arXiv subjects

Kangqiao Liu

Publications and source records attributed to Kangqiao Liu.

13 recordsLinked to original sources

arXiv2026

Collective advantage from a minimal record in a quantum information engine

For a single particle, a quantum information engine can turn measurement fluctuations into transport by raising a barrier behind the particle each time its position is measured. When many particles are present, the barrier still depends on just one number, the position of the leftmost particle, so we let the demon measure that order statistic and nothing else. A demon that resolves every position instead pays a record entropy that grows with particle number, even though the extra distinctions never change where the barrier is placed. We show that the coarser measurement supplies an energy that is bounded independently of particle number, and that this bound yields a ceiling on the record entropy that falls as the filling increases. At the same tilt, the collective engine then delivers $44\%$ more work per recorded nat than independent single-particle engines, each with its own optimized cycle time and each running at equal or greater power per particle. Pauli blocking ends this advantage once the accessible region just above the wall fills. We also evaluate the coherence that the coarse measurement leaves behind, and the cost of placing the barrier imprecisely.

quant-ph↗

arXiv2026

Horizon--orbit scale competition underlying chaos bound violation for spinning particles

In this paper, we investigate the chaos bound through the local radial instability of charged spinning test particles on unstable circular orbits in the black-bounce--Kerr--Newman spacetime. Our results show that violation of the bound is governed by the competition between the local orbital-instability scale and the surface gravity scale, with variations of the black hole background and the particle dynamics providing two complementary routes to the same threshold crossing. Background variations affect both scales and can drive the system into the bound-violating regime when the surface gravity is suppressed more strongly than the orbital instability. At fixed background, by contrast, the surface gravity remains unchanged, and the transition across the threshold is driven by changes in the unstable orbit dynamics induced by the particle parameters. The background-controlled and probe-dynamics-controlled routes therefore represent two realizations of a unified horizon--orbit scale competition rather than independent mechanisms.

gr-qc↗

arXiv2026

Maximal-velocity deficit under a finite-support constraint in a hard-wall half-line continuous-time quantum walk

Continuous-time quantum walks on a lattice spread ballistically and converge to a limiting distribution for the rescaled position. On the hard-wall half line the boundary reflects the walker but does not change the bulk dispersion, so the ballistic front remains set by the maximal group velocity. We ask how close one can get to this front when the initial state is constrained to occupy only the first $M$ sites. We show that optimizing the moment-generating function of the limiting-velocity distribution over this finite-support class reduces to the principal eigenvalue of an explicit $M\times M$ Hermitian matrix, which yields the optimal state by direct diagonalization. For large $M$, a near-front scaling limit produces a continuum description that controls the entire peak region. In particular, the maximal mean drift approaches the front with an inverse-square deficit in $M$ and a constant prefactor $π^2/4$. Numerical results verify both the finite-$M$ spectral formulation and the predicted scaling.

quant-ph↗

arXiv2026

Classical codes violate the conjectured square-root bound for quantum random access codes

We consider whether every quantum random access code (QRAC) with density-operator encodings and arbitrary decoding measurements obeys the conjectured bound $p\leq(1+\sqrt{m/n})/2$, where $n$ classical bits are encoded into $m$ qubits and $p$ is the worst-case success probability. We find that classical random access codes with private randomness, which form a subclass of this QRAC model, violate the bound. We embed these classical codes as QRACs with diagonal encoding states and commuting decoding measurements, and construct pure-state realizations with identical decoding statistics. The achievability theorem of Ambainis, Nayak, Ta-Shma, and Vazirani then yields violations for every fixed $p\in(1/2,1)$ at sufficiently large input length. The counterexamples span the full open interval between the conjectured and Nayak bounds at each fixed compression rate. A finite-blocklength analysis further yields order-optimal logarithmic qubit scaling for a recovery bias scaling as $\sqrt{\log_2 n/n}$ with a sufficiently large prefactor. These results identify the classical coding rate as the source of the separation and motivate restricted bounds based on quantitative spectral properties of decoding measurements.

quant-ph↗

arXiv2026

Chaos bound for spinning particles in Kerr-Newman-AdS black holes

In this paper, we employ spinning test particles as probes to investigate the regulatory effects of particle and black hole parameters on the violation of the chaos bound in Kerr-Newman-AdS spacetime. Our results demonstrate that the chaos bound violation is governed by the interplay of spacetime geometry, electromagnetic forces, and particle dynamics. The particle spin modulates the direction dependence and parameter thresholds of the violation through its coupling with the orbital angular momentum, which contributes to the total angular momentum. The negative cosmological constant acts as a potential well, with a larger magnitude of the cosmological constant leading to stronger chaotic behavior. A competitive coupling exists between the black hole rotation and charge -- its prograde rotation exerts a stabilizing effect that can suppress or even completely quench charge-driven violations, while the charge serves as a condition for triggering the violation, with its effect modulated by the spin stabilization. In the Kerr-AdS limit, the violation occurs only when the black hole rotates opposite to the $z$-axis with a sufficiently large rotation parameter and a sufficiently small cosmological constant. In the RN-AdS limit, the violation condition is jointly determined by the charge and the cosmological constant, with electromagnetic repulsion more readily inducing the violation than electromagnetic attraction.

gr-qc↗

arXiv2026

Response kinetic uncertainty relation for Markovian open quantum systems

Response uncertainty relations in stochastic thermodynamics extend precision bounds to the sensitivity of observables under external perturbations. Here we derive a quantum response kinetic uncertainty relation for continuously monitored Markovian open quantum systems in the steady state of the Lindblad master equation. The response precision of a measured trajectory observable is bounded by two contributions: the conventional quantum dynamical activity and a perturbation-induced intersubspace transition term. The latter is absent in the classical limit and captures a genuinely quantum part of the response cost. We identify simple conditions under which either contribution vanishes, and we further clarify the structure of the intersubspace term through a symmetry-resolved decomposition and exact sector-selection rules. The bound and its structure are illustrated in a driven two-level atom.

quant-ph↗

arXiv2026

Finite-frequency fluctuation-response bounds for open quantum systems

We derive a finite-frequency fluctuation-response inequality for Markovian open quantum systems in an input-output setting. For any downstream measurement of the emitted field, the measured lock-in response-to-noise matrix is bounded by the output-field quantum Fisher information rate. For dissipative amplitude modulation with vacuum inputs, this information rate is further bounded by a frequency-independent signal-channel activity, which reduces for kinetic modulation to the stationary channel fluxes. The result is detector-facing but unraveling-independent: it applies after choosing a measurement record, while the information ceiling is set by the quantum field before any detection scheme or trajectory representation is selected. We formulate the bound for multiple signal channels and real finite-frequency quadratures, and illustrate it with a single-sided cavity, resonance fluorescence, and a truncated Kerr-parametric cat resonator.

quant-ph↗

arXiv2026

Maxwell's demon for quantum transport

While most of the existing quantum information engines assisted by Maxwell's demon harness thermal fluctuations, those that rectify only quantum fluctuations have recently been constructed. We propose an alternative type of quantum information engine that harnesses only quantum fluctuations to achieve cumulative energy storage and unidirectional transport of a particle. This unidirectional transport makes a stark contrast with the case without Maxwell's demon where the motion of a particle is confined to a finite region due to Bloch oscillations. We find a trade-off relationship between the maximum power and the maximum velocity. With an improved definition of efficiency that includes all possible energy flows in the engine cycle, we numerically demonstrate the absence of a trade-off relationship among power, efficiency, and power fluctuations that is present for classical heat engines and classical information engines. We also evaluate the influence of experimentally unavoidable measurement imprecision on the performance of the quantum Maxwell's demon.

cond-mat.stat-mech↗

arXiv2025

Dynamical activity universally bounds precision of response in Markovian nonequilibrium systems

The exploration of far-from-equilibrium systems has been at the forefront of nonequilibrium thermodynamics, with a particular focus on understanding the fluctuations and response of thermodynamic systems to external perturbations. In this study, we introduce a universal response kinetic uncertainty relation, which provides a fundamental trade-off between the precision of response for generic observables and dynamical activity in Markovian nonequilibrium systems. We demonstrate the practical applicability and tightness of the derived bound through illustrative examples. Our results are applicable to a broad spectrum of Markov jump processes, ranging from currents to non-current variables, from steady states to time-dependent driving, from continuous time to discrete time, and including Maxwell's demon or absolute irreversibility. Our findings not only enhance the theoretical foundation of stochastic thermodynamics but also may hold potential implications for far-from-equilibrium biochemical processes.

cond-mat.stat-mech↗

arXiv2022

Strength of Minibatch Noise in SGD

The noise in stochastic gradient descent (SGD), caused by minibatch sampling, is poorly understood despite its practical importance in deep learning. This work presents the first systematic study of the SGD noise and fluctuations close to a local minimum. We first analyze the SGD noise in linear regression in detail and then derive a general formula for approximating SGD noise in different types of minima. For application, our results (1) provide insight into the stability of training a neural network, (2) suggest that a large learning rate can help generalization by introducing an implicit regularization, (3) explain why the linear learning rate-batchsize scaling law fails at a large learning rate or at a small batchsize and (4) can provide an understanding of how discrete-time nature of SGD affects the recently discovered power-law phenomenon of SGD.

cs.LG↗

arXiv2022

Power-law escape rate of SGD

Stochastic gradient descent (SGD) undergoes complicated multiplicative noise for the mean-square loss. We use this property of SGD noise to derive a stochastic differential equation (SDE) with simpler additive noise by performing a random time change. Using this formalism, we show that the log loss barrier $Δ\log L=\log[L(θ^s)/L(θ^*)]$ between a local minimum $θ^*$ and a saddle $θ^s$ determines the escape rate of SGD from the local minimum, contrary to the previous results borrowing from physics that the linear loss barrier $ΔL=L(θ^s)-L(θ^*)$ decides the escape rate. Our escape-rate formula strongly depends on the typical magnitude $h^*$ and the number $n$ of the outlier eigenvalues of the Hessian. This result explains an empirical fact that SGD prefers flat minima with low effective dimensions, giving an insight into implicit biases of SGD.

cs.LG↗

arXiv2021

Noise and Fluctuation of Finite Learning Rate Stochastic Gradient Descent

In the vanishing learning rate regime, stochastic gradient descent (SGD) is now relatively well understood. In this work, we propose to study the basic properties of SGD and its variants in the non-vanishing learning rate regime. The focus is on deriving exactly solvable results and discussing their implications. The main contributions of this work are to derive the stationary distribution for discrete-time SGD in a quadratic loss function with and without momentum; in particular, one implication of our result is that the fluctuation caused by discrete-time dynamics takes a distorted shape and is dramatically larger than a continuous-time theory could predict. Examples of applications of the proposed theory considered in this work include the approximation error of variants of SGD, the effect of minibatch noise, the optimal Bayesian inference, the escape rate from a sharp minimum, and the stationary covariance of a few second-order methods including damped Newton's method, natural gradient descent, and Adam.

stat.ML↗

arXiv2020

Thermodynamic Uncertainty Relation for Arbitrary Initial States

The thermodynamic uncertainty relation (TUR) describes a trade-off relation between nonequilibrium currents and entropy production and serves as a fundamental principle of nonequilibrium thermodynamics. However, currently known TURs presuppose either specific initial states or an infinite-time average, which severely limits the range of applicability. Here we derive a finite-time TUR valid for arbitrary initial states from the Cramér-Rao inequality. We find that the variance of an accumulated current is bounded by the instantaneous current at the final time, which suggests that ``the boundary is constrained by the bulk". We apply our results to feedback-controlled processes and successfully explain a recent experiment which reports a violation of a modified TUR with feedback control. We also derive a TUR that is linear in the total entropy production and valid for discrete-time Markov chains with non-steady initial states. The obtained bound exponentially improves the existing bounds in a discrete-time regime.

cond-mat.stat-mech↗