arXiv subjects

Wai-Keong Mok

Publications and source records attributed to Wai-Keong Mok.

At least 19 recordsLinked to original sources

arXiv2026

Function-like pseudorandom unitaries generate pseudorandom quantum processes

Haar-random unitaries provide a canonical model of generic random quantum evolution, but they typically have exponential description and circuit complexity. Although pseudorandom unitaries efficiently emulate a single Haar-random unitary, many tasks require an entire reusable family of independently random-looking operations. We introduce pseudorandom function-like unitaries (PRFU), which generate such a family indexed by public labels using only a single short key. We distinguish classical- and coherent-label access and establish security under adaptive quantum queries. For classical labels, we provide a generic construction from a post-quantum pseudorandom function and a pseudorandom unitary. For coherent labels, we use an indexed path-recording framework to analyze interference across labels and prove security of a construction based on quantum-secure function and permutation primitives. We further show that PRFUs generate pseudorandom channels and quantum combs with private memory, which are secure against adaptive interventions and concurrent sessions. Combining PRFUs with unitary gluing yields a one-key family of pseudorandom unitaries whose supported register widths can be chosen after key generation. Further applications include nonce-resolved quantum authentication, coherently masked QRAM queries, and efficient emulation of random multi-time dynamics. Our results extend quantum pseudorandomness from individual operations to efficiently generated families of random-looking quantum dynamics.

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arXiv2026

Emergent universality in Kraus maps of quantum chaotic many-body dynamics

Recent studies of "deep thermalization" have revealed universal physics in quantum many-body dynamics beyond equilibration towards Gibbs states: maximally random quantum state ensembles can emerge on local subsystems, generated by measurements on their complement. In this work, we further identify a new form of universality exhibited in the "finer fingerprints" of quantum dynamics for local subsystems, induced by global unitary time-evolution. Specifically, we consider the projected Kraus ensemble, an ensemble of Kraus operators obtained by unraveling the quantum channel on a small subsystem with respect to knowledge of the classical configurations of its complement. Our central result is a one-parameter random matrix Ansatz that captures the ensemble's emergent statistical behavior along particular spacetime scalings, valid for generic 1D circuit dynamics without conservation laws: the ensemble is described by the product of a complex Ginibre random matrix and an independent log-normal random real scalar. The former encodes scrambling within the subsystem, captured by rotational invariance of the Ginibre measure, whereas the latter encodes fluctuations in the Born probabilities, arising from locality of the underlying dynamics. Our Ansatz can be established in the special cases of dynamics generated by global Haar random unitaries and dual-unitary circuits, while we motivate it for generic circuits using arguments of spacetime duality and the multiplicative ergodic theorem on long products of spatial transfer matrices. Extensive numerical simulations for random and Floquet circuit models verify these predictions. This universality in Kraus operators also provides a microscopic mechanism for deep thermalization in generic 1D quantum circuit dynamics, and has implications for local quantum information recoverability involving classical side information tied to knowledge of the bath.

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arXiv2026

Universal equilibrium magic in quantum many-body systems

Thermalization conventionally describes local properties of isolated many-body systems at equilibrium. Magic, or nonstabilizerness $\unicode{x2013}$ the resource enabling universal quantum computation $\unicode{x2013}$ is by contrast encoded in the global structure of the many-body wavefunction. We show that, despite its global nature, the magic of equilibrium pure states of chaotic many-body systems, including late-time evolved states and energy eigenstates, is universal: it is captured by the thermal Scrooge ensemble, the minimally informative ensemble of pure states consistent with the Gibbs state at the same effective temperature. Therefore, for systems with no conserved quantities other than the total energy, equilibrium magic is a function of temperature alone, independent of the initial state and other microscopic features of the equilibrium state. This yields concrete universal predictions for the stabilizer Rényi entropies (SREs). At infinite temperature, the SRE is set by Haar-like fluctuations of the Pauli spectrum, while at finite temperature energy conservation induces a volume-law thermodynamic correction controlled by the thermal Pauli spectrum. We support these predictions with analytical arguments and extensive numerical simulations. We further show that chaotic many-body systems at high temperatures possess long-range magic and entanglement that cannot be removed by finite-depth local quantum circuits. Our results establish magic as a thermodynamic property of chaotic many-body systems and suggest that Scrooge ensembles may provide a unified framework for quantum many-body resources.

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arXiv2026

Entanglement governs early-time growth of randomness in projected ensembles

Deep thermalization concerns the emergence of universal pure-state statistics in projected ensembles at late times, yet the mechanism governing the initial growth of randomness remains unclear. Here, we study the short-time dynamics of projected ensembles generated from initially unentangled states, quantifying their randomness using frame potentials. For arbitrary Hamiltonians, provided the initial bath state has full support in the measurement basis, we show that the frame potentials to cubic order in time are determined entirely by the subsystem purity, and hence by the bipartite entanglement generated between the unmeasured subsystem and its complement. The entanglement timescale therefore sets the initial timescale for the growth of local randomness, independently of the bath measurement basis. For unitarily invariant Hamiltonian ensembles, we further relate the projected-ensemble frame potential at order $k$ to the $4k$-point spectral form factor, or equivalently to the $2k$th frame potential of the global unitary dynamics, establishing a direct connection between local and global randomness. Our results identify entanglement as the mechanism governing the onset of randomness in projected ensembles and clarify how local randomness emerges from global quantum dynamics.

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arXiv2026

Nature is stingy: Universality of Scrooge ensembles in quantum many-body systems

Recent advances in quantum simulators allow direct experimental access to ensembles of pure states generated by measuring part of an isolated quantum many-body system. These projected ensembles encode fine-grained information beyond thermal expectation values and provide a new window into quantum thermalization. In chaotic dynamics, projected ensembles exhibit universal statistics governed by maximum-entropy principles, known as deep thermalization. At infinite temperature this universality is characterized by Haar-random ensembles. More generally, physical constraints such as finite temperature or conservation laws lead to Scrooge ensembles, which are maximally entropic distributions of pure states consistent with these constraints. Here we introduce Scrooge $k$-designs, which approximate Scrooge ensembles, and use this framework to sharpen the conditions under which Scrooge-like behavior emerges. We first show that global Scrooge designs arise from long-time chaotic unitary dynamics alone, without measurements. Second, we show that measuring a complementary subsystem of a scrambled global state drawn from a global Scrooge $2k$-design induces a local Scrooge $k$-design. Third, we show that a local Scrooge $k$-design arises from an arbitrary entangled state when the complementary system is measured in a scrambled basis induced by a unitary drawn from a Haar $2k$-design. These results show that the resources required to generate approximate Scrooge ensembles scale only with the desired degree of approximation, enabling efficient implementations. Complementing our analytical results, numerical simulations identify coherence, entanglement, non-stabilizerness, and information scrambling as essential ingredients for the emergence of Scrooge-like behavior. Together, our findings advance theoretical explanations for maximally entropic, information-stingy randomness in quantum many-body systems.

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arXiv2026

Optical depth dictates universal bounds on many-body decay in atomic ensembles

Cooperative emission is well understood for idealized symmetric systems, but its limits in spatially extended, free-space ensembles remain an open question. Here, we derive a universal law for the scaling of the maximum photon emission rate with system size that unifies both ordered arrays and disordered atomic clouds in arbitrary dimensions at fixed density. We demonstrate that, for a fixed atomic density, the maximum emission rate scales universally as the product of the atom number and the system's optical depth, with the latter encoding the dimensional scaling across all regimes from independent emission to the Dicke limit. Furthermore, we establish a scaling law for directional detection, revealing that the observed rate depends on the detector's numerical aperture: small apertures yield Dicke-like quadratic scaling, whereas large apertures recover our integrated universal bound. Our results establish optical depth as the parameter governing many-body cooperative emission in both ordered and disordered ensembles, and reveal that directional and total-emission scalings must be carefully distinguished in experimental settings.

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arXiv2026

Observation of Tunable Superradiant Frequency Combs

Cavity quantum electrodynamics (QED) with quantum emitters coupled to resonators provides a powerful platform for engineering light-matter interactions and exploring collective phenomena. In particular, superradiance, arising from collective quantum interference among emitters, has been explored as a route to ultrastable continuous radiation. However, engineering superradiance in the time domain to realize periodic pulsed sources or frequency combs remains largely unexplored. Here, we investigate the non-equilibrium many-body dynamics of a driven spin ensemble coupled to an on-chip superconducting resonator and uncover a dynamical phase transition from continuous-wave to periodic pulsed superradiant emission. To quantitatively capture the observed dynamical phases, we introduce a driven-dissipative cavity-QED model that elucidates how the periodic pulsed superradiant phase emerges from collective, periodically repeating spin dynamics stabilized by the interplay of coherence growth, disorder, and dissipation. We also find that rare-earth ion spin systems exhibiting both optical and microwave transitions enable phase-synchronized, dual-rail superradiant frequency combs in both the microwave and optical domains. Our results not only open new avenues for dual-rail frequency-comb applications in quantum metrology and information processing, but also establish a fundamental connection between periodic pulsed superradiance and the emergence of a continuous time crystal as a novel nonequilibrium phase in driven open systems.

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arXiv2026

Power-law distributions in nonequilibrium open quantum systems

Power-law probability distributions are widely used to model extreme statistical events in complex systems, with applications to a vast array of natural phenomena ranging from earthquakes to stock market crashes to pandemics. We show that analogous heavy tails arise naturally in open quantum systems with nonlinear dissipation. Introducing a prototypical family of quantum dynamical models, we analytically prove the emergence of power-law tails in the steady state energy distribution, originating from an amplification of quantum noise whose microscopic fluctuations grow with energy. Moreover, our analysis suggests a general mechanism for heavy-tail statistics in the nonequilibrium steady states of open quantum systems: Nonlinear dissipation generically induces multiplicative quantum noise, enforced by the constraints of quantum mechanics, which is responsible for the heavy-tail behavior. This is supported by numerical simulations of a general class of nonlinear dynamics known as quantum Liénard systems. Remarkably, even when the corresponding classical system is stable, we find power-law tails in both steady-state populations and coherences, which occur for typical parameters without fine-tuning. This phenomenon can potentially be harnessed to develop extreme photon sources for novel applications in light-matter interaction and sensing.

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arXiv2025

Quantization of nonlinear non-Hamiltonian systems

Several important dynamical systems are in $\mathbb{R}^2$, defined by the pair of differential equations $(x',y')=(f(x,y),g(x,y))$. A question of fundamental importance is how such systems might behave quantum mechanically. In developing quantum theory, Dirac and others realized that classical Hamiltonian systems can be mapped to their quantum counterparts via canonical quantization. The resulting quantum dynamics is always physical, characterized by completely-positive and trace-preserving evolutions in the Schrödinger picture. However, whether non-Hamiltonian systems can be quantized systematically while respecting the same physical requirements has remained a long-standing problem. Here we resolve this question when $f(x,y)$ and $g(x,y)$ are arbitrary polynomials. By leveraging open-systems theory, we prove constructively that every polynomial system admits a physical generator of time evolution in the form of a Lindbladian. We call our method cascade quantization, and demonstrate its power by analyzing several paradigmatic examples of nonlinear dynamics such as bifurcations, noise-activated spiking, and Liénard systems. In effect, our method can quantize any classical system whose $f(x,y)$ and $g(x,y)$ are analytic with arbitrary precision. More importantly, cascade quantization is exact. This means restrictive system properties usually assumed in the literature to facilitate quantization, such as weak nonlinearity, rotational symmetry, or semiclassical dynamics, can all be dispensed with by cascade quantization. We also highlight the advantages of cascade quantization over existing proposals, by weighing it against examples from the variational paradigm using Lagrangians, as well as non-variational approaches.

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arXiv2025

Rise and fall of nonstabilizerness via random measurements

We investigate the dynamics of nonstabilizerness - also known as `magic' - in monitored quantum circuits composed of random Clifford unitaries and local projective measurements. For measurements in the computational basis, we derive an analytical model for dynamics of the stabilizer nullity, showing that it decays in quantized steps and requires exponentially many measurements to vanish, which reveals the strong protection through Clifford scrambling. On the other hand, for measurements performed in rotated non-Clifford bases, measurements can both create and destroy nonstabilizerness. Here, the dynamics leads to a steady-state with non-trivial nonstabilizerness, independent of the initial state. We find that Haar-random states equilibrate in constant time, whereas stabilizer states exhibit linear-in-size relaxation time. While the stabilizer nullity is insensitive to the rotation angle, Stabilizer Rényi Entropies expose a richer structure in their dynamics. Our results uncover sharp distinctions between coarse and fine-grained nonstabilizerness diagnostics and demonstrate how measurements can both suppress and sustain quantum computational resources.

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arXiv2025

Universal scaling laws for correlated decay of many-body quantum systems

Quantum systems are open, continually exchanging energy and information with the surrounding environment. This interaction leads to decoherence and decay of quantum states. In complex systems, formed by many particles, decay can become correlated and enhanced. A fundamental question then arises: what is the maximal decay rate of a large quantum system, and how does it scale with its size? In this work, we address these issues by reformulating the problem into finding the ground state energy of a generic spin Hamiltonian. Inspired by recent work in Hamiltonian complexity theory, we establish rigorous and general upper and lower bounds on the maximal decay rate. These bounds are universal, as they hold for a broad class of Markovian many-body quantum systems. For many physically-relevant systems, the bounds are asymptotically tight, resulting in exact scaling laws with system size. Specifically, for large atomic arrays in free space, these scalings depend only on the arrays' dimensionality and are insensitive to details at short length-scales. The scaling laws set fundamental limits on the decay rates of all quantum states, shed light on the behavior of generic driven-dissipative systems, and may ultimately constrain the scalability of quantum processors and simulators based on atom arrays.

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arXiv2025

Stability of macroscopic spin ensembles against inhomogeneous dephasing

Spin ensembles play a pivotal role in various quantum applications such as metrology and simulating many-body physics. Recent research has proposed utilizing spin cat states to encode logical quantum information, with logical lifetimes potentially on the order of seconds, achieved via enhanced collective interactions that scale with system size. We investigate the dynamics of spin cat states under inhomogeneous broadening, revealing a phenomenon termed 'parity-sensitive inhomogeneous dephasing': for small amplitudes, odd cat states are significantly more susceptible to inhomogeneous dephasing compared to even cat states due to the difference in parity symmetry. This discrepancy between even and odd cat states vanishes at large amplitudes, and behave similarly to a spin coherent state with the same amplitude. To analyze the stability of the spin coherent state, we perform a mean-field analysis of the driven-dissipative dynamics, from which we identify a synchronization phase transition wherein the ensemble becomes completely dephased beyond a critical inhomogeneous linewidth. The mean-field analysis suggests that the dissipative stabilization can suppress the decoherence effects from inhomogeneous broadening. We argue that the stability of the mean-field model provides a reasonable estimate for that of spin cat states with a large amplitude in the full quantum model. Our findings shed light on the stability of collective spin states, important for advancing quantum technologies.

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arXiv2025

Optimal Conversion from Classical to Quantum Randomness via Quantum Chaos

Quantum many-body systems provide a unique platform for exploring the rich interplay between chaos, randomness, and complexity. In a recently proposed paradigm known as deep thermalization, random quantum states of system A are generated by performing projective measurements on system B following chaotic Hamiltonian evolution acting jointly on AB. In this scheme, the randomness of the projected state ensemble arises from the intrinsic randomness of the outcomes when B is measured. Here we propose a modified scheme, in which classical randomness injected during the protocol is converted by quantum chaos into quantum randomness of the resulting state ensemble. We show that for generic chaotic systems this conversion is optimal in that each bit of injected classical entropy generates as much additional quantum randomness as adding an extra qubit to B. This significantly enhances the randomness of the projected ensemble without imposing additional demands on the quantum hardware. Our scheme can be easily implemented on typical analog quantum simulators, providing a more scalable route for generating quantum randomness valuable for many applications. In particular, we demonstrate that the accuracy of a shadow tomography protocol can be substantially improved.

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arXiv2025

Ground-state selection via many-body superradiant decay

For a single particle, relaxation into different ground states is governed by fixed branching ratios determined by the transition matrix element and the environment. Here, we show that in many-body open quantum systems the occupation probability of one ground state can be boosted well beyond what is dictated by single-particle branching ratios. Despite the competition, interactions suppress all but the dominant decay transition, leading to a 'winner takes all' dynamic where the system primarily settles into the dominant ground state. We prove that, in the presence of permutation symmetry, this problem is exactly solvable for any number of competing channels. Additionally, we develop an approximate model for the dynamics by mapping the evolution onto a fluid continuity equation, and analytically demonstrate that the dominant transition ratio converges to unity as a power law with increasing system size, for any branching ratios. This near-deterministic preparation of the dominant ground state has broad applicability. As an example, we discuss a protocol for molecular photoassociation where collective dynamics effectively acts as a catalyst, amplifying the yield in a specific final state. Our results open new avenues for many-body strategies in the preparation and control of quantum systems.

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arXiv2025

Pseudorandom density matrices

Pseudorandom states (PRSs) are state ensembles that cannot be efficiently distinguished from Haar random states. However, the definition of PRSs has been limited to pure states and lacks robustness against noise. Here, we introduce pseudorandom density matrices (PRDMs), ensembles of $n$-qubit states that are computationally indistinguishable from the generalized Hilbert-Schmidt ensemble (GHSE), which is constructed from $(n+m)$-qubit Haar random states with $m$ qubits traced out. For $m=0$, PRDMs are equivalent to PRSs, whereas for $m=ω(\log n)$, PRDMs are computationally indistinguishable from the maximally mixed state. PRDMs with $m=ω(\log n)$ are robust to unital noise channels and separated in terms of security from PRS. PRDMs disguise valuable quantum resources, possessing near-maximal entanglement, magic and coherence, while being computationally indistinguishable from resource-free states. PRDMs exhibit a pseudoresource gap of $Θ(n)$ vs $0$, surpassing previously found gaps. We also render EFI pairs, a fundamental cryptographic primitive, robust to strong mixed unitary noise. Our work has major implications on quantum resource theory: We show that entanglement, magic and coherence cannot be efficiently tested, and that black-box resource distillation requires a superpolynomial number of copies. We also establish lower bounds on the purity needed for efficient testing and black-box distillation. Finally, we introduce memoryless PRSs, a noise-robust notion of PRS which are indistinguishable to Haar random states for efficient algorithms without quantum memory, as well as noise-robust quantum money. Our work provides a comprehensive framework of pseudorandomness for mixed states, which yields powerful quantum cryptographic primitives and fundamental bounds on quantum resource theories.

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arXiv2025

Generation and optimization of entanglement between atoms chirally coupled to spin cavities

We explore the generation and optimization of entanglement between atoms chirally coupled to finite 1D spin chains, functioning as {\it spin cavities}. By diagonalizing the spin cavity Hamiltonian, we identify a parity effect that influences entanglement, with small even-sized cavities chirally coupled to atoms expediting entanglement generation by approximately $50\%$ faster than non-chiral coupling. Applying a classical driving field to the atoms reveals oscillations in concurrence, with resonant dips at specific driving strengths due to the resonances between the driven atom and the spin cavity. Extending our study to systems with energetic disorder, we find that high concurrence can be achieved regardless of disorder strength when the inverse participation ratio of the resulting eigenstates is favorable. Finally, we demonstrate that controlled disorder within the cavity significantly enhances and expedites entanglement generation, achieving higher concurrences up to four times faster than those attained in ordered systems.

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arXiv2025

Pseudorandom quantum authentication

We introduce the pseudorandom quantum authentication scheme (PQAS), an efficient method for encrypting quantum states that relies solely on the existence of pseudorandom unitaries (PRUs). The scheme guarantees that for any eavesdropper with quantum polynomial-time (QPT) computational power, the encrypted states are indistinguishable from the maximally mixed state. Furthermore, the receiver can verify that the state has not been tampered with and recover the original state with asymptotically unit fidelity. Our scheme is cost-effective, requiring only polylogarithmic circuit depth and a single shared key to encrypt a polynomial number of states. Notably, the PQAS can potentially exist even without quantum-secure one-way functions, requiring fundamentally weaker computational assumptions than semantic classical cryptography. Additionally, PQAS is secure against attacks that plague protocols based on QPT indistinguishability from Haar random states, such as chosen-plaintext attacks (CPAs) and attacks that reveal meta-information such as quantum resources. We relate the amount of meta-information that is leaked to quantum pseudoresources, giving the concept a practical meaning. As an application, we construct important cryptographic primitives, such as verifiable pseudorandom density matrices (VPRDMs), which are QPT-indistinguishable from random mixed states while being efficiently verifiable via a secret key, as well as verifiable noise-robust EFI pairs and one-way state generators (OWSGs). Our results establish a new paradigm of quantum information processing with weaker computational assumptions.

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arXiv2024

Variational learning of integrated quantum photonic circuits

Integrated photonic circuits play a crucial role in implementing quantum information processing in the noisy intermediate-scale quantum (NISQ) era. Variational learning is a promising avenue that leverages classical optimization techniques to enhance quantum advantages on NISQ devices. However, most variational algorithms are circuit-model-based and encounter challenges when implemented on integrated photonic circuits, because they involve explicit decomposition of large quantum circuits into sequences of basic entangled gates, leading to an exponential decay of success probability due to the non-deterministic nature of photonic entangling gates. Here, we present a variational learning approach for designing quantum photonic circuits, which directly incorporates post-selection and elementary photonic elements into the training process. The complicated circuit is treated as a single nonlinear logical operator, and a unified design is discovered for it through variational learning. Engineering an integrated photonic chip with automated control, we adjust and optimize the internal parameters of the chip in real time for task-specific cost functions. We utilize a simple case of designing photonic circuits for a single ancilla CNOT gate with improved success rate to illustrate how our proposed approach works, and then apply the approach in the first demonstration of quantum stochastic simulation using integrated photonics.

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