arXiv subjects

Ke-Mi Xu

Publications and source records attributed to Ke-Mi Xu.

9 recordsLinked to original sources

arXiv2026

Quantifying Nonstabilizerness of Quantum Codes by Removing the Inert Background

Nonstabilizerness (magic) is the quantum resource that, together with stabilizer operations, makes universal quantum computation possible. It appears in fault-tolerant codes and topological order. However, quantifying nonstabilizerness is difficult. The standard measure sums over exponentially many Pauli operators, and for quantum codes no quantitative theory has been available. We resolve this by a structural observation: the Clifford sector carries no magic and can be removed by a Clifford transformation, leaving an order-three object whose magic is an exactly evaluable fourth moment. Removing this inert background yields closed forms for several code families: a formula for all Dicke states, reducing a 100-qubit case from $4^{100}$ terms to a short binomial sum; a bound for cubic-phase codes (twisted quantum doubles and non-Abelian topological order), saturated only by the $D_4$ code; and a cyclic/zero criterion for group multiplication states. Together these results reduce the computation of nonstabilizerness for a broad class of codes to finite classical counting problems, and identify the maximally magical codes among them.

quant-ph↗

arXiv2026

Quantifying Nonstabilizerness of Codeword-Stabilized Codes

Fault-tolerant quantum computation requires non-Clifford gates, which stabilizer codes cannot supply transversally. Non-stabilizer codes are the natural place to look for them, yet no quantitative theory of the nonstabilizerness (or magic) carried by such a code has existed. We develop one for codeword-stabilized (CWS) codes and show that the key quantity is classical: a code's nonstabilizerness is fixed by how its codewords collide under translation, a question that belongs to additive combinatorics. We show that the most magical codes are exactly the Sidon sets whenever a Sidon set of the required size exists, whose pairwise differences are all distinct. No code carries more than twice its number of logical qubits of nonstabilizerness however large it is physically. Furthermore, the same reduction gives structural and operational results. Nonstabilizerness is unchanged by coset closure, which yields non-stabilizer codes with arbitrarily many logical qubits and constant nonstabilizerness as the number of logical qubits grows. A diagonal transversal gate with $k$ logic qubits that is non-Clifford on $t$ coordinates forces the code's nonstabilizerness to be at most $2(k-t)$; thus the nonstabilizerness also bounds the non-Clifford gates needed to build the code and the cost of classically simulating it. Finally, entire families become exactly computable, and we obtain closed-form values for the Kerdock codes. Together these results turn the search for magic-rich codes and transversal non-Clifford gates into classical counting problems, which can be approached with standard tools from additive combinatorics.

quant-ph↗

arXiv2026

Approximate Virtual Quantum Recovery

The recovery of quantum information after subsystem loss is a central challenge in quantum information processing. However, some states remain beyond the reach of any recovery strategies. Here we identify the algebraic origin of virtual irrecoverability, the \emph{ghost information}---correlations encoded in the global state that leave no trace on any accessible subsystem. We introduce a scalar measure quantifying its magnitude and prove a universal error floor below which no virtual recovery map can operate, irrespective of resource investment. In such cases only \emph{approximate} virtual recovery is available. We study the sampling cost when approaching the minimal attainable recovery error, and find it bounded when the underlying linear map exhibits a spectrum gap, and divergent in the gapless regime, respectively. Together with the universal error floor, this dichotomy partitions all multipartite quantum states into four classes. Moreover, we show that conditional mutual information, the standard entropic diagnostic, does not constrain virtual recoverability. As an implication, we show that the error floor imposes a detection threshold for loss-tolerant quantum metrology.

quant-ph↗

arXiv2026

Spatially variant arbitrary polarization shaping for optical skyrmions generation

Polarization is fundamental degree of freedom of light, crucial for applications from imaging to quantum optics. Although numerous methods can spatially manipulate the polarization orientation, e.g., for generating vector beam, achieving simultaneous, spatially resolved control of both the orientation ({\psi}) and ellipticity (\c{hi}) remains challenging. Here, we present an efficient and compact platform to generate spatially variant arbitrary polarization states, e.g., optical skyrmions, in free space, using cascaded spatially variant waveplates in a single silica glass plate via ultrafast laser direct writing. We propose two configurations: (1) a spatially variant half-waveplate (S-HWP) and followed by a quarter-waveplate (S-HWP); and (2) two cascaded spatially variant quarter-waveplates (S-QWPs). Design rules linking the target polarization parameters (orientation {\psi} and ellipticity \c{hi}) to the fast-axis distributions enable spatially resolved arbitrary polarization control. Using these devices, we realize N\'eel-, Bloch-, and anti-skyrmions of different orders (e.g., second and fourth) and n-{\pi} textures (2{\pi} and 3{\pi}), with polarization-resolved measurements in excellent agreement with simulations. We further demonstrate 3 by 3 arrays comprising either identical or hybrid skyrmions. This approach enables the realization of spatially variant arbitrary polarization state and scalable skyrmion lattices.

physics.optics↗

arXiv2026

Hyperfine-resolved laser excitation and detection of nuclear isomer in trapped $^{229}$Th$^{3+}$ ions

We present a comprehensive theoretical investigation of hyperfine-resolved excitation and detection of the low-energy isomeric state of $^{229}$Th in trapped $^{229}\mathrm{Th}^{3+}$ ions. Using a quantum master equation approach, we quantitatively analyze the dependence of the isomeric population on laser linewidth, detuning, and irradiation time, showing that their proper matching is essential for efficient excitation. Going beyond earlier conceptual discussions of electronic-fluorescence-based nuclear-state detection, we propose two concrete nuclear-state detection schemes based on three hyperfine-resolved electronic fluorescence channels at 690, 984, and 1088 nm. Our quantitative analysis shows that, for 50 ions, the 690- and 984-nm scheme yields detectable photon count rates on the order of $10^3~\mathrm{s}^{-1}$ at 690 nm and $10^4~\mathrm{s}^{-1}$ at 984 nm, whereas the 1088-nm scheme achieves a detectable photon rate on the order of $10^3~\mathrm{s}^{-1}$. By quantifying the trade-off between irradiation time and scan-step size, we show that the nuclear transition can be located within one month for a 100-MHz uncertainty using currently available vacuum-ultraviolet laser technology. These results provide practical guidance for trapped-ion $^{229}\mathrm{Th}$ spectroscopy and the development of nuclear clocks.

physics.atom-ph↗

arXiv2026

$1/N^2$ Precision Interferometry with Collectively Enhanced Atomic Mirror

Quantum metrology exploits quantum resources to enhance measurement precision beyond the classical limit. Conventional protocols normally rely on the preparation of delicate quantum states to acquire these resources, posing a major challenge for scaling and robustness. Here we introduce a paradigm that circumvents this requirement with a collectively enhanced quantum mirror (CEAM), i.e., a mesoscopic array of $N$ atoms coupled to a semi-infinite waveguide. When injecting single photons into the waveguide and estimating the CEAM-boundary distance from the reflection phase, a $1/N^2$ precision scaling can be obtained, which surpasses the Heisenberg limit. In this protocol, the quantum resource stems from the cooperative optical response, requiring no entangled state preparation. Our scheme is robust against positional and coupling disorder, offering a practical route to ultra-sensitive quantum metrology in integrated photonic systems.

quant-ph↗

arXiv2026

Learning Entanglement Quasiprobability from Noisy and Incomplete Data

Negativities in quasiprobability distributions, a foundational concept originating in quantum optics, serve as a fundamental signature of quantum nonclassicality, with entanglement quasiprobabilities offering a necessary and sufficient criterion for entanglement. However, practical reconstruction of entanglement quasiprobabilities conventionally requires full quantum state tomography, severely limiting scalability. Here, we propose a deep-learning framework that reconstructs entanglement quasiprobabilities directly from incomplete local projective measurements, bypassing full state reconstruction. Using a residual neural network, partial measurement outcomes are mapped to high-fidelity entanglement quasiprobabilities. Numerical benchmarks up to three qubits show more than a $30\times$ reduction in reconstruction error compared with state-of-the-art tomographic methods. Experimental validation on photonic entangled states demonstrates reconstruction and entanglement detection with substantially reduced measurement resources. Our results establish machine-learning-assisted reconstruction of entanglement quasiprobabilities as a scalable and practical tool for entanglement characterization in quantum optical systems.

quant-ph↗

arXiv2025

Unconditional quantum teleportational advantage of single photons

Photon loss is the biggest enemy in quantum communications. Direct transmission typically results in a small fraction of photons surviving over long distances, hindering advanced applications such as loophole-free Bell tests and device-independent quantum key distribution. Quantum teleportation offers a "disembodied" way of transferring particles through a virtual channel--quantum entanglement--which, in principle, could overcome the photon transmission loss. Experimentally, however, no previous quantum teleportation of single photons has shown a higher survival probability than using direct transmission. To overcome this challenge, here we first propose and demonstrate an all-optical scheme for remote preparation of entangled photons. Through an effective 15-dB channel loss, we realize a heralding efficiency of 82% for event-ready entangled photons. Based on the prior distributed entanglement, we demonstrate that teleportation-based transmission efficiency offers a 2.95-fold enhancement, compared to using direct transmission through the same channel, therefore establishing an unconditional teleportational advantage.

quant-ph↗

arXiv2024

Boosted fusion gates above the percolation threshold for scalable graph-state generation

Fusing small resource states into a larger, fully connected graph-state is essential for scalable photonic quantum computing. Theoretical analysis reveals that this can only be achieved when the success probability of the fusion gate surpasses a specific percolation threshold of 58.98% by using three-photon GHZ states as resource states. However, such an implementation of a fusion gate has never been experimentally realized before. Here, we successfully demonstrate a boosted fusion gate with a theoretical success probability of 75%, using deterministically generated auxiliary states. The success probability is experimentally measured to be 71.0(7)%. We further demonstrate the effectiveness of the boosted fusion gate by fusing two Bell states with a fidelity of 67(2)%. Our work paves a crucial path toward scalable linear optical quantum computing.

quant-ph↗