arXiv subjects

Shuming Cheng

Publications and source records attributed to Shuming Cheng.

At least 19 recordsLinked to original sources

arXiv2026

Estimation of a sparse multi-qubit Hamiltonian via compressed sensing

Hamiltonian estimation is an effective approach in studying the structure and dynamical evolution of quantum systems. The difficulty in estimating the Hamiltonian is that an $N$-qubit Hamiltonian has $4^N-1$ unknown parameters, requiring exponentially many equations for information extraction. In this paper we develop a method based on compressed sensing to estimate the Hamiltonian of a multi-qubit system. We identify a problem where as $N$ increases, the common sufficient condition (Restricted Isometry Property) for compressed sensing often fails, obstructing the application of compressed sensing in ($N\geq 3$)-qubit Hamiltonian estimation. To solve this problem, we propose a ``scale transformation" technique to restore RIP and ensure a compressive estimation of a $k$-sparse Hamiltonian using only $O(k\log(4^N/k))$ equations. In the numerical examples, we estimate the Hamiltonians of two 6- and 30-qubit systems, demonstrating the effectiveness of the method.

quant-ph↗

arXiv2026

Intensity-guided pose-free multiview fusion for single photon sensing

Single-photon light detection and ranging (LiDAR) extends active three-dimensional sensing at the fundamental level and has found applications in extreme environments involving long-range operation, low-reflectance targets, and adverse visibility. However, the acquired measurements often give rise to single-photon point clouds that are sparse, spatially non-uniform, and corrupted by outliers and depth distortions, making multi-view registration challenging especially when sensor poses are not accurately known. In this work, we present a geometry-intensity coupled registration framework (GIC-Reg) of pose-free multi-view fusion for single-photon sensing. It is established by combining physical-aware preprocessing, joint geometry-intensity grid feature aggregation, global matching, and local ambiguity disambiguation to estimate inter-view rigid transformations and hence to construct a globally consistent reconstruction. On the synthetic benchmark, it admits the lowest relative rotation error (RRE), relative translation error, and root mean square error across all background-noise and dropout rates, in comparison to baselines. Notably, under the most degraded dropout, it reduces the RRE from $13.167^\circ$ to $8.459^\circ$ compared with the learning-based baseline. Furthermore, experimental results on real multi-view data acquired at about 80~m show that it achieves more reliable global orientation and local alignment. Our results show that photon intensity provides an effective physical cue for stabilizing multiview registration in single-photon point cloud, and thus our work aids significant progress in exploring practical utility of single-photon sensing.

physics.optics↗

arXiv2026

Resource-efficient quantum approximate optimization algorithm via Bayesian optimization and maximum-probability evaluation

The quantum approximate optimization algorithm (QAOA) is a leading variational approach to combinatorial optimization, but its practical performance depends strongly on objective design, parameter search, and shot allocation. We present a resource-efficient QAOA framework that uses the cut value of the most probable measured bitstring as the optimization objective, combines it with Bayesian optimization, and adaptively allocates shots using dual criteria based on mode confidence and normalized cut-value variance. Numerical experiments on 3-regular MaxCut show that, for both unweighted and weighted instances, the proposed scheme achieves discrete-solution quality comparable to that of the conventional expectation-based objective while typically requiring fewer total shots to reach the same final mode accuracy. These results indicate that reorganizing QAOA around the maximum-probability bitstring provides an effective route to improving practical performance under limited measurement budgets.

quant-ph↗

arXiv2026

Optimization landscapes of variational quantum algorithms

Optimization plays a central role in variational quantum algorithms, where the objective function typically takes the form $F(\boldsymbol{\theta})= \sum_{m=1}^{M} f_m \left(\mathrm{Tr}[U(\boldsymbol{\theta})\rho_m U^\dagger(\boldsymbol{\theta}) O_m]\right)$, with $U(\boldsymbol{\theta})$ being a parameterized quantum ansatz. Understanding the optimization landscape of such objective functions is crucial for assessing the trainability and performance of these algorithms. For the special case $M=1$, it is known that under certain assumptions, the landscape is free of false traps (FTs), i.e., local optima that are not global. In this work, we investigate optimization landscapes of the general case $M\geq1$ and show that the landscape becomes intrinsically more complex. First, we establish a complete framework for analyzing critical features of the optimization landscape, by deriving necessary and sufficient conditions to identify and classify all critical points under some assumptions, which is also of practical importance in designing efficient algorithms independent of whether these assumptions are satisfied. Then, we show that FTs can still emerge on landscapes for $M>1$, standing in stark contrast to the $M=1$ case and further revealing that parameter sufficiency alone is not enough to guarantee a trap-free landscape. Moreover, we uncover a close connection that the emergence of FTs is necessarily attributed to the loss of distinguishability among the states and/or operators, and fundamentally, to the loss of compatibility of the spectral ordering governed by different objective terms. Our results provide a deeper understanding of the optimization complexity and practical guidance for both algorithmic and problem-setting designs.

quant-ph↗

arXiv2025

Point upsampling networks for single-photon sensing

Single-photon sensing has generated great interest as a prominent technique of long-distance and ultra-sensitive imaging, however, it tends to yield sparse and spatially biased point clouds, thus limiting its practical utility. In this work, we propose using point upsampling networks to increase point density and reduce spatial distortion in single-photon point cloud. Particularly, our network is built on the state space model which integrates a multi-path scanning mechanism to enrich spatial context, a bidirectional Mamba backbone to capture global geometry and local details, and an adaptive upsample shift module to correct offset-induced distortions. Extensive experiments are implemented on commonly-used datasets to confirm its high reconstruction accuracy and strong robustness to the distortion noise, and also on real-world data to demonstrate that our model is able to generate visually consistent, detail-preserving, and noise suppressed point clouds. Our work is the first to establish the upsampling framework for single-photon sensing, and hence opens a new avenue for single-photon sensing and its practical applications in the downstreaming tasks.

physics.optics↗

arXiv2025

The boundary of Kirkwood-Dirac quasiprobability

The Kirkwood-Dirac (KD) quasiprobability describes measurement statistics of joint quantum observables, and has generated great interest as prominent indicators of non-classical features in various quantum information processing tasks. It relaxes the Kolmogorov axioms of probability by allowing for negative and even imaginary probabilities, and thus incorporates the classical probability theory as its inner boundary. In this work, we introduce the postquantum quasiprobability under mild assumptions to provide an outer boundary for KD quasiprobability. Specifically, we present qualitative and quantitative evidence to show that the classical, KD, and postquantum quasiprobabilities form a strict hierarchy, in the sense that joint probability distributions are a strict subset of KD quasiprobability distributions that are a strict subset of postquantum ones. Surprisingly, we are able to derive some nontrivial bounds valid for both classical probability and KD quasiprobability, and even valid for the KD quasiprobability generated by an arbitrary number of measurements. Finally, other interesting bounds are obtained, and their implications are noted. Our work solves the fundamental problems of what and how to bound the KD quasiprobability, and hence provides a deeper understanding of utilizing it in quantum information processing.

quant-ph↗

arXiv2024

The polygon relation and subadditivity of entropic measures for discrete and continuous multipartite entanglement

In a recent work [Ge {\it et al.}, arXiv: 2312. 17496 (2023)], we have derived the polygon relation of bipartite entanglement measures that is useful to reveal the entanglement properties of discrete, continuous, and even hybrid multipartite quantum systems. In this work, with the information-theoretical measures of R\'enyi and Tsallis entropies, we study the relationship between the polygon relation and the subadditivity of entropy. In particular, the entropy-polygon relations are derived for pure multi-qubit states and generalized to multi-mode Gaussian states, by utilizing the known results from the quantum marginal problem. Moreover, the equivalence between the polygon relation and subadditivity is established, in the sense that for all discrete or continuous multipartite states, the polygon relation holds if and only if the underlying entropy is subadditive. As byproduct, the subadditivity of R\'enyi and Tsallis entropies is proven for all bipartite Gaussian states. Finally, the difference between polygon relations and monogamy relations is clarified, and generalizations of our results are discussed. Our work provides a better understanding of the rich structure of multipartite states, and hence is expected to be helpful for the study of multipartite entanglement.

quant-ph↗

arXiv2023

Faithful geometric measures for genuine tripartite entanglement

We present a faithful geometric picture for genuine tripartite entanglement of discrete, continuous, and hybrid quantum systems. We first find that the triangle relation $\mathcal{E}^\alpha_{i|jk}\leq \mathcal{E}^\alpha_{j|ik}+\mathcal{E}^\alpha_{k|ij}$ holds for all subadditive bipartite entanglement measure $\mathcal{E}$, all permutations under parties $i, j, k$, all $\alpha \in [0, 1]$, and all pure tripartite states. It provides a geometric interpretation that bipartition entanglement, measured by $\mathcal{E}^\alpha$, corresponds to the side of a triangle, of which the area with $\alpha \in (0, 1)$ is nonzero if and only if the underlying state is genuinely entangled. Then, we rigorously prove the non-obtuse triangle area with $0<\alpha\leq 1/2$ is a measure for genuine tripartite entanglement. Useful lower and upper bounds for these measures are obtained, and generalizations of our results are also presented. Finally, it is significantly strengthened for qubits that, given a set of subadditive and non-additive measures, some state is always found to violate the triangle relation for any $\alpha>1$, and the triangle area is not a measure for any $\alpha>1/2$. Hence, our results are expected to aid significant progress in studying both discrete and continuous multipartite entanglement.

quant-ph↗

arXiv2023

Experimental verification of the steering ellipsoid zoo via two-qubit states

Quantum steering ellipsoid visualizes the set of all qubit states that can be steered by measuring on another correlated qubit in the Bloch picture. Together with local reduced states, it provides a faithful geometric characterization of the underlying two-qubit state so that almost all nonclassical state features can be reflected in its geometric properties. Consequently, the various types of quantum ellipsoids with different geometric properties form an ellipsoid zoo, which, in this work, is experimentally verified via measurements on many polarization-path photonic states. By generating two-qubit states with high fidelity, the corresponding ellipsoids are constructed to certify the presence of entanglement, one-way Einstein-Podolsky-Rosen steering, discord, and steering incompleteness. It is also experimentally verified that the steering ellipsoid can be reconstructed from using the twelve vertices of the icosahedron as measurement directions. Our results aid progress in applying the quantum steering ellipsoid to reveal nonclassical features of the multi-qubit system.

quant-ph↗

arXiv2022

Tripartite entanglement measure under local operations and classical communication

Multipartite entanglement is an indispensable resource in quantum communication and computation, however, it is a challenging task to faithfully quantify this global property of multipartite quantum systems. In this work, we study the concurrence fill, which admits a geometric interpretation to measure genuine tripartite entanglement for the three-qubit system in [S. Xie {\it et al.}, Phys. Rev. Lett. \textbf{127}. 040403 (2021)]. First, we use the well-known three-tangle and bipartite concurrence to reformulate this quantifier for all pure states. We then construct an explicit example to conclusively show the concurrence fill can be increased under local operation and classical communications (LOCCs) {\it on average}, implying it is not an entanglement monotone. Moreover, we give a simple proof of the LOCC-monotonicity of three-tangle and find that the bipartite concurrence and the squared can have distinct performances under the same LOCCs. Finally, we propose a reliable monotone to quantify genuine tripartite entanglement, which can also be easily generalised to the multipartite system. Our results shed light on studying genuine entanglement and also reveal the complex structure of multipartite systems.

quant-ph↗

arXiv2022

Quantum Steering: Practical Challenges and Perspectives

Einstein-Rosen-Podolsky (EPR) steering or quantum steering describes the "spooky-action-at-a-distance" that one party is able to remotely alter the states of the other if they share a certain entangled state. Generally, it admits an operational interpretation as the task of verifying entanglement without trust in the steering party's devices, making it lying intermediate between Bell nonlocality and entanglement. Together with the asymmetrical nature, quantum steering has attracted a considerable interest from theoretical and experimental sides over past decades. In this Perspective, we present a brief overview of the EPR steering with emphasis on recent progress, discuss current challenges, opportunities and propose various future directions. We look to the future which directs research to a larger-scale level beyond massless and microscopic systems to reveal steering of higher dimensionality, and to build up steered networks composed of multiple parties.

quant-ph↗

arXiv2022

Efficient factored gradient descent algorithm for quantum state tomography

Reconstructing the state of quantum many-body systems is of fundamental importance in quantum information tasks, but extremely challenging due to the curse of dimensionality. In this work, we present an efficient quantum tomography protocol that combines the state-factored with eigenvalue mapping to address the rank-deficient issue and incorporates a momentum-accelerated gradient descent algorithm to speed up the optimization process. We implement extensive numerical experiments to demonstrate that our factored gradient descent algorithm efficiently mitigates the rank-deficient problem and admits orders of magnitude better tomography accuracy and faster convergence. We also find that our method can accomplish the full-state tomography of random 11-qubit mixed states within one minute.

quant-ph↗

arXiv2022

Experimentally ruling out joint reality based on operational completeness

Whether the observables of a physical system admit real values is of fundamental importance to a deep understanding of nature. In this work, we report a device-independent experiment to confirm that the joint reality of two observables on a single two-level system is incompatible with the assumption of operational completeness, which is strictly weaker than that of preparation noncontextuality. We implement two observables on a trapped $^{171}{\rm Yb}^{+}$ ion to test this incompatibility via violation of certain inequalities derived from both linear and nonlinear criteria. Moreover, by introducing a highly controllable dephasing channel, we show that the nonlinear criterion is more robust against noise. Our results push the fundamental limit to delineate the quantum-classical boundary and pave the way for exploring relevant problems in other scenarios.

quant-ph↗

arXiv2021

Quantized Primal-Dual Algorithms for Network Optimization with Linear Convergence

This paper studies the network optimization problem about which a group of agents cooperates to minimize a global function under practical constraints of finite bandwidth communication. Particularly, we propose an adaptive encoding-decoding scheme to handle the constrained communication between agents. Based on this scheme, the continuous-time quantized distributed primal-dual (QDPD) algorithm is developed for network optimization problems. We prove that our algorithms can exactly track an optimal solution to the corresponding convex global cost function at a linear convergence rate. Furthermore, we obtain the relation between communication bandwidth and the convergence rate of QDPD algorithms. Finally, an exponential regression example is given to illustrate our results.

math.OC↗

arXiv2021

Generalising the Horodecki criterion to nonprojective qubit measurements

The Horodecki criterion provides a necessary and sufficient condition for a two-qubit state to be able to manifest Bell nonlocality via violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality. It requires, however, the assumption that suitable projective measurements can be made on each qubit, and is not sufficient for scenarios in which noisy or weak measurements are either desirable or unavoidable. By characterising two-valued qubit observables in terms of strength, bias, and directional parameters, we address such scenarios by providing necessary and sufficient conditions for arbitrary qubit measurements having fixed strengths and relative angles for each observer. In particular, we find the achievable maximal values of the CHSH parameter for unbiased measurements on arbitrary states, and, alternatively, for arbitrary measurements on states with maximally-mixed marginals, and determine the optimal angles in some cases. We also show that for certain ranges of measurement strengths it is only possible to violate the CHSH inequality via biased measurements. Finally, we use the CHSH inequality to obtain a simple necessary condition for the compatibility of two qubit observables.

quant-ph↗

arXiv2021

Recycling qubits for the generation of Bell nonlocality between independent sequential observers

There is currently much interest in the recycling of entangled systems, for use in quantum information protocols by sequential observers. In this work, we study the sequential generation of Bell nonlocality via recycling one or both components of two-qubit states. We first give a description of two-valued qubit measurements in terms of measurement bias, strength, and reversibility, and derive useful tradeoff relations between them. Then, we derive one-sided monogamy relations for unbiased observables, that strengthen the recent Conjecture in [S. Cheng {\it et al.}, Phys. Rev. A \textbf{104}, L060201 (2021) ] that if the first pair of observers violate Bell nonlocality then a subsequent independent pair cannot, and give semi-analytic results for the best possible monogamy relation. We also extend the construction in [P. J. Brown and R. Colbeck, Phys. Rev. Lett. \textbf{125}, 090401 (2020)] to obtain (i)~a broader class of two-qubit states that allow the recycling of one qubit by a given number of observers on one side, and (ii)~a scheme for generating Bell nonlocality between arbitrarily many independent observers on each side, via the two-sided recycling of multiqubit states. Our results are based on a formalism that is applicable to more general problems in recycling entanglement, and hence is expected to aid progress in this field.

quant-ph↗

arXiv2021

Detecting quantum entanglement with unsupervised learning

Quantum properties, such as entanglement and coherence, are indispensable resources in various quantum information processing tasks. However, there still lacks an efficient and scalable way to detecting these useful features, especially for high-dimensional and multipartite quantum systems. In this work, we exploit the convexity of samples without the desired quantum features and design an unsupervised machine learning method to detect the presence of such features as anomalies. Particularly, in the context of entanglement detection, we propose a complex-valued neural network composed of pseudo-siamese network and generative adversarial net, and then train it with only separable states to construct non-linear witnesses for entanglement. It is shown via numerical examples, ranging from two-qubit to ten-qubit systems, that our network is able to achieve high detection accuracy which is above 97.5% on average.Moreover, it is capable of revealing rich structures of entanglement, such as partial entanglement among subsystems. Our results are readily applicable to the detection of other quantum resources such as Bell nonlocality and steerability, and thus our work could provide a powerful tool to extract quantum features hidden in multipartite quantum data.

quant-ph↗

arXiv2021

Limitations on sharing Bell nonlocality between sequential pairs of observers

We give strong analytic and numerical evidence that, under mild measurement assumptions, two qubits cannot both be recycled to generate Bell nonlocality between multiple independent observers on each side. This is surprising, as under the same assumptions it is possible to recycle just one of the qubits an arbitrarily large number of times [P. J. Brown and R. Colbeck, Phys. Rev. Lett. 125, 090401 (2020)]. We derive corresponding 'one-sided monogamy relations' that rule out two-sided recycling for a wide range of parameters, based on a general tradeoff relation between the strengths and maximum reversibilities of qubit measurements. We also show if the assumptions are relaxed to allow sufficiently biased measurement selections, then there is a narrow range of measurement strengths that allows two-sided recycling for two observers on each side, and propose an experimental test. Our methods may be readily applied to other types of quantum correlations, such as steering and entanglement, and hence to general information protocols involving sequential measurements.

quant-ph↗