Papers

We construct Feynman rules for Lindblad master equations in the operator language of quantum optics: a fixed algebra of elementary operator moves and closed-form propagators for perturbation theory about an exactly solvable, in most cases Gaussian, generator. The expansion separates into a kinematic part (the shift algebra on the Wick-ordered eigenoperators $O_{mn}=:(c^\dagger)^m c^n:$, from which the vertex table for a specified interaction is assembled) and a dynamical part that enters only through the resolvent of the unperturbed generator, diagonal and additive for any stable, diagonalizable Gaussian $L_0$, including thermal and squeezed reservoirs and correlated decay, and equally available for a two-level emitter, driven or undriven. In the driven Kerr cavity the loop expansion is the semiclassical expansion and the series is asymptotic. In a strongly driven two-level atom, dressed lines replace a series of finite radius by one accurate deep into saturation, one line per Mollow component. For Kerr rings and chains the cost is polynomial in the number of sites at fixed perturbative order. On a three-site ring the diagrams recover the non-Gaussian part of the three-photon correlation that the Gaussian cumulant closure lacks; carried to tenth order they give the smallest $g^{(3)}$ error of the methods compared for $U\leq0.25\kappa$ at a cost below that of a fourth-order closure, and third- and fourth-order closures are more accurate at moderate coupling. The same rules, extended to the counting-field-tilted generator, give the photon-counting cumulants of a disordered eight-site chain beyond direct diagonalization; quantum-jump trajectories at three couplings agree with them to within $1.6$ standard errors, within one at the strongest coupling, where they place the third cumulant six standard errors above the Gaussian value.

We introduce a finite-dimensional state-space representation of bisexuality in Dirac notation, specify normalized amplitude weights, and analyze the limits of inference from one single observation. We extend the basis for discussing attraction across genders, then define a distinct state space for gender identity with an illustrative normalized time-dependent trajectory. The model is an analogy, not a physical theory or a measurement procedure for human sexuality.

Non-ergodic quantum many-body dynamics offers a route to persistent quantum coherence far from equilibrium, beyond the conventional expectations of thermalizing statistical mechanics. Most known examples have been identified through intuition, analogy, or numerical search, rather than by systematic Hamiltonian design. This leaves few general methods for engineering robust non-ergodic dynamics in disorder-free interacting quantum many-body systems, especially in higher dimensions where enhanced connectivity generally disfavors ergodicity breaking. Here, we use an eigenstate-to-Hamiltonian construction approach to systematically engineer two-dimensional quantum spin Hamiltonians with tunable non-ergodic properties. Starting from a common parent model and input eigenstate, we construct two target Hamiltonians on the square lattice that differ in their interaction geometry: axial versus diagonal. We show that the resulting interaction geometry and coupling pattern control the Hilbert-space structure and dynamics. The axial model forms a connected Hilbert-space network and exhibits an anisotropy-driven crossover from ergodic to non-ergodic behavior through the suppression of resonances. In contrast, the diagonal model exhibits Hilbert-space fragmentation and, within its largest irreducible sector, signatures of quantum many-body scar dynamics including towers of highly localized, low-entanglement eigenstates, and long-lived coherent revivals. These results establish a direct link between Hamiltonian design, Hilbert-space network structure, and emergent non-ergodic dynamics.

In quantum mechanics, the properties of an unstable system are closely related to its corresponding energy distribution. One of the predictions of the theory is the emergence of a late-time power law in the survival probability $P(t)$ of the unstable state. However, in complex systems, similar effects may emerge due to other phenomena. This is the case for nonextensive statistical models, for some continuous lifetime distribution models, and also for certain energy-migration models applied to fluorescence. In this work, these alternative interpretations are confronted with data from time-resolved fluorescence spectroscopy experiments with erythrosine B and eosine Y as fluorophores. It turns out that some of the features expected within the quantum-mechanical description, such as the sharp transition from the exponential to the power-law regime, cannot be reproduced by the specific statistical and energy-migration parametrizations fitted in the analysis.

Bell nonlocality allows secret key to be certified without trusting the internal operation of the devices, and even against eavesdroppers constrained only by the no-signaling principle. We ask whether generalized contextuality, a notion of nonclassicality available in prepare-and-measure experiments on a single system, can play an analogous role. In our approach, Alice and Bob first establish operational equivalences among their local preparation and measurement procedures, which are then treated as theory-independent constraints that any physical intervention on the communication channel, including that of an adversary, must respect. Eve is otherwise unrestricted, that is, her intervention on the transmitted system is not assumed to be described by quantum theory. Within this adversarial model, we show that Eve's optimal guessing probability against individual attacks is the solution of a finite linear program, and hence that a worst-case asymptotic key rate follows from the observed statistics and the operational equivalences alone. We prove that contextuality is necessary for a positive key rate. However, we also show that it is not sufficient. Concretely, the (3,2)-parity-oblivious random access code, known to yield secret key against a quantum eavesdropper, yields none certifiable key rate against a post-quantum one. Conversely, operational equivalences with no analogue among no-signaling constraints can strictly increase the asymptotic key rate. We illustrate this with the prepare-and-measure version of the standard CHSH protocol with an aligned key-generating setting.

It is well-known that every n-qubit unitary can be decomposed into a product of controlled single-qubit unitaries. We show that the control conditions in such a decomposition naturally define a quasi-process function, an object that originally came up in the study of indefinite causal order. Here quasi-process functions yield a representation of every n-qubit unitary in a canonical form, namely, as a quasi-process function unitary (qPFU). We use this representation to show how quantum nonlocality without entanglement (QNLWE) can be understood in terms of unitaries that encode the trade-off between causal order and locality noted in R. Kunjwal and Ä. Baumeler, arXiv:2202.00440. Specifically, we obtain two sufficient (but not necessary) criteria—mutual exclusivity of control conditions (MECC) and Unambiguity—for a unitary to be a process function unitary (PFU), i.e., it admits a qPFU representation where the quasi-process function is a process function, an object that can model paradox-free classical causal loops. We also show the inequivalence of these criteria, neither implying the other. We then show that the circuit depth of MECC unitaries admits a characterization in terms of clique-partitioning problems on Hamming graphs and use this correspondence to provide bounds on the circuit depth of n-qubit MECC unitaries. Finally, we show how MECC unitaries provide a recipe for constructing a unitary purification of the associated process function, thereby providing a large class of unitary processes of interest in quantum causality. The generality of this causality-inspired representation of unitaries makes it a versatile tool for analyzing the structure of quantum circuits in other domains.

When non-adiabatic coupling mixes electronic states of a molecule, vibronic states of different electronic symmetry become interleaved across the same spectral region. The symmetry of these states cannot be accessed in conventional spectroscopy due to orientation averaging. We show that molecular-frame angular signatures, which are preserved even when states with different symmetry overlap in energy, can be used to resolve them. Using vacuum-ultraviolet transient absorption spectroscopy of aligned carbon dioxide molecules, we separate two electronically distinct classes of vibronic states ($A^{'}$ and $A^{''}$) that arise from Renner-Teller splitting of the $^1\Delta_u$ state. We reconstruct molecular-frame anisotropy continuously across the vibronic manifold showing that the anisotropy crosses over from perpendicular to parallel transition character and maps the interleaved electronic symmetry landscape. By scanning the femtosecond delay between the VUV and a near-infrared pulse through temporal overlap, we measure symmetry-dependent coherence dephasing times of these states and find that the parallel ($A^{'}$) states dephase faster than the perpendicular ($A^{''}$) states. We attribute this to faster departure of the $A^{'}$ wavepacket from the Franck-Condon region due to the distinct topology of the $A^{'}$ excited-state surface. These measurements probe symmetry-resolved ultrafast wavepacket dynamics on the coupled excited-state potential energy surfaces.

Photon loss is a dominant noise process in bosonic quantum hardware, including superconducting cavities. Fixed-total-photon-number qubit encodings in two bosonic modes retain the loss-detection advantage of dual-rail qubits while supporting photon loss correction. Optimizing entanglement fidelity in this setting for $4\leq n\leq25$ over arbitrary encoders and decoders reveals finite-group structure in every best-found code: 11 correspond to two-dimensional irreducible representations and 11 to reducible ones. Motivated by this emergence, we derive the necessary-and-sufficient Knill-Laflamme conditions for arbitrary finite-group-invariant codes, reducing their construction to equations on representation multiplicity spaces. For every finite subgroup of $SU(2)$ and every tensor rank, we explicitly construct the minimum number of operators required to impose all corresponding loss-correction constraints. These results produce analytic counterparts to most numerical codes and predict constructions missed by the initial search. Exact MacWilliams-Farkas certificates show that our codes achieve the maximum possible loss distance in 21 of the 22 sectors, and we prove that the resulting distance bound is monotone in total photon number. Beyond the scan, we identify a binary-polyhedral sequence with photon number $n_d=\lceil(3d^2+1)/4\rceil$ and construct each corresponding code through distance $d=10$. To our knowledge, the constructed $(n,d)=(28,6),(49,8),(76,10)$ codes give the smallest reported $n$ for their respective distances; all members through $d=9$ attain the fixed-$n$ LP distance bound. Together, these constructions, certificates, and a symmetry-reduced constraint count provide evidence for an infinite code family conjectured to attain every distance at the minimum photon number.

Developing classical simulation algorithms for noisy quantum circuits is essential to delineating the limits of quantum advantage. Existing classical sampling approaches for general circuits require circuit depths to grow logarithmically with system size, so that noise drives the global output state close to a trivial state. Here we show that local accumulation of noise at a depth independent of system size is already sufficient. Specifically, we prove that any geometrically local circuit composed of unital operations and interspersed with single-qubit depolarizing noise of strength $p$ after $\Theta(p^{-1} \log p^{-1})$ depth can be approximately sampled from a polynomial-time classical computer. This generalizes existing results that impose anticoncentration assumptions or non-universal gate sets in order to obtain a classical sampler at such shallow depths. Our proof maps the output state of the circuit to a polymer model in statistical mechanics, and combines a convergent cluster expansion with hypercontractivity of the depolarizing channel.

We establish functional aggregate queries (FAQs) as a unifying language for exact classical simulation of quantum circuits. A circuit becomes a sum-product query: factors encode gates, internal wire variables are aggregated, and free boundary variables index transition amplitudes. The central insight is that distinct sources of simulation tractability can be exploited within the same InsideOut evaluation scheme. The query specifies what is computed; the evaluation plan, semiring, and representation of intermediate factors determine the cost. This view unifies structural and algebraic simulation guarantees. With explicit factor representations, FAQ evaluation recovers the treewidth bound for tensor-network contraction and yields finer sparsity-sensitive bounds via fractional covers. Over a formal phase semiring, compressed intermediate factors recover rank-width-based simulation for compatible quadratic phase representations. For Clifford circuits, affine-quadratic factors are closed under multiplication and marginalization and remain polynomial in size, yielding polynomial-time exact amplitude computation without any bounded-width assumption. Beyond these recoveries, the framework yields a new tractability criterion: tensor layout symmetry width. This parameter combines local cut-rank with separator symmetry through exact tree-tensor representations. We give a constructive evaluation bound and exhibit a circuit family with bounded tensor layout symmetry width but unbounded phase-graph rank-width and circuit line-graph treewidth. These results establish representation-aware FAQ evaluation as a common algorithmic foundation for classical simulation and a systematic route to new tractable regimes.

The Hamiltonian of a natural quantum system is usually determined indirectly, by proposing microscopic models and comparing their predicted observables with experiment. A more direct approach is to extract information about the Hamiltonian from measurements on the system itself. In many settings, however, direct access to the full system is unavailable and measurements can be performed only through controllable probes, as in quantum sensing and boundary spectroscopy. Existing Hamiltonian learning protocols under such restricted access typically require a special symmetry, a known parametric form, or controlled operations beyond free evolution. We introduce Quantum Krylov Learning (QKL), a restricted-access framework that avoids these requirements. QKL uses single temperature probe autocorrelators and their operator Krylov structure to extract model-independent spectral information about the unknown system. Rather than fitting a parametrized Hamiltonian, it reconstructs the operator Krylov Jacobi matrix representing the dynamical modes accessible to the probe. The method assumes that the unobserved system is at, or near, infinite temperature. Under this condition, the Jacobi matrix can be reconstructed directly from the autocorrelation of a probe observable, without oracle access to the Hamiltonian. The required operations are free evolution under the unknown $H$, together with probe state preparation and measurement. The learning core therefore requires no symmetry, no parametric model, and no controlled-unitary gates. We show a Lieb–Robinson bound for the operator Krylov chain and derive a data-driven criterion for the required observation window. We also establish an end-to-end sample complexity guarantee: under generic conditions on the spectral gaps and weights, the number of measurement shots required to achieve spectral precision $\varepsilon$ is polynomial in $1/\varepsilon$.

Local-unitary (LU) equivalence asks whether two quantum states differ only by independent changes of basis on their qubits. For graph states, whether this relation can be decided in polynomial time has remained open for over a decade. We give a deterministic algorithm that decides LU equivalence for graphs on $n$ labelled vertices in $\widetilde O(n^{6.38})$ bit operations and constructs exact single-qubit unitaries whenever the states are equivalent. Building on Claudet and Perdrix's quasipolynomial algorithm, we replace the enumeration of vertex subsets by a compact system of constraints generated from pairs and triples. The remaining graph transformation is found by solving linear equations over the binary field. These new steps cost $\widetilde O(n^5)$ bit operations; the inherited graph preprocessing sets the overall bound. We also count the local-Clifford (LC) classes of graph states within any LU class: their number is a power of two, computable within the same bound. For any given graph state, this decides whether single-qubit Clifford gates reach every graph state in its LU class, and supplies a counterexample when they do not. The method also decides LU equivalence of stabilizer codes encoding one logical qubit.

Sipser and Spielman constructed LDPC codes from either bipartite spectral expanders or one-sided lossless expanders. In higher dimensions, spectral expansion similarly played a central role in the constructions of asymptotically good classical LTCs and qLDPC codes by Dinur, Evra, Livne, Lubotzky, and Mozes and by Panteleev and Kalachev. Alternatively, Lin and Hsieh constructed classical LTCs and qLDPC codes from two-dimensional lossless cubical complexes. In this work we develop the higher-dimensional lossless approach. We do not construct the required high-dimensional lossless cubical complexes; rather, we investigate what their existence would imply. We associate with a high-dimensional cubical complex a level chain complex, whose chain groups are supported on the level sets of the Boolean cube rather than on its cells. Our main technical contribution is a clean local-to-global theorem for this structure: suitable one-dimensional lossless expansion in the directional graphs implies small-set coboundary expansion of the global level complex. As a consequence, sufficiently imbalanced, two-sided lossless four-dimensional cubical complexes give rise to asymptotically good quantum locally testable codes. We expect the local-to-global principle developed here to have further applications.

Quantum simulations based on first-quantized approaches can offer lower space and gate complexities than second-quantized approaches. The gate requirements for these simulations can be further reduced by employing pseudopotentials, a technique widely used in classical quantum chemistry calculations to decrease the number of simulated electrons. However, implementing pseudopotentials in quantum circuits remains challenging due to their non-local nature. In this study, we proposed a method to efficiently implement non-local potentials using matrix product state (MPS) encoding. MPS encoding allows us to efficiently implement a Trotter step operator with a circuit depth of $O(\mathrm{deg}(V_{\mathrm{loc}}) n^{\mathrm{deg}(V_{\mathrm{loc}})} + 8Lnn_{\mathrm{atom}}\chi^2 + 2n^2)$, where $\mathrm{deg}(V_{\mathrm{loc}})$ is the degree of the polynomial local potential, $n_{\mathrm{atom}}$ is the number of atoms in the system, $L$ is the maximum number of projector functions across all atoms, and $n$ is the number of qubits used to represent the binary-encoded wave function in one-dimensional space. We demonstrated the effectiveness of this approach by applying it to a model of the ionization of a one-dimensional hydrogen atom driven by an ultrashort laser pulse. Our results showed that MPS encoding significantly reduces the required circuit depth compared to a direct unitary decomposition, providing a pathway for practical first-quantized simulations.

Ground-state preparation, energy estimation, and property estimation are fundamental tasks in quantum simulation. Existing ground-state preparation algorithms achieve near-optimal complexity using block encodings or controlled Hamiltonian evolution, raising a natural question: is controlled Hamiltonian evolution necessary, or can the same scaling be attained in the weaker access model that provides access to only uncontrolled Hamiltonian evolution? We resolve this question by giving two algorithms that access the input Hamiltonian $H$ only through queries to $U_H$ and its inverse $U_H^\dagger$, where $\|H\|\le\alpha_H$ and $\tau=\Theta(1/\alpha_H)$. Given an input state with ground-state weight at least $\eta$ and a spectral gap of $H$ of at least $\gamma$, our first algorithm uses fresh copies of the input state and requires $\widetilde O(\alpha_H/(\gamma\eta))$ queries to $U_H$ and $U_H^\dagger$, while our second algorithm uses coherent access to the input-state preparation unitary and its inverse to improve this complexity to $\widetilde O(\alpha_H/(\gamma\sqrt{\eta}))$. The latter bound matches the known lower bound up to logarithmic factors, showing that algorithms with additional access to controlled Hamiltonian evolution cannot improve the query complexity for ground-state preparation beyond logarithmic factors. Both algorithms are based on a simple mechanism that we call the spectral descent principle, in which the algorithm starts from the input state $|\psi\rangle$ and progressively descends through the energy spectrum, moving closer to the ground state until the desired fidelity is reached. We also extend this framework to ground-state property and energy estimation and give explicit complexity guarantees for both tasks.

We prove that quantum blind-unforgeability implies quantum plus-one unforgeability, settling an open question in the literature. Since plus-one unforgeability is known not to imply blind-unforgeability, our result establishes that blind-unforgeability is strictly stronger than plus-one unforgeability in the quantum setting. The implication is proven using a new smoothing technique that coherently rescales the query histories of a quantum-query algorithm in a black-box manner. This enables us to transform any successful plus-one attacker into a blind-unforgeability attacker with only inverse-polynomial loss. Our proof represents a conceptual shift from merely extracting a useful query history as in earlier attempts, which we show inevitably fails in general, to first coherently reshaping how query histories interfere.

We study quantum query complexity under several models of imperfect oracle access, and develop lower bounds through a common framework based on fractional block sensitivity ($\operatorname{fbs}$). For a negligent oracle that applies the correct query with probability $1-p$, we prove a lower bound in terms of $\operatorname{fbs}(f,0^n)$. We also show, perhaps surprisingly, that negligence need not destroy quantum speedups: any function $f$ can be transformed into a partial function $f'$ whose negligent query complexity essentially preserves the quantum query complexity of $f$. This gives partial functions with exponential quantum speedups even under negligent queries, and in particular rules out a general lower bound in terms of $\operatorname{fbs}(f)$ for partial functions in this model. For two other models, we obtain general lower bounds in terms of $\operatorname{fbs}(f)$ for all Boolean functions. For hybrid algorithms using $Q$ coherent and $C$ classical queries, we prove the tradeoff $C+Q^2=\Omega(\operatorname{fbs}(f))$. For an IID dephasing noisy model where each query dephases the query-index register at rate $p$ independently, we prove $\Omega\!\left(p\,\operatorname{fbs}(f)\right)$ queries are necessary. Finally, we introduce a broader family of time-varying dephasing models and identify a variational resource that is always lower bounded by $\operatorname{fbs}(f)$. Computing this resource reduces to a convex optimization problem, providing a simple way to derive lower bounds for new noise schedules. As applications, we recover the hybrid and IID dephasing bounds and determine the query complexity of unstructured search when the dephasing rate grows over time.

Neural quantum states (NQS) have emerged as powerful representations of quantum states with rapidly expanding applications across quantum many-body physics. Yet our understanding of when neural networks can efficiently represent physical quantum states remains limited, in part due to the nonlinear parameterization of NQS, the intricate sign structure of quantum states, and the sensitive dependence on basis choice. We introduce Walshness, a complexity metric of a quantum state which quantifies whether it admits a compact neural-network representation. We rigorously prove that a general quantum many-body state admits an efficient NQS representation if and only if it has bounded Walshness for various NQS architectures. We provide an algorithm for finding the optimal basis by minimizing the energy of a corresponding classical spin model. This allows us to empirically improve the learnability of various physical quantum states, including ground states of the transverse-field Ising model and mixed-field toric code, often reducing infidelity by orders of magnitude, and recovers and generalizes the basis choice given by the well-known Marshall sign rule in frustrated antiferromagnets. Our results provide an intrinsic complexity metric for quantum states with provable connections to their neural-network representability.

Post-selection improves the logical reliability of quantum computation by rejecting shots which are likely to result in logical failure. We introduce graph neural networks that predict decoder failure without additional decoder executions, using only syndromes, and for high-rate quantum low-density parity-check (qLDPC) codes, existing belief-propagation posteriors. We evaluate rotated surface and bivariate bicycle (BB) code memories under uniform depolarising circuit-level noise. Retaining 90% of shots gives approximately 3700x and 740x reductions in logical error rates for [[72,12,6]] and [[144,12,12]] BB codes at realistic physical error rates. For the distance 5 surface code at physical noise p=0.003, our neural post-selector achieves logical error suppression comparable to the leading complementary gap method without running the decoder.

Regev's reduction quantumly finds codewords satisfying nonlinear constraints by decoding the dual code. To date, applications that have not been dequantized have relied on efficient classical decoders and coordinate-wise constraints. We overcome these restrictions separately. Our first contribution uses a quantum decoder to find solutions $\mathbf{y}\in(\mathbb{F}_q\setminus\{0\})^m$ to $\mathbf{B}\mathbf{y}=0$, where $\mathbf{B}\in\mathbb{F}_q^{n\times m}$. For fixed prime $q>2$, Chen, Liu, and Zhandry solve this problem for random matrices with $m=\Omega(n^2)$, a regime now covered by classical algorithms. We adapt their template to codes (spanned by the rows of $\mathbf{B}$) that satisfy a "two-fold multiplication property": the coordinate-wise products of pairs of codewords span a space of dimension smaller than $m$. Under suitable distance conditions, this allows us to solve instances with $m\leq n^{2-\Omega(1)}$, beyond the established guarantees of classical algorithms. We also give an efficient classical algorithm under a stronger three-fold multiplication property, leaving intermediate regimes as candidates for quantum advantage. For Reed-Muller codes punctured at random points, our algorithm finds a word in the unpunctured dual code supported exactly on those points. This works beyond known efficient classical decoding regimes. Our second contribution retains classical decoding but allows global constraints on symbol frequencies. We study "histogram-local" constraints, which specify the allowed numbers of occurrences of each symbol. For broad families, stability under resampling one coordinate yields efficient quantum algorithms for variants of optimal polynomial intersection (OPI) combining coordinate-wise and histogram-local constraints. Adapting Yamakawa-Zhandry, we prove a quantum-classical separation for these problems relative to a classical random oracle.

Extensions of relativity that include superluminal reference frames have recently been proposed by Dragan and Ekert as a way to reconcile relativistic symmetry with quantum uncertainty. In this work, we develop a causal modelling framework to formally study this proposal and prove a no-go theorem demonstrating that a theory permitting superluminal reference frames can avoid superluminal signalling only if it severely constrains which spacetime regions are accessible to operational protocols, if the choice of reference frame has observable consequences or if free variables do not exist or their existence depends on the reference frame. Crucially, our result goes beyond the familiar intuition that superluminal transformations may lead to superluminal signalling; our no-go result shows that Dragan and Ekert's proposal of introducing objective uncertainty does not, by itself, eliminate this conflict. In fact, because superluminal signalling might instead be avoided by relaxing other fundamental assumptions in the presence of superluminal reference frames, the proposed objective uncertainty may not be necessary at all. Our results clarify the limitations of uncertainty-based resolutions and the causal trade-offs faced by superluminal extensions of relativity.

Open quantum systems can exhibit inherently mixed quantum orders, such as strong-to-weak spontaneous symmetry breaking (SW-SSB), which have no analogue in pure states. It is generally expected that a finite-depth local quantum channel cannot induce a phase transition to SW-SSB in one spatial dimension. We circumvent this obstruction by introducing a long-range quantum channel, which implements two-body dephasing on pairs of sites with probability falling off according to a power-law in the site separation. Applying this channel to a one-parameter family of matrix product states interpolating between trivial and symmetry-protected topological (SPT) phases, we construct a phase diagram that hosts trivial, mixed SPT, and SW-SSB phases with respect to Rényi-2 diagnostics. Notably, the mixed SPT phase is distinct from previously studied decohered SPT phases: it hosts two logical qubits and exhibits nonvanishing Rényi-2 string order, despite vanishing conventional string order. Through a series of mappings to a classical statistical mechanics model, we establish a direct connection between the loss of logical information and the onset of SW-SSB in this model. Finally, we consider the feasibility of experimental realization of the phenomena we have studied. We emphasize that our family of mixed states can be tuned to regimes of high purity, substantially reducing measurement overhead and enabling their experimental realization and detection on near-term quantum hardware.

In a previous work 2511.21852, we explored the hypothesis that in general theories of quantum gravity, spacetime regions known as generalized entanglement wedges (introduced by Bousso and Penington) have an associated subalgebra of observables in a semiclassical limit. We defined an entropy associated with these subalgebras that obeys the same monotonicity and strong subadditivity properties as the generalized gravitational entropy of generalized entanglement wedges. Here, we test aspects of these ideas making use of tensor network toy models for holography. In this context, the analog of a generalized entanglement wedge is a region for which no region containing it has a smaller number of boundary legs. In the limit of large bond dimension (analogous to the semiclassical limit), we argue that each such region has a canonically associated subalgebra of the full algebra of observables on the boundary Hilbert space, as well as a family of unitarily related von Neumann factor subalgebras. We investigate in detail how various algebraic operations on these subalgebras (e.g. their intersections, joins, and commutants) are related to corresponding geometrical operations on the tensor network regions. We study to what extent the monotonicity and strong subadditivity properties of generalized entropy for generalized entanglement wedges follow from properties of our algebraic entropy. We also introduce an alternative entropic quantity $S(\omega || \omega \circ E_{\mathcal{A}'})$ associated with a subalgebra $\mathcal{A}$ that also obeys monotonicity and strong subadditivity properties with suitable conditions. Finally, we explain how to define a type $II_1$ von Neumann algebra based on an infinite family of random tensor networks with increasing bond dimension such that the regions corresponding to generalized entanglement wedges can be associated with exact subalgebras of this full algebra.

Strong-to-weak spontaneous symmetry breaking (SW-SSB) is a distinctive phenomenon of mixed quantum states, characterized by nonlinear long-range order associated with strong symmetry. In realistic open quantum systems, however, strong symmetry is macroscopically fragile and can be explicitly reduced to weak symmetry through local charge exchange with the environment. In this paper, we investigate how the SW-SSB order decays under such strong-symmetry-breaking Liouvillian dynamics. For discrete $\mathbb{Z}_2$ symmetry, a local symmetry-breaking perturbation drives an exponential decay of the Rényi-1 long-range correlator, revealing the fragility of discrete SW-SSB order. By contrast, for continuous $U(1)$ symmetry, local charge exchange broadens the distribution over symmetry-charge sectors and leads to parametrically slower algebraic relaxation. We establish a rigorous algebraic lower bound on the connected Rényi-1 long-range correlation, demonstrating the robustness of this slow relaxation. In the thermodynamic limit, we further uncover a two-stage dynamical scaling: $\tilde{R}_1\sim t^{-1}$ at early times and $\tilde{R}_1\sim t^{-1/z}$ at long times, with $z$ set by the underlying hydrodynamic dynamics. As a numerical verification, we consider fermionic chains with $z=2$ and $z=4$, which are excellent agreement with the theoretical predictions.

For a quantum code defined by an isometry $T:H_{\rm code} \to H_{\rm phys}$, an operator map is a *-homomorphism $\varphi: B(H_{\rm code}) \to B(H_{\rm phys})$ from the space of operators on the logical Hilbert space to the space of operators on the physical Hilbert space satisfying $\varphi({\cal O}) T = T {\cal O}$ for every operator ${\cal O}$ on $H_{\rm code}$. This can additionally be taken to be unital $\varphi(I_{code}) = I_{phys}$ if and only if $\dim H_{\rm code}$ divides $\dim H_{\rm phys}$. In this case, $\varphi(B(H_{\rm code})$ is a von Neumann factor subalgebra of $B(H_{\rm phys})$ and we call the pair $(T,\varphi)$ a factor code. A code network is a family of Hilbert spaces $\{{\cal H}_i\}$ indexed by a partially ordered set with isometries $T_{ji}:{\cal H}_i \to {\cal H}_j$ for $i < j$ satisfying $T_{kj} T_{ji} = T_{ki}$ for $i < j < k$. In this paper, we ask when this can be promoted to a factor code network by defining unital operator maps $\varphi_{ji}$ so that $(T_{ji}, \varphi_{ji})$ is a factor code and $\varphi_{kj} \varphi_{ji} = \varphi_{ki}$. We show that the divisibility conditions on Hilbert space dimensions are sufficient for any code network with a tree structure but not in general. For a diamond-shaped network, we show that promotion is possible if and only if the principle angles between $T_{42} H_2$ and $T_{43} H_3$ all have multiplicity divisible by $H_1$. For incomparable $i_1,i_2 < j$, we characterize when $\varphi_{j i_1} (B(H_{i_1}))$ and $\varphi_{j i_2} (B(H_{i_2}))$ commute, when they generate all of $B(H_j)$, and when they intersect only on multiples of the identity. For $i < j_1,j_2 < k$, we characterize when $\varphi_{k j_1} (B(H_{j_1})) \cap \varphi_{k j_2} (B(H_{j_2})) = \varphi_{k i} (B(H_{i}))$ and when these algebras together with $B(H_k)$ form a nondegenerate commuting square.

As a work selected for the Frontiers of Science Award, we present in the Proceedings of the ICBS an overview of how the techniques from the field of Quantum Information (QI) can be implemented in High-Energy Physics (HEP), including also some novel insights. We focus on the paradigmatic case of the top quark, a drosophila of a relativistic qubit. We study the presence of entanglement, perhaps the most genuine feature of Quantum Mechanics, in top-antitop quark production in high-energy colliders such as the LHC. We also analyze our experimental proposal of a quantum tomography protocol for the top-antitop quark pair, eventually leading to the entanglement observations by the ATLAS and CMS collaborations, which constituted the highest-energy observations of entanglement ever. We discuss how the concepts and techniques developed in our work have effectively spawned an already vast and rich field of QI in HEP.

Recent work has shown that quantum double models can be used to circumvent the Bravyi-Koenig bound. In particular, this is achieved through code-switching protocols in which non-Pauli stabilizer phases appear as intermediate codes. We introduce the $X\mathcal C^{(k)}_d$ stabilizer formalism, which generalizes the Pauli stabilizer formalism by combining Pauli-$X$ operators with diagonal operators drawn from a fixed level $k$ of the Clifford hierarchy on prime-dimensional qudits. This yields a natural class of beyond-Pauli stabilizer models, including many twisted quantum double phases. We classify a large class of these $X\mathcal C^{(k)}_d$ stabilizer states, showing that they are uniform superpositions over affine-linear subspaces with diagonal phases. In particular, when the stabilizers of a state require operators from level $k$ of the Clifford hierarchy, we show that the diagonal gates required to produce the phases in the wavefunction sit one level higher. We further show that every 2D twisted quantum double ${\cal D}^\omega(\mathbb{Z}_p^n)$ with $\omega$ a product of type-III cocycles and $p$ an odd prime admits a realization using only Clifford ($k=2$) stabilizers, and we conjecture that phases where $\omega$ contains a type-I or type-II cocycle require level-$p$ Clifford-hierarchy stabilizers for $p$-dimensional qudits. Finally, we demonstrate that a pair of qudit toric codes may be deterministically prepared in a logical magic state by measuring $X\mathcal C^{(k)}_d$ stabilizers. Together, these results provide a concrete stabilizer framework for topological codes beyond Pauli stabilizer models and their logical gates.

Parity superselection forbids direct measurement of odd Majorana observables. We learn time-independent, parity-covariant, $k$-mode-local Lindbladians on $m$ modes using even preparations and measurements with uninterrupted short-time evolution. Internal markers turn odd probes into even observables, and pair measurements among three separated markers calibrate their dynamical contributions. Signed Fierz inversion recovers canonical coefficients, while semidefinite fitting yields a valid generator. For finite-range models on known bounded-degree graphs with suitable marker access and a supplied weighted-strength bound $\bar\alpha$, entrywise error $\varepsilon$ is achieved using $\widetilde{\mathcal{O}}(\bar\alpha^2\varepsilon^{-2}\log(m/\delta))$ samples, without external modes or known nonzero coefficient locations. Recovery to diamond-norm error $\varepsilon$ costs an additional factor $m^2$, matching lower bounds for short-time experiments on fresh systems up to logarithmic and fixed geometric factors. Without a supplied graph, one idle ancillary mode per system mode and potentially nonlocal pair operations give total absolute coefficient error at most $\varepsilon$ per mode using $\widetilde{\mathcal{O}}_k(\bar\alpha^2\mathsf d^2m^{\lfloor k/2\rfloor}\varepsilon^{-2}\log(m/\delta))$ samples, under a supplied approximate coefficient-degree bound $\mathsf d$ and controlled weak-coefficient tails. All guarantees hold with probability at least $1-\delta$. For geometric models, fixed-support even observables can be predicted with logarithmic system-size sample complexity at fixed time and accuracy. We also give finite-volume and exponential-tail extensions.

We give a generic compiler for turning a wide class of device-dependent protocols with trusted state preparation into sequential device-independent protocols. In order for our compiler to apply, the trusted-preparation protocol needs to satisfy certain minimal conditions: having an entanglement-based realization in the first place, and the entanglement-based realization corresponding to the optimal strategy of any non-local game that satisfies a fairly weak rigidity condition. We apply our generic compiler to give sequential device-independent protocols for uncloneable encryption, copy-protection of point functions, and blind randomness expansion. Our technical contribution is a new class of rigidity theorems based on Rényi divergences, with flexible cryptographic applications. They allow our compiler to achieve a constant rate (i.e., the ratio of trusted states prepared to device uses), while tolerating a constant level of noise per device usage. This overcomes a fundamental scaling obstacle faced by previous rigidity theorems for trace distance or fidelity. For the generic sequential case, our proof is based on the sharp-divergence chain rule by Fawzi and Fawzi (2021), which suffices for a constant but fairly low rate. In the special case when the devices retain no memory, we improve the rates by deriving a novel subadditivity property for a modified channel sandwiched divergence, which may be of independent interest. Finally, as a prospect for future improvements, we also prove a chain rule for the iterated-mean divergences from Brown, Fawzi and Fawzi (2021).

The independent and identically distributed (iid) paradigm for asymptotic communication through quantum channels describes $n$ uses of a channel $\Phi$ by $\Phi^{\otimes n}$. Since exact tensor-power behaviour is an idealization, we ask whether the asymptotic capacities of $\Phi$ remain achievable for channel sequences that are almost-iid along $\Phi$. We consider sequences of Choi-almost-iid channels whose normalized Choi states are Mazzola-Sutter-Renner (MSR) almost-iid along the normalized Choi state of $\Phi$, with defect parameters $r_n=o(n)$. In Renner's exponential de Finetti theorem for quantum states, almost-iid states appear in the approximating mixture and motivate the MSR almost-iid class. Choi-almost-iid channels play the corresponding role in an exponential de Finetti theorem for quantum channels established in a companion paper. In this paper, we prove that the universal unassisted classical and quantum capacities of the class of Choi-almost-iid channels along $\Phi$ equal those of the channel $\Phi$. Here universality is within this class: for each rate below the relevant capacity, a code sequence depending on $\Phi$ and the rate, but not on the particular channel sequence, achieves vanishing error for every sequence in the class.