Papers

We show that assuming the existence of homomorphic encryption, parallel repetition of all interactive arguments (after being run under homomorphic encryption) reduces the soundness error at a tight exponential rate even in the post-quantum setting. Moreover, we generalize this result to hold for threshold verifiers, where the parallel repeated verifier accepts if and only if at least $t$ of the executions are accepted (for some threshold $t$). Prior to this work, these results were known only when the cheating prover was assumed to be classical, and it was not known how to achieve tight bounds. As a corollary, we construct the first constant-round succinct argument for $\mathsf{QMA}$ with negligible completeness and soundness errors assuming only the existence of quantum homomorphic encryption.

In this work, we propose a defect-aware parallel atom reloading protocol that reloads atoms based on defect information to increase the atom filling rate. The proposed protocol is useful for neutral-atom quantum computers, where reloading atoms into the defects, or atom-loss positions, is mandatory for continuous operation against atom loss. Our protocol takes advantage of both parallelism and defect awareness to improve atom-reloading efficiency. The proposed protocol consists of the coherent atom reloading operation and the defect-aware planner. The former replenishes the defects with atoms preserving the quantum information coherently. This coherence allows us to adaptively choose the reloading strategy based on the current defect configuration. The latter determines the atom reloading pattern to efficiently replenish the defects. In numerical experiments assuming a low-noise environment, we confirmed that the average atom filling rate improved from 98.61% to 99.94% for a 36 x 90 atom array, matching the filling rate obtained with a mixed integer programming solver to within 0.001 percentage points while planning each reload in under 0.1 ms. These results demonstrate that defect-aware parallel reloading can achieve and sustain high atom filling rates while the performance of the defect-aware planner meets the real-time requirements of neutral-atom quantum computers.

Number-conserving cooling can fail to prepare an interacting flat-band target when Pauli exclusion blocks its transfer destinations. We study this failure on vertex-edge decorated graphs at one particle per flat orbital. The rank of a cut block of the flat-orbital Gram matrix bounds the number of residual source directions that can remain flat. For sublinear-range cooling with no Hamiltonian term, separated spin domains on periodic decorated hypercubic lattices support exponentially many stationary states with a nonzero bright-particle density. For a chain with fixed finite cooling range, we construct a physical Fock initial state whose overlap with a wrong dark state is independent of system size. This gives fidelity and bright-density bounds valid at every time. In higher dimensions, the bare overlap decays with boundary area, while local boundary rotations prepare states with a finite failure weight in constant circuit depth. Dephasing the occupations of all compact bright modes restores global attraction to the ferromagnetic target when the graph and cooling destinations satisfy the stated conditions. The result allows Hamiltonians that preserve the target. The compressed dynamics in the strong-dephasing limit also remains attractive and has a positive gap at each fixed size. Gram calculations, finite-system dynamics, and Liouvillian spectra test the analytic results. Weak-dephasing and particle-transport bounds constrain the preparation time despite eventual convergence.

Certified deletion allows a client to upload encrypted data to a server as a quantum state, then later request that the server delete their data and detect whether the server complies. If verification passes, then the data on the server will remain hidden even if the decryption key is later leaked. In publicly verifiable certified deletion, the verification key is published so that anyone may check for deletion compliance. In this work, we give a general compiler to publicly verifiable certified deletion that allows the client to initially upload the *quantum* ciphertext using purely *classical* communication, assuming the post-quantum hardness of LWE in the plain model. Our approach can be applied to a wide variety of primitives, including commitments and public-key, attribute-based, identity-based, and fully-homomorphic encryption. Moreover, our constructions allow the client to classically manage the encrypted data beyond just verifying its deletion. The classical client may non-destructively audit the ciphertext via a Proof of No Intrusion to check whether it has been leaked to a third party. The classical client may also retrieve the data while simultaneously verifying its deletion from the server. Thus, they do not have to choose between retrieving the data and protecting it against future key leakage. As our core technical contribution, we give a classical-communication protocol and simulation technique that allows adapting purification-based security arguments for BB84-style states which are prepared through classical interaction. It makes the required purification available in a hybrid experiment, despite the classical transcript uniquely determining the prepared state in a real execution.

A time-lock puzzle allows a sender to hide a message in a puzzle such that recovering the message requires substantially more sequential computation than the time required to generate the puzzle, even when parallel computation is allowed. Applications of time-lock puzzles include timed-release encryption, sealed-bid auctions, electronic voting, fair contract signing, coin flipping, and Byzantine consensus. However, time-lock puzzles are known to be impossible in the classical random oracle model. To overcome the classical barrier, in this work we consider quantum time-lock puzzles, in which the puzzle itself is a quantum state. Our construction in the quantum random oracle model achieves generation in one oracle round, solving in at most $T$ oracle rounds, and security against polynomial-width quantum adversaries of depth $o(T)$ for every polynomially bounded delay $T=T(\lambda)$, resolving an open problem posed by Mahmoody, Moran, and Vadhan (2011).

Neodymium-doped gadolinium vanadate (Nd:GdVO$_4$) is a popular laser material at room temperature. It has received limited attention for quantum technologies because of the linebroadening effects of disordered gadolinium spins in the host. Here we investigate the optical properties at temperatures below the 2.5 K Néel temperature, revealing narrow optical transitions. We demonstrate that rare earth ions in magnetic hosts give us a new way of observing the signs of magnetic g-factors. The interplay between the exchange and Zeeman interactions means that we see clear evidence of negative g-factors. These results provide a detailed spectroscopic foundation for Nd:GdVO$_4$ and expand the understanding of its candidacy as a material for hybrid quantum systems.

Gaussian boson sampling (GBS) seeks quantum advantage by sampling photon-number patterns generated with squeezed inputs and passive linear optics. Many proposed GBS applications instead target function computation by applying functions to mode-resolved photon-number outcomes—a natural form of experimental postprocessing that produces classical outputs. Sampling hardness alone, however, does not determine the complexity of these tasks. By analyzing the irreducible decomposition of fixed-photon-number operator spaces, we prove that the expectation value of every such function in the average case over passive linear-optical networks can be classically evaluated for inputs with finite squeezing strength. We also provide a classical algorithm that estimates this value to inverse-polynomial additive error. The result provides new theoretical tools for analyzing linear-optical quantum systems, helps clarify the origin of current GBS hardness evidence, and inspires new applications of GBS with genuine quantum advantages.

Clifford augmented methods have emerged as a powerful technique to simulate quantum circuits and many-body systems by exploiting the stabiliser structure found in said systems, whilst additionally enabling one to readily quantify the non-stabilizerness (i.e.\ magic) present. In this work, we utilise a qudit Clifford augmented simulation method to probe the presence of magic in the Affleck-Kennedy-Lieb-Tasaki (AKLT) model, finding that its ground state and scar states are highly magical as quantified by their Stabiliser Rényi Entropy (SRE). Nevertheless, owing to its low entanglement structure, these states are still readily expressible as a Clifford augmented Matrix Product State with low bond-dimension and moreover may be time-evolved using the Clifford augmented time-dependent variational principle (TDVP) algorithm. We utilise Clifford augmented TDVP to study the string order dynamics in the scar states of the AKLT model after a quench within the Haldane phase to the anti-ferromagnetic Heisenberg Hamiltonian. We observe that there is a decay of string order following the quench, which is more pronounced with increasing bimagnon number. This finding highlights the sensitivity of string order in the AKLT scar states to symmetry-preserving quenches, even when the initial and final Hamiltonians belong to the same topological phase.

An unbiased qubit positive operator-valued measure (POVM) can be uniquely expressed in terms of the Bloch vector. We prove that for POVMs with coplanar Bloch vectors, they are jointly measurable if and only if the perimeter of the convex closure of Bloch vectors is less than or equal to 4. Moreover, as a corollary, we give an affirmative answer to the conjecture suggested by [Andrejic-Kunjwal 2020] on the existence of a joint device for POVMs whose Bloch vectors lie on the same circle.

Optimistic matrix mirror-prox (OMMP) computes $\epsilon$-approximate Nash equilibria in quantum zero-sum games with an $O(1/\varepsilon)$ average-iterate guarantee [arXiv:2311.10859]. We investigate whether this dependence on accuracy is tight and whether geometric last-iterate convergence can be guaranteed. We study these questions through explicit games with one qubit per player. First, we prove an $\Omega(1/\varepsilon)$ lower bound for the uniform-average output that includes the maximally mixed initial state, independently of the regularizer and step size. Second, we construct a fixed game on which optimistic gradient descent-ascent (OGDA), initialized at the maximally mixed state, has last-iterate Frobenius distance to equilibrium $\Theta(1/t)$ and duality gap $\Theta(1/t^3)$ for every sufficiently small fixed step size. A separate fixed game exhibits arbitrarily long delays in reducing the initial error by a constant factor across a family of initial states. Finally, we give a fixed game with a unique, strictly complementary equilibrium on which optimistic matrix multiplicative weights updates (OMMWU) converge only polynomially from the maximally mixed state for every fixed positive step size. The last-iterate Frobenius distance and quantum relative entropy from the equilibrium to the iterates decay as $\Theta(1/t)$, while the duality gap decays as $\Theta(1/t^2)$.

We propose a holographic dual of the relative entropy of entanglement for a boundary tripartition $A:B:C$. Our proposal is that, at the leading order, \begin{align} E_R(\rho_{AB}) = \frac{1}{4G_N}\Big[\mathrm{Area}(\Gamma_{\min}) - \mathrm{Area}(\gamma_{AB})\Big] \notag \end{align} where $\Gamma_{\min}$ is the minimal bulk tripartition surface and $\gamma_{AB}$ is the minimal surface homologous to $AB$. For a general random tensor network, we prove the corresponding upper bound by constructing a separable state associated with $\Gamma_{\min}$ and evaluating its relative entropy. We also establish the matching lower bound rigorously for networks of one, two, and three Haar random tensors by bounding the maximal tripartite product-state overlap. In appropriate geometries, the minimal tripartition surface can form a nontrivial tri-junction resembling the Mercedes logo. The proof proceeds by sequential optimization over candidate product states, which has a natural geometric interpretation as a local search for the minimal tripartition surface.

High-order coherent-state modulation and collective midpoint measurements enable multi-ebit entanglement distribution between cavity-coupled atomic memories. An SRM-inspired 16-QAM receiver achieves $1.75$ ebits per network mode use at $0.5$~dB end-to-end loss, exceeding single-qubit-per-mode benchmarks by $5.8$~dB and lying $3.8$~dB below the half-link capacity bound. The advantage persists for per-interface loss below $0.2$~dB and calibrated phase errors below $0.2\pi$. For 4-QAM, an optimized POVM with twice as many outcomes raises the achievable rate by $4.0\%$, revealing measurement-design headroom.

Variational Quantum Algorithms (VQAs) rely heavily on classical optimization routines to navigate high-dimensional, noisy parameter landscapes. However, the evaluation of analytical gradients via the parameter-shift rule requires $\mathcal{O}(p)$ circuit executions, rendering this approach computationally prohibitive for deep circuits. While simultaneous perturbation methods provide an $\mathcal{O}(1)$ alternative, their gradient estimates suffer from severe $\mathcal{O}(p)$ spatial variance, which impedes convergence. To resolve this tension, we introduce the Cached Recycled Variance-Reduced Gradient (CRVG) by leveraging variance reduction techniques. We formulate two variants: a 3-Circuit (1-Sided) Non-Recursive CRVG and a Recursive CRVG. By introducing a center-point caching mechanism, the 3-Circuit CRVG mathematically recycles quantum measurements to reduce the inner-loop circuit complexity by 25% across both variants. We establish a theoretical separation between the two routing paths to achieve an $\epsilon^2$-stationary point: the non-recursive variant reaches a sample complexity of $\mathcal{O}(\max\{p/\epsilon^2, p^{2/3}/\epsilon^{10/3}\})$, while the recursive variant achieves an improved complexity of $\mathcal{O}(\max\{p/\epsilon^2, \sqrt{p}/\epsilon^3\})$. Empirically, extensive evaluations on MaxCut and Maximum Independent Set (MIS) benchmarks validate these findings. While standard simultaneous perturbation remains a robust baseline across varying depths, CRVG demonstrates targeted advantages in specific amortizable regimes, such as the non-recursive variant on EfficientSU2 circuits and both variants on depth-three QAOA, yielding superior energy minimums and tighter output variances. Ultimately, CRVG establishes a principled bias-throughput trade-off for scaling near-term quantum optimization.

We introduce a framework for combinatorial optimization using sum-constrained continuous quadratic programs solvable by QCi's Dirac-3S photonic entropy computer. This is enabled by the Motzkin-Straus theorem which provides a powerful bridge between discrete clique problems and optimization over the probability simplex. We demonstrate this framework's versatility by solving constraint satisfaction problems, providing extensive benchmarks on the DIMACS suite. The Dirac-3S platform matches or outright leads two independently implemented classical baselines on more than four-fifths of the benchmark instances, reaching the best known solution on nearly all structured graph families, even outperforming both classical solvers on several of the largest instances tested. On the other hand, well-tuned classical continuous optimizers retain an edge only on the hardest planted-clique instances. This work establishes a viable pathway for solving combinatorial optimization problems using natively analog unconventional computing platforms, while positioning entropy computing as a competitive approach for navigating non-convex landscapes and providing rigorous baselines for an emerging computational paradigm.

Experimental tests of shallow-circuit quantum advantage require explicit classical bounds at finite circuit sizes. We refine the finite-size classical soundness bound of Aasnaess's graph-distributed construction to depend linearly on the number of players. Combined with standard disjoint-player repetition, this gives a two-round test on a single processor for any finite nonlocal game with a finite-dimensional perfect quantum strategy and classical winning probability $\gamma<1$, with arbitrarily small classical success. The method is based on playing $m$ copies with disjoint players and teleporting each player's register to a uniformly random one of $N$ sites before the questions are revealed. Each answer bit of a depth-$D$, fan-in-$K$ classical response with fixed wiring depends on at most $K^D$ question wires, making cross-player dependencies unlikely when $N$ is large. The quantum implementation has constant depth per round and wins with certainty. A classical device wins with probability at most $\gamma^m+O(mK^D/N)$, which vanishes as $O(\log N/N)$ for $m=\lceil\log_{1/\gamma}N\rceil$ at fixed $D$ and $K$. We present an explicit proposal for an experimentally testable quantum advantage with 99 qubits.

Two-dimensional atomic arrays provide versatile free-space quantum optical interfaces by coupling photons to collective lattice modes. Here we show that the Rayleigh–Wood anomaly provides a sharp control mechanism for both linear and nonlinear photon scattering from a single atomic layer. As the lattice spacing crosses the diffraction threshold, newly opened radiative channels rapidly broaden the dominant collective modes, converting specular reflection into diffuse off-axis scattering. In transmission, momentum-space Fano interference between the incident and collectively scattered fields produces single-photon intensity zeros that strongly reshape the momentum-space correlation pattern. An integrated nonlinear contrast reveals a pronounced channel asymmetry: upon opening the Rayleigh channels, the connected two-photon contribution drops by several orders of magnitude relative to the factorized background in transmission, while remaining close to unity in reflection. These results establish radiative diffraction thresholds as a control principle for quantum nonlinear optics in single-layer atomic arrays.

The Clifford hierarchy $\mathsf{C}_1 \subset \mathsf{C}_2 \subset \cdots$ was introduced by Gottesman and Chuang (arXiv:quant-ph/9908010) to characterize gates that admit fault-tolerant implementation by gate teleportation. Yet, despite its rich mathematical structure and the attention it has received in recent years, little is known about $\mathsf{C}_k$ for $k > 3$. Most progress has focused on identifying structural properties of restrictions of the hierarchy, such as diagonal gates and gates on systems of small dimension $d$ or with few qudits. The generalized semi-Clifford conjecture, proposed by Zeng et al. (arXiv:0712.2084), states that every gate in $\cup_k \mathsf{C}_k$ is, up to multiplication by Cliffords, the product of a permutation and a diagonal matrix. Beigi and Shor proved the case $d=2$, $k=3$ (arXiv:0810.5108) and Pllaha et al. found an alternative proof by exploiting fixed points of the conjugation map induced by (a Clifford correction of) $U \in \mathsf{C}_3$ on the span of maximal stabilizer subgroups (arXiv:2006.14040). By extending their fixed-point arguments to the group $\Gamma_1(U)$ generated by $U \mathsf{P} U^\dagger$ and beyond, we prove the conjecture for $k \leq 4$ and any prime dimension $d$. Our proof centers on conjugation groups $\Gamma_1(U), \Gamma_2(U), \ldots$ of $U \in \mathsf{C}_k$, which we expect to be a useful tool in the study of the Clifford hierarchy more generally. We also show a natural sufficient condition on such groups for gates in higher levels to be generalized semi-Clifford.

Nitrogen-vacancy (NV) centers in diamond exist in neutral (NV0) and negatively charged (NV-) states, and quantifying their respective photoluminescence (PL) contributions is important for charge-state-based measurements. Existing methods either require additional experimental control or may suffer from limited physical identifiability. Here, we introduce a geometric method for determining NV charge-state contributions from PL spectra acquired at different excitation intensities. Each spectrum is mapped into a low-dimensional space through broadband spectral weighting, where changes in the relative NV0 and NV- contributions trace a one-dimensional trajectory. Zero-phonon-line (ZPL) information from two spectra physically calibrates this trajectory, enabling the NV-PL contribution to be determined by geometric projection. Measurements on two bulk single-crystal diamond samples yielded NV- contributions in close agreement with those obtained using an independent dual-excitation reference-spectrum method, with root-mean-square errors of 1.11 and 0.31 percentage points. Under additive spectral noise, the proposed method exhibited more than an order of magnitude less variation than a ZPL-only method. Fisher-information analysis further showed that the three-dimensional CIE XYZ representation retained approximately 81% of the information about the NV- contribution available in the full spectrum. These results establish a physically calibrated approach to low-dimensional spectral estimation that combines reduced experimental overhead with robust parameter estimation and provides a general framework for spectral sensing governed by a small number of physical degrees of freedom.

Random unitary operations are a fundamental resource for quantum information processing, yet provably generating them with experimentally available controls remains challenging. Existing approaches often require calculating higher-order operator expectation values, relying on statistical assumptions about the experimental Hamiltonian's spectrum to make these calculations tractable. We show how to implement random unitaries by a sequence of evolutions generated by a fixed Hamiltonian conjugated by a global control operator. We give a geometric argument that establishes exponential convergence to the uniform random (Haar) measure on the accessible unitary group under uniform parameter sampling, beyond a finite sequence-length threshold that we bound. We show this holds when the connected Lie subgroup generated by the conjugated Hamiltonians is closed. Native dynamics and global control thus provide a constructive route to uniform randomness, with applications to many experimental platforms including Rydberg atoms, bosons and fermions in optical lattices, transmons, and trapped ions.

Searching in a linked list is one of the most basic problems in classical algorithms. Although the nodes of the list come with memory addresses, classically those addresses play no role in the cost of search: one simply starts at the head and follows successor pointers to search for an element. In this paper, we show that the quantum setting is different. Here, the ambient address space from which the list vertices are drawn can itself affect the query complexity. We study the following problem analogous to search in a linked list in the query complexity model: the input consists of an address universe $[N]$, a public start symbol $s$, a successor oracle $f$ whose non-$\perp$ values trace a hidden simple path $s \to a_1 \to a_2 \to \cdots \to a_\ell \to \perp$, and a marking oracle $g$ that marks at most one list vertex. The task is to decide whether the list contains a marked vertex. We prove that both the decision and search versions of this problem for all $N \ge \ell \ge 1$ have quantum query complexity $\Theta\!\bigl(\min\{\ell,(N\ell)^{1/4}\}\bigr)$. Thus, quite surprisingly, when $N < \ell^3$ the optimal quantum complexity is $(N\ell)^{1/4}$, which is strictly smaller than the $\Theta(\ell)$ cost of ordinary linked-list traversal. This gives a precise characterization of when the ambient address space yields a genuine quantum advantage for linked-list search. We extend our results and give the same tight asymptotic bounds for the natural double linked-list version as well.

Unused encoding states offer opportunities to simplify quantum circuits. For algorithms restricted to reachable subspaces, unspecified diagonal-operator entries can be optimized without changing ideal computation. We investigate exact diagonal completion for the quantum approximate optimization algorithm (QAOA) applied to placement, using permutation-preserving register swaps. We construct exact Manhattan-distance operators through weighted-$\ell_1$ optimization of Walsh coefficients and a sparse recurrence requiring $O(\sqrt{m})$ terms on balanced rectangles, avoiding $O(m^4)$ dense constraint storage. Across 160 geometries, weighted-$\ell_1$ completion reduces controlled-NOT (CX) counts relative to four alternative extensions in all 96 cases with unused binary codes under Gray-code synthesis. On an independently specified 60-case cohort, median reductions relative to virtual-coordinate extension are 28.0%, 53.9%, and 21.6% at six, nine, and twelve sites. Under generic diagonal synthesis, reductions decrease to 10.9%, 1.3%, and 0.7%, demonstrating compiler dependence. Additional ancillas reduce mixer serialization, but token circuits remain deeper than one-hot baselines. Ideal placement simulations show baseline-dependent solution quality, with classical search performing better. OpenROAD integration takes 72 QAOA and 216 classical placements across six RTL designs through clock-tree synthesis and global routing with zero overflow. Completion improves phase construction; no end-to-end advantage is established.

We study the ergotropy and the thermodynamic potentials of a qubit battery charged by repeated interactions with clusters of thermal ancillas, qubits or oscillators, through a composite system-bath coupling that generates steady-state coherence in the energy basis. A single parameter encoding the bath quantum statistics yields the coherence and ergotropy in closed form for any cluster size. For large clusters, the ergotropy becomes independent of the bath statistics and, at optimal couplings, reaches a universal fraction of the equilibrium internal energy of the qubit at the bath temperature. Since the charged state has no population inversion, all extractable work comes from coherence. The ergotropy is flat at low temperatures. We trace this plateau to the third law, and show that the ergotropy is proportional to the equilibrium enthalpy of the qubit, whose slope vanishes with the heat capacity. For a battery composed of multiple qubits, the coherence grows exponentially with the number of qubits while the ergotropy grows linearly, both remaining a nearly constant fraction of their respective maxima. The charged state is a non-equilibrium steady state with finite entropy at zero temperature, sustained by the work of switching the collisional interaction on and off. The cost is nonzero whenever the parallel coupling is nonzero, and, unlike the ergotropy, it depends on the bath statistics.

Readout-side residual hybrids concatenate raw inputs with measured quantum features. Under single-example gradient sharing, a biased first linear layer admits standard analytic recovery of its input, so the bypass exposes raw coordinates without requiring inversion of the quantum circuit. We audit this mechanism using two tabular datasets, four architectures, and metrics conditioned on feature visibility. Iterative gradient matching gives median full-record PSNR of 73-96 dB for residual and input-only heads. Quantum-only heads score 8-11 dB on the full record but 54-96 dB on the six input coordinates they actually encode. These are reconstruction results for the tested six-input, six-observable circuits, not a general statement about quantum encodings. A loss-threshold membership attack remains near chance. The contribution is a visibility-conditioned privacy audit: omitted coordinates must not be credited as protection supplied by quantum processing, and near-exact PSNR differences must not be interpreted as meaningful privacy rankings. Our findings concern individual gradients and do not establish leakage under aggregation or multiple local training steps.

Error mitigation is expected to turn noisy quantum measurements into more useful estimates. We show that it can instead amplify error. Under control-offset miscalibration, the evaluated unconstrained zero-noise extrapolation (ZNE) estimators are worse than no mitigation on 38-63% of simulated instances and produce extreme tail errors. A small IBM Heron study finds worsening on 80-88% of 18 instances across two depths, with mean error 3.0-4.1 times the raw error. In simulation, the median changes little, so median-only monitoring misses the failures. We then compare methods at the same online shot budget per evaluation and report offline training cost separately. After that cost is amortized, a budget-conditioned neural corrector occupies the low-budget end of the simulated accuracy-cost frontier and falls back to the raw estimate when an ensemble disagrees; its hardware transfer remains unsuccessful. Finally, we treat provider-reported calibration as an input that is not bound to the execution-time device state. A white-box projected-gradient stress test on this metadata increases the corrector's error 8.1 times within the feature ranges used for training and evades the disagreement monitor on half of the worsened cases. Together, the results connect budget-aware evaluation, tail risk, and calibration integrity in near-term quantum learning pipelines.

Recent works have demonstrated that quantum oracles have subtle behavior, as access to inverse, conjugate or controlled queries can exponentially change the query complexity of certain tasks. Inspired by these works, we introduce the notion of meta-complexity of quantum relativization. We ask: for any two quantum complexity classes, under which "types" of quantum oracles are they equal or separated? Different pantheons of oracles (or quantum oracle types, e.g. unitary vs state, poly- vs superpoly-dimensional, closed under inverse or not) form a partially ordered set based on their power in separating complexity classes. Moreover, two oracle pantheons A and B are separated if there exists a pair of complexity classes that are separated under an oracle from pantheon A but yet the complexity classes are equivalent under all oracles from pantheon B. We show that this meta-complexity can be nontrivial by giving a complete classification, within the family of oracle pantheons defined in this paper, of which models can separate the complexity classes $\mathsf{PostBQP}$ and $\mathsf{PreciseBQP}$, the exponentially precise variant of $\mathsf{BQP}$. Both classes equal $\mathsf{PP}$ in the unrelativized setting. Within our taxonomy, they remain equal relative to real or polynomial-dimensional unitary oracles and whenever inverse or conjugate access is supplied. In contrast, we give a separation relative to forward-only complex diagonal unitaries of superpolynomial dimension, as well as a separation relative to single-qubit state-preparation oracles. We view this as a test case for the meta-complexity of oracles which underscores the subtlety inherent to the relativization of quantum complexity classes.

Integrated quantum photonics benefits from photon-pair sources that generate photons directly in waveguides, where they can be efficiently collected, routed, and manipulated. Here, we investigate spontaneous four-wave mixing (SFWM) in a fused tapered-fibre microcoupler formed from two single-mode fibres, and report four contributions. First, we observe SFWM photon pairs in this multimode device: its elliptical central region supports three spatial mode profiles, each with two polarisations, giving six guided modes, and pumping it near 800 nm yields two photon pairs at 648/1048 nm and 660/1021 nm. Second, because several allowed SFWM processes produce similar wavelengths and wavelength alone does not identify their origin, we distinguish the processes by combining phase-matching calculations and selection rules with two independent polarisation measurements: the dependence of the coincidence rate on pump polarisation and polarisation tomography of the generated photons. Third, within the present geometrical model, we find that the 660/1021 nm pair is generated by co-polarised pump photons in a process occurring entirely within a single higher-order mode, whereas the 648/1048 nm pair is generated by orthogonally polarised pump photons in an intermodal process coupling a fundamental and a higher-order mode; the signal photons from the two processes have similar output polarisations, while the idler photons are nearly orthogonal. Fourth, extending the analysis beyond the measured operating point, we theoretically identify pairs of simultaneous SFWM processes driven by a common pump that could generate either polarisation entanglement or composite spatial-polarisation entanglement, depending on the pump wavelength. More generally, this work provides a practical strategy for identifying intermodal SFWM processes in multimode waveguides when spectral information alone is insufficient.

Quantum sensing traditionally focuses on using quantum resources such as squeezing and entanglement to improve precision for sensing fixed signals. However, in many applications such as gravitational-wave detection and electromagnetic-field sensing, the signal evolves continuously and varies through time. Additionally, the learner is free to prepare, control, and measure the sensor at arbitrary times, possibly chosen adaptively. In this work, we establish exponential separation in sensing time for continuously evolving signals due to the available squeezing. The signals we study are characterized by a pattern size $T$, and we find that a sensor with squeezing at least $\omega(\sqrt{\log T})$ offers a $\mathrm{poly}(T)$ sensing time, whereas those with squeezing at most $o(\sqrt{\log T})$ must use an exponential sensing time in $T$.

We analyze a novel approach for quantum magnetic sensing via optical detection of nuclear spin precession in a noble gas. The detection is carried out with an ultraviolet frequency comb laser, so no alkali vapor is required to be mixed with the noble gas during the sensing stage, allowing for hours-long spin relaxation time at room temperature. Our analysis reveals that combining high laser power and low laser intensity noise is crucial to achieving and exceeding state-of-the-art magnetometric performance, including that of cryogenic magnetometers. We find operational regimes where either fundamental or technical noise dominate, which directs experimental effort towards increasing laser power or lowering laser intensity noise, respectively. We also show that optimizing beam size is key to achieving optimal sensitivity. Our calculations predict that a record-breaking sensitivity of $24~\mathrm{aT}/\sqrt{\mathrm{Hz}}$ is achievable in 10 minutes with a 10 W ultraviolet laser with a relative intensity noise of -100 dBc/Hz.

We introduce the terminology passive realism to encapsulate the scale-independent assumption that a physical system's pre-existing properties can be passively observed without altering its subsequent dynamics. A necessary condition for passive realism is provided by the no-signalling in time (NSIT) condition, which states that a measurement outcome is independent of whether or not a prior measurement was performed. While closed quantum systems generically violate NSIT due to measurement back action, we investigate whether open-system dynamics can dissipate this disturbance to the environment and restore NSIT. By modeling the time evolution between sequential measurements as an arbitrary quantum channel, we show that such environmental masking is possible only in two special cases. Specifically, we show that if the initial state of a two-time sequential measurement scenario is not maximally mixed, and if the channel governing the dynamics between measurements is not a discard-and-prepare channel, then there necessarily exist binary projective measurements violating NSIT, hence violating passive realism. By providing a constructive procedure for determining these violating measurements—applied here to depolarizing and dephasing channels—we demonstrate that, outside these two cases, system-environment interactions cannot erase the statistical footprint of a quantum measurement for all measurement choices.

High-dimensional spatial entanglement generated via spontaneous parametric down-conversion (SPDC) provides a powerful resource for quantum information processing, yet its mode structure becomes increasingly complex when the pump occupies a higher-order Laguerre–Gaussian (LG) mode. Here, we develop an algebraic framework for characterizing biphoton spatial-mode entanglement by factorizing LG-pumped SPDC into a spatial-mode beam-splitter transformation followed by spatial two-mode squeezing. By choosing the biphoton LG basis radius as the geometric mean of the pump-beam radius and the crystal-induced correlation width, we obtain a natural modal basis in which the two operations can be treated separately. When the pump-beam radius matches the correlation width, spatial squeezing vanishes, and the two circular-mode components of the pump are independently conserved across the signal and idler photons, leading to conservation of both orbital angular momentum and the total spatial mode number. We further derive an analytical expression for the Schmidt number for arbitrary LG pump modes and squeezing strengths, revealing how the radial and azimuthal pump indices govern the dimensionality of the spatial entanglement. This algebraic characterization provides a unified description of the mode structure, conservation laws, and entanglement dimensionality of higher-order-LG-pumped SPDC.