Papers

We show that for any potential with a discrete energy spectrum, the well-known interpolation between ideal boson and fermion partition functions at discrete values of $\xi=-1/m$ yielded zero temperature ground state energies corresponding to $m$ fermions occupying a single quantum state. The grand canonical partition function in this case can be a result from genuine parastatistics.

Quantum imaginarity is an essential physical resource that underpins key functionalities of modern quantum technologies. We improve imaginarity witnessing via the prior knowledge of imaginarity-witness operators. To this end, we derive a rigorous upper bound on the maximum expectation value of an imaginarity witness operator over the set of all free (real) quantum states, which is given by the spectral norm of the real component of the corresponding witness operator. We demonstrate via detailed examples that this bound substantially improves imaginarity detection. We further classify all imaginarity-witness operators into four distinct families based on this bound. For these four witness classes, we perform a comprehensive analysis of their completeness and finite completeness, the joint detection of shared imaginary quantum states by different witnesses, and the conditions for distinct witnesses to identify identical imaginary states. Our results advance the fundamental understanding of imaginarity detection and offer useful insights for both theoretical studies and experimental implementations of quantum imaginarity.

Combining attosecond science with semiconductor physics provides a promising interdisciplinary platform for the attosecond control of semiconducting properties. In each field, the reconstruction of attosecond beating by interference of two-photon transitions (RABBIT) and the time-resolved and angle-resolved photoemission spectroscopy (tr-ARPES) have been central experimental techniques for probing microscopic dynamics of electrons. However, the integration of the two techniques, bridging the two fields, has been missing so far although they have many technical similarities. Here, we develop a theoretical framework that integrates the two techniques based on the second-order time-dependent perturbation theory. Within this framework, we investigate the RABBIT spectroscopy in semiconductors focusing on the recent hallmark of tr-ARPES, namely quantum path interference between Floquet and Volkov states. Moreover, we theoretically identify a novel quantum path incorporating the virtual excitation, which substantially interferes with the Floquet and Volkov states in both the RABBIT spectroscopy and tr-ARPES of semiconductors. Importantly, we find that such virtual excitation channel induces an attosecond topological interference with the Floquet-Volkov paths, encoding topological quantities such as the local Berry curvature into the time shift of RABBIT sidebands, which is directly related to the photoelectron emission delay. Our findings establish a theoretical framework connecting attosecond spectroscopy to tr-ARPES, paving the way for future applications of attosecond science in semiconductors.

We determine the quantum value of the three-setting, two-outcome Bell functional I3322. The value is the unique intersection \(q_\dagger\) of an analytic A-high stable curve of the exact Jacobi characteristic map with a central reverser curve. A computer-assisted proof isolates this intersection in a rational interval of width \(10^{-55}\), beginning 0.2508753845139765356173366109459512989013219739714764755. We prove that the supremum over finite-dimensional tensor-product strategies, the unrestricted spatial value and the commuting-operator value all equal \(q_\dagger\). No finite-dimensional strategy attains the value, whereas a normal infinite-dimensional spatial strategy and a commuting GNS strategy do. The proof combines an exact Bellman/path variational reduction, extraction of a positive bilateral calibrated Jacobi fibre from a maximizing weak-star state, a reflected-fibre central-incidence theorem and interval certificates for the unique stable/central intersection. A separate operator-positive three-remainder decomposition gives the commuting upper bound. The complete verification record is archived at DOI 10.5281/zenodo.22160086.

Atom interferometers (AIFs) are highly precise inertial sensors and are considered promising instruments for the detection of gravitational waves (GWs) and certain dark matter (DM) candidates in the mid-frequency band. While GW detection with AIFs was initially proposed for space-based experiments with baselines spanning thousands of kilometers, recent developments suggest that terrestrial setups with baselines of at least 100 meters may also be capable of detecting GWs. In this work, we analytically derive the GW phase response formula of a ground detector, find an additional term compared to the existing literature and check it our findings numerically. Based on this treatment, we analyze the optimal geometric parameters for earth-bound AIF experiments. Subsequently, we numerically simulate GW detection schemes for these optimized interferometers using an open-source Python algorithm. Numerical simulations of these schemes have are not available to the community, yet crucial for the accurate modeling of noise and non-trivial gravitational backgrounds.

This work studies hybrid quantum-classical neural networks for learning routing heuristics. Specifically, this paper asks whether small quantum neural networks can replace parameter-heavy modules inside a competitive attention-based routing model while maintaining solution quality. For the capacitated vehicle routing problem, encoder feed-forward replacement emerges as the most promising design: it reduces the number of model parameters by 56.6% while keeping the hybrid model close to the classical neural baseline at small and medium instance sizes, although the gap grows for larger instances. This work also compares to classical routing algorithms, which remain highly competitive and often superior on the fixed Euclidean test sets. Our results therefore do not indicate quantum advantage or solver dominance, but identify encoder feed-forward replacement as a viable hybrid-module compression strategy for neural combinatorial optimization.

Angle-encoded quantum kernels on tabular data collapse when the feature map is wider than the intrinsic dimension of the data. We propose the correlation fractal dimension D2 as an a priori qubit budget: encode D2 coordinates chosen by FD-ASE instead of the PCA-95% width or all E attributes. On nine data sets and a statevector simulator (n= 32), a one-layer ZZ fidelity kernel at q=D2 stays geometrically alive while the same kernel at the PCA-95% width has already collapsed. The budget is map-dependent: product-state and IQP maps overshoot it; a second ZZ layer undershoots it. Packed dense-angle and re-uploading encodings still live at the fractal q, but not when PCA-95% features are stacked onto those qubits. Shrinking the angle bandwidth moves the ZZ knee later; stretching it kills the kernel earlier. On IBM Quantum (ibm_fez, 256 shots, n=8) the one-layer ZZ kernel at the fractal width matches the exact kernel (MAE 0.021); past that width both hardware and simulator have collapsed. The ceiling is a property of the map-data pair at a stated bandwidth, not of the classical table alone.

With quantum sensors, simulators and networks emerging, a future of quantum technology may produce quantum states as data—that is, coherently rather than as classical measurement records—thus motivating the study of suitable quantum generalisations of modern machine learning, including the automated, unsupervised extraction of useful representations. Two ingredients are central to the latter: inference, mapping observations to latent representations, and generation, mapping latent states back to synthetic data. Both are related to each other and to joint distributions for training models by the chain-rule of classical probability theory. The fact that quantum states however lack such universal, standard factorisation property thus poses a challenge. Here we develop a conceptual and mathematical framework for unsupervised representation learning from quantum data. Models are joint quantum states over visible and latent systems; state-over-time maps provide a notion of factorisation into a marginal state and inference (generation) channel; models with inference (generation) are ambiguous states—states for which such factorisation obtains—subject to a further consistency condition on extended inference maps as data extension. These stipulations are restrictive: we show that non-trivial models must feature non-linear such maps to the extended space. For three representative state-over-time maps, we completely characterise the ambiguous states, uncovering a hierarchy tied to the positive-partial-transpose (PPT) criterion from entanglement theory. Notably, the Leifer-Spekkens construction supports inference and generation exactly for model classes of PPT states, thus allowing genuinely quantum visible-latent correlations. We also formulate quantum counterparts of exact and approximate inference training, explore weaker notions of data extension and sketch a future research programme.

Lattice vibrations carrying angular momentum give rise to fundamental phenomena such as the phonon Hall effect and the Einstein-de Haas effect, offering new opportunities for manipulating angular momentum in condensed-matter systems. Generating such circularly polarized phonons requires either the use of an external magnetic field, or of polarized light pulses. The latter approach does not require the use of any magnetic response of the material, but it has limitations, in particular regarding the duration of the pulse. Consequently, any effect stemming from phonons generated by light pulses is transient. In this paper, we propose the use of a driven electromagnetic cavity as a route to generate a steady-state population of chiral phonons. We derive a general description of cavity-chiral phonon interaction, with a particular focus on modes of chiral cavities. We show that, under optimized conditions, a significant effective phonon-induced magnetic field can be generated by means of an external drive with realistic power. Our approach is specially tailored for Gamma point phonons with THz frequencies, and opens a new route for investigating chiral phonons with electromagnetic cavities.

The spherical-to-deformed quantum phase transition of the Interacting Boson Model (IBM) is investigated using the variational quantum eigensolver (VQE). The $U(5)$–$SU(3)$ transitional Hamiltonian is studied with $\chi=-\sqrt{7}/2$. We develop a symmetry-preserving, minimum-qubit VQE framework for collective nuclear models, achieving a substantial reduction in qubit requirements without compromising the finite-size quantum-phase-transition physics. The transition is characterized through the normalized $d$-boson occupation and ground-state energy derivatives. Finite-size results are found to approach the analytic critical point $\xi_c=8/17\simeq0.470588$, with an independent order-parameter extrapolation yielding $\xi_\infty=0.46986(61)$. The VQE reproduces ground-state energies and structural observables to numerical precision. These results demonstrate the potential of symmetry-reduced VQE for efficient quantum simulations of collective nuclear dynamics and quantum phase transitions.

We develop a theory of the transverse spatial dynamics of two interacting photons in a Rydberg nonlinear medium. Extending the well-studied one-dimensional case, we explore both longitudinal and transverse correlations of photons propagating as Rydberg polaritons. We identify distinct behaviors and scaling laws for these correlations, arising from fundamentally different mechanisms in the two directions: diffraction for transverse correlations and diffusion for longitudinal correlations. We develop a model incorporating a Gaussian optical beam and an inhomogeneous atomic density distribution, from which we derive quantitative predictions for correlation functions in both directions. We further show that the propagation equations can be reduced to a single Schrödinger-like equation, allowing approximate solutions that are supported by full numerical results. Our findings indicate that the transverse correlation length is determined primarily by the blockade radius, whereas the longitudinal correlation length is limited by bandwidth. These results establish transverse Rydberg blockade as a distinct and measurable correlation mechanism and show that spatial photon correlations provide a direct means of measuring the blockade radius.

In this work, we propose a scheme for generating superpositions of Fock states whose numbers differ by four or eight. The proposed protocol is based on photon-number-resolving measurements on multimode Gaussian states. We compare of the generated states with multicomponent Schrödinger cat states. We evaluate the fidelity and determine how it scales with the number of detected particles. Furthermore, we derive the optimal configuration for the generation such states.

A general thermal machine is characterized by distinct time or energy scales: temperature, coupling to the heat baths, internal free dynamics and interactions, and external driving. We address the question: what parameters determine the speed of a given engine, and how can they be used to reliably compare different types of engine? Specifically, we consider four realizations of the Otto engine, each operating with the same Otto efficiency, and aim to characterize and compare their power outputs. The main insight of this paper is that, irrespective of their very different dynamical implementations, the power of each engine can be factorized into a common characteristic work and an implementation-specific characteristic time. The characteristic work depends only on the internal frequencies of the machine and the temperatures, whereas the characteristic time depends on the coupling strength to the baths and on the implementation-specific driving. This observation allows us to compare the power of different engines through their characteristic times and thereby reduce the relevant parameter space to parameters that capture the dynamical aspects of engine performance. Despite different dynamical implementations, this framework reveals simple common features. In all cases, the maximum operating speed is limited by a common timescale given by the sum of the characteristic thermalization times of the hot and cold baths. Moreover, the four engines fall into two distinct asymptotic classes: implementations in which driving and thermalization occur simultaneously exhibit quadratic scaling, whereas those in which work extraction and thermalization alternate exhibit linear scaling. These results expose general dynamical features that determine the operational speed of quantum Otto engines.

Higher-order topological insulators are materials with a bulk energy gap featuring gapless modes at $(d-n)$-dimensional edges, where $n > 1$. Despite this modified bulk-boundary correspondence, their nontrivial topology can nevertheless be observed through the bipartite entanglement spectrum. Inspired by works suggesting fluctuations in conserved quantities could be used to study topology in one-dimensional systems, which likewise feature zero-dimensional edge modes, we extend this treatment to a two-dimensional second-order topological insulator where corner states play an analogous role. We show that the standard bipartite entanglement entropy and particle number fluctuation lack striking signals of topological phase transitions, both in the static case and in the time evolution after a quench, obscured by an area-law term from the subsystem edges. By introducing a quadripartite construction of the subsystem, we show that it is possible to isolate the topological contributions, producing sharp transition peaks in both quantities, observable by studying subsystems much smaller than the full system. As particle number fluctuations are accessible in existing experiments, these results establish a concrete and scalable path to experimental detection of the entanglement in higher-order topological insulators.

We benchmark eight classical optimizers for exact-statevector VQE calculations on a controlled hierarchy of frustrated spin models, ranging from a diagonal Ising glass to transverse-field Ising and anisotropic Heisenberg models. The benchmark includes local, stochastic-gradient, evolutionary, covariance-adaptation, and swarm-based optimization methods under matched function-evaluation budgets. To understand their performance beyond final energies, we characterize the underlying Hamiltonian–ansatz landscapes in terms of local minima, gradients, curvature, and ground-state reachability. We use simple variational circuits, from an $R_y$ product-state ansatz for the diagonal model to shallow $R_y$–CNOT hardware-efficient circuits for the noncommuting models, and study how increasing circuit depth changes their expressivity, reachability, and optimization geometry. We find that optimizer performance changes substantially across the model hierarchy and is closely connected to landscape structure, while the variational gap represents a separate source of error. These results show how classical optimization, variational expressivity, and landscape geometry jointly determine VQE performance for frustrated spin models.

Helper quantum secret sharing is a form of secret sharing defined by its unique access structure. One special fixed party, called the helper, can work together with any other party to fully decode the secret. A blind helper is one who can provide this assistance while not holding any local information about the encoded secret. In this work, we analyze the general structure of QSS helper codes and present new code constructions. We fully characterize the structure of blind helper stabilizer codes and show that for the encoding of a single qubit, recovery is always possible using one-way local operations and classical communication (LOCC) from the helper to the targeted party. Furthermore, we demonstrate how such codes also allow for the helper to target larger subsets of parties by one-way LOCC, enabling them to be authorized to recover the secret. Finally, when each party only holds a qubit, we identify the general form of all helper codes (including non-stabilizer codes) and find that LOCC recovery is only possible in special cases.

Quantum secret sharing (QSS) is a process in which the state of a quantum system is partitioned into multiple shares, allowing only specific subsets of shareholders to reconstruct the state, while others gain no information about its identity. In this work, we propose a variant of QSS, called “helper QSS,” which designates a special shareholder whose participation with any other group of parties is sufficient for recovering the state. We present different families of helper codes that function for an arbitrary number of parties and system sizes. As an application, we introduce the idea of a programmable access structure in QSS, which allows for a third-party programmer to independently choose the access structure of the code even after the shares are delivered to all the shareholders. This choice is made blindly, meaning that the programmer has no information about the secret being encoded, and it is implemented using the nonlocal process of quantum steering.

Accurate noise models are essential for high-performance quantum error correction, yet characterizing the noise of a quantum device typically requires dedicated experiments. We present a variational framework that learns the noise model directly from quantum-error-correction syndrome and logical-observable data collected during error-corrected memory experiments. The fault-event probabilities are treated as variational parameters and optimized via gradient descent to minimize the binary cross-entropy between the decoder's predictions and experimental logical-observable outcomes. We prove that this objective is principled rather than ad hoc: a sufficiently expressive noise ansatz attains the information-theoretic minimum logical error rate. We instantiate this framework using a tensor-network decoder, which provides exact maximum-likelihood decoding and analytically differentiable gradients with respect to all noise parameters. Using circuit-level data from Google's Sycamore processor, and starting from an uninformed prior, the optimization recovers noise models whose logical error rates agree to within $2\%$ with those of Google's independently characterized detector error model. The mean squared error between the learned and reference noise parameters shows a clear overall decrease throughout training, confirming that the method recovers physically meaningful noise structure, not merely parameters that happen to decode well. We further demonstrate that the optimization can track device drifts in real time via warm-started updates, maintaining near-optimal decoding performance under synthetically evolving noise without the need for re-characterization. The approach is decoder-agnostic in its formulation and naturally extends to correlated noise models.

We analytically characterize entanglement generation by two paradigmatic coherently controlled quantum processes, the quantum switch and time-flip. Retaining rather than measuring or discarding the control, we treat the control and target as the bipartite system and assume pure product inputs, so that any output entanglement reflects the entangling capability of the process. For the switch of qubit unitaries, we derive exact expressions for entanglement, together with a geometric characterization and a coherence-entanglement conservation relation. We then extend our analysis to binary random unitary, Pauli, amplitude damping, and generalized amplitude damping channels. We prove that switch of channels commuting under composition cannot entangle a separable input. Yet maximal entanglement is possible even with dissipation, e.g., an entanglement-breaking damping channel switched with a bit-flip can transform a product input into a maximally entangled state. For two generalized amplitude damping channels, a common stationary state prevents entanglement, while different stationary populations can enable it. We present an analogous study for the time-flip of unitary and binary random unitary channels. Our findings provide a systematic analysis of how much entanglement can be generated by coherent control of channel order or input-output direction.

Compact lattice gauge theories are formulated in terms of angular variables and integer electric fluxes, while bosonic quantum hardware provides oscillator modes with continuous, unbounded quadratures. We bridge this gap with a one-to-one encoding. After Gauss's law is solved, each remaining gauge degree of freedom is carried by a single oscillator mode, with its interactions built from trigonometric gates, and a Gottesman–Kitaev–Preskill (GKP)-type stabilizer provides the compactness that the hardware does not. The encoding becomes exact in the limit of infinite squeezing, and at finite squeezing, the leading imperfections act as small, computable shifts of physical observables rather than uncontrolled leakage. We apply the construction to compact QED$_3$ and derive the error budget at finite squeezing, characterizing the leading errors in closed form, and showing that they can be corrected, subtracted, or extrapolated away. We construct syndrome-extraction protocols that detect and remove the displacement component of photon loss, delimit the noise it does not reach, compare two choices of dynamical variables, and collect the scaling of mode count, gate count, and measurement cost. A one-plaquette example reproduces the exact compact-rotor dynamics, and real-time spectroscopy with controlled extrapolations recovers the exponentially small energy splitting between charge sectors, the seed of the monopole physics of the theory, at the percent level against its exact value.

Determining exact joint eigenvalue densities is central to random matrix theory. We solve this long-standing problem for non-Hermitian matrices with transposition symmetry (complex symmetric and complex self-dual) at arbitrary matrix size. Up to a Vandermonde factor, they are scattering-state wave functions of the Calogero model, a line of particles interacting through an inverse-square potential, with the coupling strength set by the symmetry. In contrast to many previously known joint densities, the densities cannot be written as a gas of eigenvalues with pairwise interactions. We further compute the complex level spacing distributions and two-point spectral correlation functions, which carry power-law tails, absent in a Coulomb gas. Our results shed light on the interplay among random matrices, integrability, and symmetry.

The complex spectral statistics of non-Hermitian random matrices provide a standard diagnostic of dissipative quantum chaos. Yet an analytical understanding of how symmetry enriches these universal correlations remains limited. We establish an exact duality between the spectral statistics of Hermitian and non-Hermitian random matrices in the limit of large matrix size. This duality resolves a longstanding analytical problem by yielding the previously unknown eigenvalue pair-correlation functions for complex symmetric (class AI$^\dagger$) and complex self-dual matrices (class AII$^\dagger$), completing the analytical description of bulk pair correlations in the non-Hermitian threefold way. It further gives closed-form spectral densities near the origin for seven additional symmetry classes. Numerical tests in interacting and dissipative quantum models support the universality of these predictions beyond Gaussian ensembles. The duality suggests a deeper connection between chaos in closed and open quantum systems.

A universal characterization of non-equilibrium steady states in interacting quantum many-body systems remains one of the central challenges of statistical physics. Here, we address this problem for a paradigmatic model of diffusive interacting quantum matter—the boundary-driven XXZ spin chain with bulk dephasing—and derive, directly from its microscopic Lindblad dynamics, an emergent classical Macroscopic Fluctuation Theory (MFT) governing its large-scale fluctuations. Crucially, the resulting hydrodynamics carries a density-dependent diffusivity and mobility as the fingerprint of interactions. This effective description enables the exact computation of the stationary density profile, long-range correlations, and the full counting statistics of the current, in excellent agreement with tensor-network simulations. Our work demonstrates that noisy quantum many-body systems can realize the universality class of genuinely interacting diffusive matter, beyond the constant-diffusivity class of the symmetric simple exclusion process, and establishes MFT as a powerful universal framework for interacting diffusive quantum systems.

We revisit the quantum Hall analog of Hawking radiation in which a Fermi sea of electrons occupying half of a plane, subjected to a quadrupolar electric potential, gives rise to analog Hawking radiation of chiral edge modes. We show that the phenomenon is accurately captured by quantization of the classical guiding center theory, where the gyroscopic motion of the electrons is coarse grained and only the drift motion is resolved. The quantum dynamics takes place on a non-commutative plane, which requires an electron localized in the half-plane to be supported everywhere along the edge direction. This kinematical constraint on the quantum state leads directly to the radiation, which propagates in both directions away from the origin along the edge. The radiation is thermal with respect to laboratory time, which is equal (up to a constant factor) to the boost angle in the analog Minkowski spacetime in which the chiral edge modes propagate, so in fact it corresponds to analog Unruh radiation.

We develop a general dressed-state framework for computing fluorescence spectra, probe absorption spectra, and photon-photon correlations of light scattered by ensembles of $N_\mathrm{at}$ two-level atoms with arbitrary $J_g \to J_e$ transitions driven by intense coherent fields. The approach employs a full vectorial treatment of the electromagnetic field, handles any atomic geometries, illumination directions, and polarizations, and yields optical observables as explicit sums of Lorentzian lines whose positions, widths, and weights are directly tied to the eigenvalues and eigenvectors of the Lindbladian. The framework is implemented in an open-source Python package and benchmarked against exact single- and two-atom calculations. We identify geometries in which the full vectorial description is essential, and the scalar approximation fails qualitatively. Applying the method to pairs of atoms with a $J_g=0\to J_e=1$ transition, we show that elastic and inelastic scattered intensities collapse onto universal master curves controlled by a single collective saturation parameter built from the dominant superradiant mode, across several orders of magnitude in drive strength and interatomic distance. We identify collective phenomena that require a description beyond this single-mode picture. Extending the analysis to atoms with ground-state degeneracy, we find that most collective features carry over, while two qualitatively new effects emerge: an incoherent spontaneous Raman channel that modifies the scaling of inelastic emission, and a slow timescale in the time-delayed correlations $g^{(2)}(\tau)$ governed by the competition between Raman scattering and subradiant decay, controlled by a single dimensionless parameter. These results provide both physical insight and practical computational tools for engineering collective optical responses in few-atom systems such as optical tweezer arrays.

Quantum complexity has emerged as a natural probe of chaos, thermalization, and the black hole interior on timescales long after local observables have equilibrated. However, its time evolution has been studied almost exclusively in subsystems confined to a single connected region. We show, using complementary tools from holography and random quantum circuits, that noncontiguous subsystems composed of multiple disjoint regions give rise to qualitatively new physics compared to the contiguous case. First, at finite temperature, a subsystem occupying less than half of the total system can carry high complexity at late times, even as the complexity of its larger complement remains low. This inversion of the usual hierarchy is intrinsically thermal: it vanishes in the infinite-temperature limit, which is the regime modeled by random quantum circuits. Second, if a subsystem's complexity equilibrates at an early time, then fragmenting it into $m$ disjoint components can further reduce this timescale by a factor of $m$, a phenomenon we exhibit in both holography and random quantum circuits. These results not only sharpen the correspondence between geometric and computational notions of complexity, but also motivate the search for novel complexity phenomena in quantum dynamics.

Strongly-coupled light-matter exciton-polaritons constitute an on-chip solid-state platform where the macroscopic quantum phenomenon of condensation is not only achievable at elevated temperatures, but can also be optically controlled, including through their interaction with inaccessible "dark" states. A recent study has shown that polariton condensation can be established under nonlinear two-photon pumping, paving the way towards dark state-condensate coherent control and highly-efficient terahertz (THz) lasing. In this letter, we show for the first time a temporal signature of dark exciton induced bosonic stimulation by investigating one- and two-photon pumped condensation with time-resolved photoluminescence spectroscopy. Our results show a clear difference in the detuning dependence of the buildup and relaxation rates of the condensate-induced blueshifts under one- and two-photon pumping. This difference is associated with the stronger exciton-fraction dependence expected for one-photon pumped condensation, where polariton-polariton stimulation dominates, compared with two-photon pumped condensation, where a 2p-exciton-to-lower-polariton THz transition can provide another stimulation channel, together with various spin-flip, electron-hole exchange and phonon-based mechanisms. These observations indicate the presence of a new dark state originated stimulation channel that could facilitate highly-efficient THz lasing in semiconductor microcavities.

The apparent incompatibility between foreknowledge and free will is traditionally formulated in terms of the implication of knowledge of a future event for the freedom of that event. This paper reexamines the problem using the notions of causal order and physical determination provided by modern physics. I consider measurements of two entangled particles at spacelike-separated events, where a measurement outcome is taken to be free if it is not determined by the previous history of the part of the universe accessible to it. Relativity allows the temporal order of the two measurements to be reversed between reference frames while preserving their causal independence. Quantum correlations nevertheless allow an observer at one measurement event to know the outcome at the other. I show that there is, therefore, a frame in which an observer possesses foreknowledge of a measurement outcome that remains free in this sense. The argument demonstrates that epistemic access to a future event need not be grounded in physical conditions that determine it.

We present a quantum computing framework for simulating open-quantum-system approaches based on Markovian and non-Markovian dynamics, which is relevant to heavy-ion collisions. To simulate the non-Markovian evolution on quantum computers, we introduce an auxiliary two-level pseudomode that carries the memory forward and couples to both the subsystem and the residual Markovian bath. We explicitly show that tracing out the pseudomode reproduces the non-Markovian evolution with the exact memory kernel. Moreover, in the relevant time scale hierarchy, the quantum circuit construction of the pseudomode smoothly converges to the Markovian limit. For a given bath memory kernel, our results demonstrate the feasibility of quantum simulations of both Markovian and non-Markovian dynamics, establishing a framework for future studies of hard probes such as jets, heavy quarks, and quarkonia in heavy-ion collisions.

Kinetically constrained systems, such as those representing Rydberg atom arrays in the blockade regime, have gathered considerable attention due to the presence of atypical eigenstates in their spectrum. The latter manifests itself through the presence of quantum many-body scars as well as unusually large zero-mode (ZM) subspaces which contain analytically tractable eigenstates with various entanglement scalings. In particular, some of the latter are excitable zero-modes (EZMs), meaning that they can be promoted to a non-zero energy for open boundary conditions. In this work, I present an efficient protocol for finding analytical expressions for translation-invariant EZMs in constrained systems, based on the eigendecomposition of the local unconstrained Hamiltonian. I demonstrate the power of this method on a decorated Rydberg chain. In that model, my protocol directly produces a continuous matrix-product-state manifold located entirely in the zero-energy eigenspace for periodic boundary conditions. The span of that manifold grows exponentially with the system, and for odd system sizes it covers the entire zero-momentum eigenspace with zero energy. I then show how the physical structure of the manifold, which is tied to the local eigenbasis, also allows one to derive analytical expressions for ZMs at non-zero momentum and for a polynomial number of exact scars at $E=\pm\sqrt{3}$.