatially dependent Raman coupling between staggered bilayer lattices, we realize a Kekulé supercell with tunable intercell hopping and staggered flux. We demonstrate that the band can be engineered into a quasiflat band with nearly ideal quantum geometry through these tunable parameters. Over a broad parameter range, our system hosts almost ideal flat bands, making it a promising platform for fractional Chern insulator (FCI) states. Performing exact diagonalization on the engineered flat band, we confirm the existence of the FCI state at fractional fillings $\nu =\frac{p}{2p\pm 1}$. Our work provides a practical scheme for engineering flat Chern bands, implementing FCI phase and opening up new possibilities for exploring strongly correlated flat band physics analogous to that in moiré systems using ultracold atoms.

An atomic bright soliton realized in a quasi-one-dimensional Bose-Einstein condensate can be considered as an open quantum system. The soliton’s breathing mode, for example, is damped by emission of atoms from the soliton to spatial infinity, which thus acts as a Markovian environment for the soliton. If the soliton is held in a shallow harmonic trap, however, the environment becomes non-Markovian: emitted atoms oscillate in the trap and eventually return to the soliton, interfering with it, producing periodic revivals of the breathing mode (“resuscitations”). The amplitude envelopes of these breathing revivals show a curious asymmetry, with a gradual increase in breathing amplitude followed by a sudden drop in amplitude that becomes more and more pronounced in later revivals. We explain this asymmetrical revival pattern in the non-Markovian revivals by deriving a close analytical approximation to the Bogoliubov–de Gennes frequency spectrum for the weakly trapped soliton.

We consider ponderomotive forces acting on small particles in propagating wave packets (pulses). Specifically, we analyze simple point particles as well as composite dipole and dumbbell particles in the fields of forward-propagating (parallel phase and group velocities) and backward-propagating (antiparallel phase and group velocities) wave packets. Depending on the characteristics of the wave packet, particles may be pushed away from the wave source or pulled toward it. We also examine particle dynamics in the field of a beat wave generated by two forward-propagating waves with slightly different frequencies. Such a beat wave can emulate a periodic sequence of either forward- or backward-propagating pulses. In particular, this provides a simple mechanism for realizing pulling forces as employed in optical and acoustic "tractor beams."

We present a theoretical study of entanglement between the continuous motional degrees of freedom of two massive, optically trapped particles coupled via the Coulomb interaction in the presence of optimal control. We analytically investigate the effect of temporal modulation on the entanglement strength and derive closed-form expressions for the conditional entanglement. These expressions not only reproduce the numerical results, but also explicitly reveal that entanglement emerges from the competition between parametric gain and decoherence.

Symmetries play a central role in both equilibrium and nonequilibrium phase transitions, yet their quantitative characterization in dynamical quantum phase transitions (DQPTs) remains an open challenge. In this work, we establish a direct connection between the symmetry properties of a many-body model and measures of quantum asymmetry, showing that asymmetry monotones provide a robust and physically transparent indicator of dynamical quantum criticality. Focusing on the quenched Lipkin-Meshkov-Glick model, we demonstrate that asymmetry measures associated with collective spin generators faithfully capture the onset of DQPTs, reflecting the dynamical restoration or breaking of underlying symmetries. Remarkably, the time-averaged asymmetry exhibits clear signatures of the dynamical critical point, in close correspondence with both the dynamical order parameter and the behavior of entropy production. We further uncover a quantitative link between asymmetry generation and thermodynamic irreversibility, showing that peaks in asymmetry coincide with maximal entropy production across the transition. Our results position asymmetry as a unifying concept bridging symmetry, information-theoretic quantifiers, and nonequilibrium thermodynamics in DQPTs, providing a powerful framework for understanding critical dynamics beyond traditional order parameters.

We investigate an optomechanical system as a model of an autonomous mechanical pendulum clock in the quantum regime, whose operation relies only on incoherent (thermal) resources. The escapement of the clock, the mechanism that translates oscillatory motion into ticks, is provided by an emitter in the optical cavity and the operation of the clock relies on the existence of a limit cycle. Since the clock is based on an oscillatory degree of freedom, it can overcome the thermodynamic uncertainty relation and is thus more accurate than clocks that rely only on stochastic transitions. Furthermore, by increasing the amount of emitters in the cavity, the clock approaches the behavior expected for a macroscopic pendulum clock, where fluctuations become irrelevant while the clock dynamics becomes completely irreversible. This allows for investigating the quantum-to-classical transition of pendulum clocks.

We investigate the ultimate quantum limits to the achievable uncertainty in the estimation of the transition frequency between two atomic levels. We focus on Rabi, Ramsey, and coherent-population-trapping (CPT) techniques, which are widely employed in experiments. We prove that in the Rabi and Ramsey schemes, measuring the atomic population allows one to reach the minimum uncertainty, but for the CPT setup, a measurement involving the coherences between the levels results in a further improvement of the estimation. As a paradigmatic example of possible noises, the effect of cavity coupling fluctuations is considered in the Rabi and Ramsey scenarios. As a figure of merit, we assess the Fisher information of the population measurement and compare its value with the maximum one given by the quantum Fisher information, which is achieved by optimizing over all the possible measurements allowed by quantum mechanics.

Entanglement classification of pure multipartite quantum states is a challenging problem in quantum information theory that can be mathematically stated as orbit classification for some given group action on the ambient Hilbert space. The group action depends on the grained classification one expects, the finer-grained one being the classification up to local unitary transformation. In this article, we show how a variational quantum circuit approach can be used to learn entanglement orbits, and we apply our findings to build a classifier for four-qubit states.

Localizable measurements are joint quantum measurements that can be implemented using only nonadaptive local operations and shared entanglement. We provide a protocol-independent characterization of localizable projection-valued measures (PVMs) by exploiting algebraic structures that any such measurement must satisfy. We first show that a rank-1 PVM on ${\mathbb{C}}^d\otimes {\mathbb{C}}^d$ containing an element with the maximal Schmidt rank can be localized using entanglement of a Schmidt number of, at most, $d$ if and only if it forms a maximally entangled basis corresponding to a nice unitary error basis. This reveals strong limitations imposed by nonadaptive local operations, in contrast to the adaptive setting where any joint measurement is implementable. We then completely characterize two-qubit rank-1 PVMs that can be localized with two-qubit entanglement, resolving a conjecture of Gisin and Del Santo, and, finally, extend our characterization to ideal two-qudit measurements, strengthening earlier results.

Orbital angular momentum (OAM) as both classical and quantum states of light has proven essential in numerous applications, from high-capacity information transfer to enhanced precision and accuracy in metrology. Here, we extend OAM metrology to relativistic scenarios to determine the Lorentz factor of a moving reference frame, exploiting the fact that OAM is not Lorentz invariant. We show that the joint OAM spectrum from entangled states is modified by length contraction when measured by two observers moving relative to the entanglement source. This relative motion rescales the spatial dimensions, thus breaking the orthogonality of the OAM measurement process and resulting in a broadening of the joint OAM spectrum that can precisely determine the Lorentz factor. We experimentally simulate velocities up to $0.99c$, confirm the predicted broadening, and use the measurement outcomes to extract the Lorentz factor. Our work provides a pathway for measurement techniques suitable for relativistic conditions that leverage OAM structured light as a resource.