Papers

Quantum metrology promises phase sensitivity surpassing the shot-noise limit by exploiting entanglement and photon-number correlations. NOON states-maximally path-entangled $N$-photon superpositions $(|N,0\rangle + |0,N\rangle)/\sqrt{2}$ -achieve the Heisenberg limit $1/N$ for single-parameter estimation, as demonstrated experimentally by Afek et al. (2010) using hybrid coherent-plus-squeezed light up to $N=5$. We present an end-to-end differentiable quantum-optical framework-implemented in Strawberry Fields (Killoran et al., 2019) with a TensorFlow backend -that learns optimal circuit parameters by maximising the classical Fisher information (CFI) across all coincidence channels for $N=2,3,4,5$. Starting from proper numerical reproductions of the Afek et al. coincidence fringes, verified by FFT analysis and parity measurements, we apply gradient descent (Adam) to the eight trainable circuit parameters. Raw CFI improvements grow dramatically with photon number: $+153\%$ ($N=2$), $+834\%$ to $+956\%$ ($N=3$), $+829\%$ to $+1598\%$ ($N=4$), and $+1775\%$ ($N=5$), alongside post-selection rate improvements of $+153\%$ to $+3269\%$, and an $8\times$ to $133\times$ improvement in useful measurement events per pulse across $N=2$-$5$. A fundamental inter-channel trade-off is identified at $N=2$ but weakens at higher $N$ where the Afek initialisation is further from optimal. These results provide numerically rigorous benchmarks for adaptive single-parameter quantum sensing and demonstrate that the Afek working point is significantly suboptimal at $N\geq 3$. QFI calculations confirm that the optimised probe reaches $82\%$ of the Heisenberg limit at $N=2$ and improves from $36\%$ to $58\%$ at $N=5$, while useful measurement events per pulse improve by $8\times$ to $133\times$ across all $N$, making quantum-enhanced sensing at $N\geq 3$ experimentally practical.

The kicked rotor provides a simple yet powerful model for introducing many of the central concepts of classical and quantum chaos. Despite its apparent simplicity, it exhibits rich dynamical behavior and has found applications across a wide range of fields, including atomic and optical physics, condensed matter physics, and emerging quantum technologies. This chapter begins by exploring foundational ideas using the kicked rotor as a unifying framework. We first discuss the transition from regular to chaotic motion in the classical system, and then introduce key quantum phenomena such as dynamical localization and quantum resonances. Special attention is devoted to the emergence of characteristic time scales and their role in the quantum-classical correspondence. To make these ideas more concrete, we also provide a brief overview of experimental realizations of the kicked rotor and its variants, illustrating how theoretical concepts are implemented in practice. In the second part of the chapter, we guide the reader toward more recent and advanced developments. Topics include near-resonant dynamics, topological features of kicked systems, the emergence of quantum dynamical phases inferred from classical transport properties, and extensions to non-Hermitian physics. We conclude with a discussion of open problems and future perspectives, outlining directions in which the kicked rotor continues to offer valuable insights.

One of the promising applications of digital quantum processors is the simulation of many-body quantum systems. They have been already used to investigate several ergodicity violating mechanisms, which were initially discovered in synthetic quantum matter, such as many-body localisation, Hilbert space fragmentation and quantum many-body scars (QMBS). In addition to conventional QMBS, a recently discovered mechanism for ergodicity violation are the so-called asymptotic quantum many-body scars (AQMBS). These become more stable as system size is increased, leading to progressively longer thermalisation timescales. In this work, we show a connection between gapless excitations and AQMBS in certain qudit-based models. We then consider a 2-local model, hosting both conventional and asymptotic scars, in which the AQMBS states are gapless excitations of a ground state localisation transition. By exploiting the structure of the found AQMBS states and the all-to-all connectivity of the Quantinuum H1-1 quantum processor, we prepare these states in logarithmic circuit depth, and probe their thermalisation behaviour under Floquet dynamics. Performing simulations on up to N = 20 qubits and up to 418 entangling ZZ gates, we find slower thermalisation times as the system size is increased, providing the first experimental signatures of asymptotic scars.

We numerically optimized a scheme for a symmetric controlled-Z (CZ) gate based on the Rydberg blockade in neutral atoms, with the aim of increasing its robustness to variations in the Rabi frequency. The scheme exploits analytically defined phase profiles of the laser pulse and proves almost an order of magnitude more robust to Rabi-frequency variations than previously proposed protocols. We designed this amplitude-robust protocol with a smooth pulse shape and optimized it for a finite Rydberg blockade strength, which makes it suitable for experimental implementation in both single-photon and two-photon configurations. We further show that the protocol can be applied to individually addressed Rydberg excitation, accounting for the asymmetry of the Rabi frequencies of two atoms excited by tightly focused laser beams. This allows the effects of residual thermal motion of the trapped atoms to be reduced. Finally, we examined the performance of the protocol for single-photon and two-photon Rydberg excitation schemes at finite blockade strength, and demonstrated its advantages for individual addressing at finite temperatures of the trapped atoms.

A quadratic well plays a central role in a wide variety of modern physical theories and applications. In this work, we investigate many-body dynamics in a quadratic well, using an Ising chain as a paradigmatic example. In contrast to a uniform Ising chain, where the quantum phase transition is driven by the field strength, the present system exhibits spatially varying quantum phases along the chain. Through analysis of the Majorana representation, we obtain exact solutions for localized modes, revealing a topologically degenerate spectrum in the thermodynamic limit. In the case of a finite-size quantum phase region, the Kramers-like degeneracy is lifted by a constant shift, leading to periodic oscillations for a finite-temperature thermal initial state. Numerical simulations of the magnetization, local density of state, and quench fidelity support our conclusions. Our findings enrich the understanding of many-body dynamics in a trapping field.

Entanglement-based quantum key distribution (QKD) relies on the distribution of high-fidelity maximally entangled Bell states, typically generated via spontaneous parametric down-conversion (SPDC). In practical systems, unwanted relative phases arise from birefringence, pump-beam contributions, imperfect photon-pair generation, transmission through physical channels, and collection, transforming Bell states into phase-shifted states. This degrades interference visibility, increases the quantum bit error rate (QBER), and limits secure key generation. Conventional compensation techniques, such as birefringent crystals, interferometric stabilization, and spatial light modulators, are often impractical in real-world deployments. Here, we demonstrate a simple and versatile phase-compensation scheme that can be implemented at either the source or the receiver to eliminate arbitrary relative phases in Bell states. We theoretically and experimentally quantify the dependence of QBER in the BBM92 protocol on the relative phase and show that geometric-phase-based control can effectively restore entanglement quality. In a proof-of-concept experiment using a nondegenerate polarization Bell state, we achieve a fidelity exceeding 95% and reduce QBER below the 11% security threshold required for secure QKD. This robust approach enables practical phase control in entangled-photon systems and can be extended to time-bin QKD via time-polarization mapping, offering a promising route toward stable, low-QBER quantum communication.

The notion of Shannon entropy is crucial for the theory of classical information. In quantum information theory, an analogous key role is played by the von Neumann entropy: quantum information processing is closely related to entropy dynamics. This reveals a direct link with the theory of quantum chaotic systems, which can be characterized by a positive entropy production. Furthermore, noise, which inevitably affects any quantum system, can be modeled by a random quantum operation or by coupling to an environment in a generic chaotic state. In this contribution, we emphasize the universality of quantum chaotic dynamics and discuss its implications for quantum information processing.

The path toward practical superconducting quantum processors requires the integration of a large number of high-performance qubits. Modular architectures could offer a way to address the scaling limitations of monolithic designs by partitioning a large quantum processor into physically separated modules, or chiplets, linked through long-range interconnects. In this context, although fluxonium qubits have emerged as a compelling platform for quantum computing due to their long coherence times and high-fidelity gates, existing coupling schemes remain restricted to qubits in close proximity on a single chip. This limitation inherently precludes the long-range interconnects essential for modular integration. In this work, we propose a long-range tunable coupler designed to interconnect fluxonium qubits separated by more than one centimeter, thereby supporting the realization of modular fluxonium quantum processors. Under realistic assumptions, the proposed coupler has the potential to achieve inter-module two-qubit gate performance, specifically sub-100-ns gates with intrinsic errors below $10^{-4}$, comparable to that of intra-module (intra-chiplet) gates, while enabling modular integration with low quantum crosstalk, a key requirement for scalable systems. We further discuss the integration of this coupler into modular fluxonium lattices and explore its feasibility for achieving the higher connectivity and longer coupling range required for complex quantum error correction codes. This work could contribute to the development of large-scale fluxonium quantum processors by bridging their demonstrated potential with modular scalability.

Quantum circuit simulation is crucial for the development of quantum algorithms, particularly given the high cost and noise limitations of physical quantum hardware. While full-state quantum circuit simulation is commonly employed for prototyping and debugging, it poses challenges because of the exponential increase in simulation time for large quantum systems. In this work, we propose an extensible framework designed to enhance simulation performance by optimizing both data locality and computational efficiency, thereby addressing these challenges. This framework is seamlessly integrated with an optimizer that restructures quantum circuits and a simulator that adjusts execution strategies for various quantum operations. For the newly developed components, merge booster and diagonal detector, the underlying algorithms are inspired by the principles of quantum entanglement and gate fusion, as well as by the limitations identified in existing third-party simulation libraries. The experiments were conducted on eight DGX-H100 workstations, each equipped with eight NVIDIA H100 GPUs, employing both gate-level and circuit-level benchmarks. The results indicate a speedup of up to 160 times for circuit-level benchmarks and an acceleration of up to 34 times for diagonal-heavy gate-level benchmarks compared to existing simulators. The proposed methodologies are anticipated to deliver more robust and faster quantum circuit simulations, thereby fostering the advancement of novel quantum algorithms.

We investigate the stationary amplitude and current properties of a charged particle in a uniform magnetic field within the Bohm–Madelung formulation. The analysis is organised around two complementary questions: the effect of steady currents on amplitude evolution, and the influence of the singular radial behaviour on the energy spectrum of the Landau problem. For the zero-current system, corresponding to the standard Landau problem, the Hamilton–Jacobi equations lead to an Ermakov–Pinney reference structure for the separated amplitudes. The azimuthal sector additionally admits periodic branches in which the magnetic flux is constrained by the angular periodicity condition. Allowing nonvanishing component currents under global current conservation introduces nonlinear amplitude evolution, most prominently through the magnetic-vector-potential coupling in the azimuthal sector. Under the minimum choice of equal and opposite radial and azimuthal currents, the radial contribution remains analytically tractable, while the nonlinear angular momentum and action are bounded through two complementary solvable comparison equations. The Bohmian formulation also makes it possible to examine directly the singular structure of the radial energy equation. A Fisher-based regularisation associated with the current-branching construction is shown to closely parallel the role of Langer- and JWKB-type radial regularisation, while arising from the Bohm–Madelung amplitude–momentum description itself. The resulting modification of the radial index re-orders the Landau energy spectrum and lifts the corresponding azimuthal degeneracy. Keywords: Landau problem; Bohm–Madelung mechanics; nonlinear current dynamics; Ermakov–Pinney equation; radial regularisation; comparison bounds; spectral splitting.

We establish a rigorous bundle isomorphism between the complex velocity field $\eta_{\mu} = \pi_{\mu} - i u_{\mu}$, obtained by averaging matter dynamics over stochastic gravitational fluctuations, and the symmetric logarithmic derivative (SLD) operator $L_{\mu}$ of quantum estimation theory. The isomorphism $\widetilde{\mathcal{T}}: \Gamma(E/{\sim}) \to \Gamma(\mathcal{L})$ maps gauge-equivalence classes of sections of the pullback bundle $E = \pi_2^*(T^*M)$ over $\mathcal{C} \times M$ to SLD operators on the Hilbert space $\mathcal{H}_0 = L^2(\mathcal{C}, \nu_0)$, where $\mathcal{C}$ is the infinite-dimensional Fréchet manifold of matter fields and $\nu_0$ is a fixed Gaussian measure. We prove that $\widetilde{\mathcal{T}}$ and the associated quantum Fisher metric are independent of the choice of $\nu_0$, rendering the construction intrinsic to the physical probability density. The Fisher metric acquires a simple form in terms of the Madelung–Bohm velocities: $g_{\mu\nu}^{\mathrm{FS}} = \frac{4m^2}{\hbar^2} \bigl[\operatorname{Cov}(\pi_\mu,\pi_\nu) + \operatorname{Cov}(u_\mu,u_\nu)\bigr]_{\mathcal{P}}$. As a consequence, the flat $U(1)$ connection defined by $\eta_{\mu}$ yields a quantized holonomy for non-contractible spacetime loops, predicting topological phases that may be observable in atom interferometry.

We develop a quantum message-passing framework for factor graphs over finite abelian groups. Our starting point is the task of discriminating between a collection of quantum states indexed by the elements of a finite abelian group $\mathcal{G}$ whose overlaps respect the structure of a group-covariant pure-state channel (PSC). For such channels, we show that the Gram matrix constructed from the output states is diagonalized by the character basis of the dual group $\widehat{\mathcal{G}}$. Hence, the channel is characterized, up to isometric equivalence, by its character-indexed eigen list. Based on this representation, we analyze the induced classical-quantum channels associated with check, equality, homomorphism, marginalization, and automorphism factors. For each factor, we derive explicit update rules showing that if the incoming messages are heralded mixtures of group-covariant PSCs, then the outgoing message remains in the same class. This provides a closed quantum message-passing framework for tree-structured factor graphs assembled from these primitives. The framework applies directly to several standard code families over finite abelian groups, including polar codes, LDPC codes, and convolutional and turbo codes. It recovers the previously studied $q$-ary formulation as the special case $(\mathcal{G}=\mathbb{Z}_q)$, while extending the belief propagation with quantum messages (BPQM) framework introduced by Renes to non-cyclic alphabets and more general factor-graph constraints described by homomorphisms between products of abelian groups.

Transferring the information stored in the expansion coefficients of a multi-qubit state to the coefficients of a continuous-variable state is an important protocol for communicating quantum information. It was shown in previous work how to transfer an $n$-qubit state to a single qumode in $\mathcal{O}(2^n)$ time. We show that by transferring this state to $m$ qumodes, the runtime can be improved to $\mathcal{O}(2^{n/m})$. Furthermore, we demonstrate how multi-qumode state transfer can be used as a subroutine for approximately realizing the $n$-qubits quantum Fourier transform on $m$-qumode with runtime scaling $\mathcal{O}(m2^{n/m}/\epsilon+m^2)$, accelerating qubit quantum Fourier transform using qumodes. This work presents a scalable approach to convert discrete and continuous quantum information between an arbitrary number of qubits and qumodes. It represents a crucial step forward in mixed analog-digital quantum signal processing for computing, sensing, and communication.

We study deterministic multi-user identification over bosonic channels using coherent-state signatures. Each user is assigned a coherent product state under an average energy constraint, and identification is performed by a user-specific binary quantum test. In contrast to classical multi-user identification models based on shared codebooks, this formulation associates each receiver with a geometric signature in high-dimensional phase space. Using metric entropy bounds, we show that the identification capacity exhibits a near-k log k scaling behavior.

Quantum algorithms with a proven theoretical speedup over classical computation are rare. Among the most prominent is the Harrow-Hassidim-Lloyd (HHL) algorithm for solving sparse linear systems. Here, HHL is applied to encode melodic preference: the system matrix encodes Narmour implication-realisation and Krumhansl-Kessler tonal stability, so its solution vector is a music-cognition-weighted note-pair distribution. The key constraint of HHL is that reading its output classically cancels the quantum speedup; the solution must be consumed coherently. This motivates a coherent Fourier harmonic oracle: a unitary that applies chord-transition weights directly to the HHL amplitude vector, so that a single measurement jointly selects both melody notes and a two-chord progression. A two-note/two-chord (2/2) block is used to contain the exponential growth of the joint state space that would otherwise make classical simulation of larger blocks infeasible. For demonstrations of longer passages, blocks are chained classically - each block's collapsed output conditions the next – as a temporary workaround until fault-tolerant hardware permits larger monolithic circuits. A four-block chain produces 8 notes over 8 chords with grammatically valid transitions at every block boundary. Independent rule-based harmony validation confirms that 97% of generated chord progressions are rated strong or acceptable. The primary motivation is that HHL carries a proven exponential speedup over classical linear solvers; this work demonstrates that a coherent HHL+oracle pipeline - the prerequisite for that speedup to be realised in a musical setting - is mechanically achievable. Audio realisations of representative outputs are made available for listening online.

Accurately treating strong electron correlation in quantum chemistry typically requires multireference wave-function methods with steep computational scaling. The recently proposed i-DMFT method promises near configuration-interaction accuracy at mean-field cost by invoking an empirical linear relation between correlation energy and entropy (Collins' conjecture), whose validity remains unclear. We systematically assess this relation across a range of di- and polyatomic molecules, including diverse bond types, third-row elements, different types of geometric distortions, and excited states. We find that the conjectured linearity holds for bond-breaking processes dominated by electron redistribution within orbital pairs, but breaks down for heterolytic dissociation and excited states. In simple molecules, i-DMFT provides a reasonable description of total energies, but does not reliably reproduce reduced density matrices or individual energy components. It further degrades in more complex cases such as ethylene. Based on these results, we formulate criteria for the validity of the conjecture and outline implications for entropy-based reduced density matrix functionals.

Electron spin-dependent chemical reactions in proteins, often discussed under the 'radical-pair mechanism', remain the leading microscopic proposal for magnetic field sensing in biology. Yet the essential physics is often obscured by the complexity of realistic models. In this work, we present a physicist-friendly primer on the simplest radical-pair Hamiltonian that already captures many of the mechanism's best-known qualitative features. The contributions of this work are fourfold. First, we place on record a complete analytical solution of this toy model, which has previously been studied extensively, mostly through numerical and partial analytical approaches. Working in the experimentally relevant singlet-triplet basis, we derive closed-form expressions for the instantaneous singlet population and for two related time-averaged singlet yields. Second, we introduce a new interpretation of these results that makes several familiar features of radical-pair physics transparent. In particular, we show that the dynamics admit a bright-dark decomposition (in the sense of spin mixing), similar to structures studied in atomic physics. Third, through this bright-dark perspective, we clarify experimentally relevant features of the toy model. In particular, we show that the so-called 'low-field effect' arises from a coherence term between bright and dark sectors, and that the special role of zero field is best understood as a phase-locking phenomenon rather than merely as enhanced mixing. Fourth, we import methods developed in the context of technological quantum sensing to obtain further insight into the model. This allows us to clarify the role of initial state preparation and the trade-off between coherent phase accumulation and time-averaging penalties. The resulting toy model serves both as an analytically tractable benchmark and as a conceptual starting point for future work.

Strongly correlated materials are a natural target for fault-tolerant quantum computers, but they require tools beyond those developed for molecules. Electronic wavefunctions vary rapidly near nuclei yet remain delocalized across many unit cells, and bulk properties must be converged systematically with respect to finite-size errors. To resolve such issues, we present the Bloch–UPAW framework that combines Bloch-orbital $k$-space structure with unitary projector-augmented-wave (UPAW) augmentation. The UPAW Hamiltonian, expressed directly in the Bloch basis, retains explicit control of Brillouin-zone sampling, and incorporates near-nuclear physics through strictly local on-site corrections. The construction is independent of the underlying one-particle representation, so it applies to both plane-wave and localized bases, and it handles supercells for symmetry-breaking phenomena more efficiently. We derive a linear-combination-of-unitaries decomposition and a block-encoding circuit suitable for qubitization; UPAW augmentation adds one ancilla qubit and no Toffoli gates at leading order relative to a Bloch-only block encoding. Asymptotically, the Toffoli cost scales as $\mathcal{O}(N_k^3)$ when refining the $k$-mesh and as $\mathcal{O}(N_a^{3.5})$ when enlarging the supercell, enabling convergence to be steered by the most favorable route for a given material. Resource estimates for bulk diamond show approximately an order-of-magnitude reduction in Toffoli count relative to prior work on periodic solids.

We review the ideas of how random matrix theory has to be properly applied to quantum physics; particularly we focus on how the spectrum has to be properly prepared and the random matrix correctly identified before the random matrix and the physical eigenvalue spectrum can be compared. We explain the ideas of the symmetry classification of symmetric matrix spaces and how that yields Dyson's threefold and Altland-Zirnbauer's tenfold way. We also outline how the joint probability density function of the eigenvalues can be calculated from a given probability density function on the matrix space. Furthermore, we dive into the subtleties of the unfolding procedure. For this purpose, we explain the ideas of the local mean level spacing, the local level spacing distribution and the $k$-point correlation functions. We outline the techniques of orthogonal polynomials, determinantal and Pfaffian point processes and their related Fredholm determinants and Pfaffians as well as the supersymmetry method. Moreover, we relate the local spectral statistics to effective Lagrangians that give the relation to non-linear $\sigma$-models. In all these discussions, we also make brief excursions to non-Hermitian random matrix theory which are useful when studying open quantum systems, for instance.

The short-path quantum algorithm introduced by Hastings (Quantum 2018, 2019) is a variant of adiabatic quantum algorithms that enables an easier worst-case analysis by avoiding the need to control the spectral gap along a long adiabatic path. Dalzell, Pancotti, Campbell, and Brandão (STOC 2023) recently revisited this framework and obtained a clear analysis of the complexity of the short-path algorithm for several classes of constraint satisfaction problems (MAX-$k$-CSPs), leading to quantum algorithms with complexity $2^{(1-c)n/2}$ for some constant $c>0$. This suggested a super-quadratic quantum advantage over classical algorithms. In this work, we identify an explicit classical mechanism underlying a substantial part of this line of work, and show that it leads to clean dequantizations. As a consequence, we obtain classical algorithms that run in time $2^{(1-c')n}$, for some constant $c'>c$, for the same classes of constraint satisfaction problems. This shows that current short-path quantum algorithms for these problems do not achieve a super-quadratic advantage. On the positive side, our results provide a new “quantum-inspired” approach to designing classical algorithms for important classes of constraint satisfaction problems.

By an idealized quantum mechanical model, we formally describe the dispersion of nonretarded electromagnetic waves that express charge density oscillations near a fixed plane in three spatial dimensions (3D) at zero temperature. Our goal is to capture the interplay of microscopic scales that include a confinement length in the emergence of the surface plasmon, a collective low-energy charge excitation in the vicinity of the plane. We start with a time-dependent Hartree-type equation in 3D. This model accounts for particle binding to the plane and the repulsive Coulomb interaction associated with the induced charge density relative to the ground state. By linearizing the equation of motion, we formulate a homogeneous integral equation for the scattering amplitude of the particle wave function in the (z-) coordinate vertical to the plane. For a binding potential proportional to a negative delta function and symmetric-in-z wave function, we apply the Laplace transform with respect to positive z and convert the integral equation into a functional equation that involves several values of the transformed solution. The scattering amplitude and dispersion relation are derived exactly in terms of rapidly convergent series via the Mittag-Leffler theorem. In the semiclassical regime, our result furnishes an asymptotic expansion for the energy excitation spectrum. The leading-order term is found in agreement with the prediction of a classical hydrodynamic model based on a projected-Euler-Poisson system.

Rydberg atomic quantum receivers (RAQRs) have recently emerged as a promising technology for radio-frequency (RF) reception by directly transducing incident RF fields into optical signals. Existing receiver architectures, however, exploit only subsets of the dipole-allowed transitions within a given atomic manifold, limiting the number of simultaneously accessible RF channels. In this paper, a hybrid six-level Rydberg atomic quantum receiver (H-RAQR) is proposed by integrating parallel and cascaded RF coupling pathways within a single vapor-cell receiver. A communication-oriented analytical framework is developed by deriving a closed-form steady-state atom–field interaction model and establishing an equivalent baseband signal representation. The achievable ergodic sum rate is analyzed, and a resource-efficiency metric is introduced to quantify throughput per unit optical receiver resource. The analytical model is validated against full Lindblad master-equation simulations over its identified operating region. Numerical results show that the proposed H-RAQR supports four simultaneous RF channels within a single atomic system, achieves higher ergodic sum rate than conventional parallel Rydberg state (PRS) and cascade Rydberg state (CRS) receivers, and provides about 29% higher resource efficiency than a combined PRS-CRS deployment with equivalent four-band coverage. The proposed framework provides a scalable foundation for multi-band atomic wireless receivers.

I argue that there is a straightforward way to understand the occurrence of wavefunction collapses or 'quantum events' in relational approaches to quantum mechanics: we necessarily encounter a discontinuity in our description when a system interacts with the reference relative to which we are describing it, since the reference system cannot be described relative to itself. This makes it clear how recent concerns around quantum events in relational quantum mechanics should be resolved. However, the solution requires accepting that quantum mechanics is not a complete description of all physical facts, and moreover I argue that this is most likely inevitable if we want to be able to give a precise description of quantum events.

We explore here how to generate a two-mode squeezed output using reservoir engineering in a double-cavity optomechanical system coupled to a common mechanical resonator. Such hybrid platforms are experimentally accessible in electro-optomechanical interfaces and are relevant for high-fidelity state transfer, quantum communication, and metrological applications. By examining violations of the CHSH Bell inequality, we demonstrate that maximal squeezing does not necessarily imply nonlocality; instead, nonlocal correlations can emerge in states with lower squeezing. Furthermore, by analyzing the CHSH inequality across different cavity finesse values, we find that the parameter region supporting nonlocality can broaden even as the squeezing region shrinks. Across all regimes considered, our results emphasize the crucial influence of the mixedness of the state in determining the relationship between squeezing and nonlocality.

Nonlinear light-matter interaction and, in particular, high-harmonic generation (HHG) are fundamentally interesting and frequently discussed as versatile probes of quantum materials with potential for optical information processing applications. Meanwhile, there has also been significant progress in graphene-based multilayer systems to engineer interesting band structures and boost correlation effects. Motivated by the successful demonstration of HHG in graphene, we here study this effect in rhombohedral stacks of $n$ layers of graphene, a recent very prominent representative of correlated multilayer graphene systems. We show how the chiral Bloch states of the valleys of this system crucially affect the HHG. The "winding" of the Bloch states scales linearly with $n$, just like the dominant harmonic order. The location of the strongest quantum geometry in momentum space on a ring of finite radius is shown to be imprinted on the time-dependent momentum distribution at the beginning of the strong laser pulse. We further demonstrate that the presence of an interaction-induced splitting of the two valleys leads to a complex interplay of the opposite chiralities of the two valleys, directly visible in the $n$ dependence of the circular dichroism. We also analyze the impact of doping and identify a quantity that tracks the net chirality of the occupied states. Our findings show that rhombohedral graphene constitutes a promising platform for exploring rich nonlinear optical phenomena.

We introduce a two state vector formalism of quantum mechanics by generalizing Bell hidden variable model to higher dimensions and by attributing a physical significance, a state evolving backward in time, to the hidden variable. A simple deterministic and time symmetric rule for measurement outcomes allows us to obtain the Born rule. It turns out that probabilistic outcomes can be derived from a deterministic assignment and averaging over future states that propagate backward to the present. The assignment rule provides an alternative statement and demonstration of the Pusey, Barrett, Rudolph theorem.

Quantum error correction assumes that all syndrome activations represent errors requiring correction. We present evidence from 756 QEC runs across three IBM Eagle r3 processors that this assumption is wrong. The hardware exhibits sub-Poissonian syndrome statistics (Fano factor F = 0.856, t = -131 against Poisson, zero dependence on code distance), indicating that a fraction of syndrome events are not random noise but structured cooperative transitions. We introduce a regime classifier decoder that distinguishes binary errors (which should be corrected) from ternary transitions (which should not). On a mixed binary/ternary error model calibrated to IBM hardware statistics, the classifier reduces logical error rates by 7-19% at static detection depth (tau = 1) across all cell sizes, with statistical significance p < 0.05 in 7 of 8 test conditions (p < 0.0001 in all four tau = 1 conditions). The improvement mechanism is selective abstention: the classifier correctly identifies 75-98% of ternary transitions and leaves them uncorrected (75-81% at tau = 1, 88-98% at tau = 5), whereas a standard decoder miscorrects them, introducing errors that would not otherwise exist. A cross-platform control on Google's 105-qubit Willow processor (420 experiments, d = 3, 5, 7) shows the opposite: super-Poissonian statistics (F = 2.42), super-linear burst scaling, and positive spatial correlation – confirming that the sub-Poissonian signal is absent from standard surface-code circuits that lack the P-gate asymmetry. The result demonstrates that standard QEC actively destroys quantum information by correcting valid ternary states, and that less correction produces better performance when the hardware has cooperative error structure.

Complexity class containments involving interactive proof classes are famously nonrelativizing: although $\mathsf{IP} = \mathsf{PSPACE}$, Fortnow and Sipser showed that that there exists an oracle relative to which $\mathsf{coNP} \not\subseteq \mathsf{IP}$. In contrast, the question of whether the containment $\mathsf{BQP} \subseteq \mathsf{IP}$ is relativizing remains wide open. In this work we make progress towards resolving this question by showing that the containment $\mathsf{BQP} \subseteq \mathsf{MIP}$ holds with respect to any classical oracle. We obtain this result by constructing, for any classical oracle $O$, a $\mathsf{PCP}$ proof system for $\mathsf{BQP}^{O}$ where the verifier makes polynomially many classical queries to an exponentially-long proof, and to the oracle $O$. Our construction is inspired by the state synthesis algorithm of Grover and Rudolph, and serves as a complement to the "exponential PCP" constructed by Aharonov, Arad, and Vidick, which achieves similar parameters but which is based on different ideas and does not relativize. We propose relativization as a proxy for prover efficiency, and hope that progress towards an $\mathsf{IP}$ for $\mathsf{BQP}$ in the oracle world will lead to a non-cryptographic interactive protocol for proving any quantum computation to a classical skeptic in the unrelativized world, which is a longstanding open problem in quantum complexity theory.

Quantum correlations in networks with independent sources have revealed novel forms of nonclassical behavior. While entanglement in the sources is a necessary ingredient, the role played by entanglement in the measurements remains largely unexplored. In particular, all existing demonstrations of full network nonlocality, certifying the nonclassicality of every source in the network, have relied on entangled measurements performed at a central node with no inputs. In this work, we construct an explicit strategy that does not rely on entangled measurements, yet still achieves full network nonlocality. Our approach is based on separable measurements augmented with bidirectional classical feedforward. We further show that this same class of measurements can give rise to another recently proposed form of network nonlocality, the minimal network nonclassicality, which ensures that the observed correlations cannot be attributed to any fixed subset of nonclassical sources within the network. Finally, building on a recently developed certification framework, we quantify the amount of device-independent randomness that can be extracted from full network nonlocal correlations under different measurement strategies. Beyond their foundational significance, our results also offer a practically attractive route toward experimental implementations of network nonlocality, as they remove the need for entangled measurements.

Programmable quantum hardware provides an emerging platform for exploring and controlling non-unitary quantum dynamics through measurement-based operations. In this work, we introduce feedback-directed circuit architectures that integrate spatially structured mid-circuit measurements with real-time conditional operations to steer the evolution of random dynamics, and perform their large-scale simulations (up to 100 qubits) on programmable digital quantum processors. By promoting measurement from a passive readout to an active control signal, these adaptive monitored circuits enable directional information flow and generate intrinsic asymmetry in random circuit simulations. We implement this framework on IBM superconducting quantum processors and observe robust, noise-resilient signatures of feedback-induced asymmetry distinct from the more well-known non-Hermitian skin effect. Our results establish feedback as a programmable resource for non-unitary control, opening new avenues for engineering measurement-based dynamics, non-equilibrium phenomena, and tunable open-system behavior on large-scale quantum hardware.