In this work, we investigate maximum-confidence discrimination, which encompasses minimum-error and unambiguous discrimination, for ensembles of separable states by considering global and separable measurements. We demonstrate that global measurements outperform separable ones, thereby establishing nonlocality without entanglement (NLWE) in terms of confidence in a detection event, a fine-grained state-identification strategy that maximizes the probability of a correct guess given a measurement outcome. Conversely, verifying achievable confidence in measurement outcomes can certify global measurements, namely, semi-device-independent certification of NLWE. Our results make it feasible to experimentally demonstrate NLWE using present-day quantum measurement devices, even with non-unit detection efficiencies, since maximum-confidence measurements rely only on detected measurement outcomes. less

Non-isometric encoding arises in various important contexts in quantum error correction, most notably in the finite-energy, non-ideal codewords inevitable in experimental realizations of continuous-variable codes, and holographic quantum gravity. In this work, we present a general and systematic theory of non-isometric quantum error-correcting codes. In particular, we employ the approximate quantum error correction framework to quantitatively study the fundamental limitations imposed by non-isometric encodings on the accuracy of quantum error correction and implementation of logical operations. We apply our theory to analyze GKP and tiger codes under energy constraints, and discuss the implications to holography. less

Projected quantum feature maps provide a strategy for using quantum processors as feature generators for classical machine-learning models. Building on counterdiabatic Ising-glass and one-dimensional Heisenberg PQFMs, we introduce a generalized two-qubit Hamiltonian-based PQFM that provides a unified way to encode classical features through local Pauli fields and pairwise two-qubit Pauli interactions. This construction allows distinct classical variables to be embedded along different Pauli axes of the same qubit, increasing the information density of shallow circuits while remaining compatible with hardware constraints. We develop and implement these methods in pqfmlib, a publicly available Python library for constructing, executing, and benchmarking Hamiltonian-based PQFMs.We then benchmark the generalized Hamiltonian PQFMs against reference PQFMs on four biomedical classification datasets under a nested cross-validation protocol with paired statistical tests. Quantum features are generated using both IBM quantum processors with up to 156 qubits and statevector simulations. Our results show that the generalized two-qubit Hamiltonian family provides the most consistent pattern of statistically supported gains over matched classical baselines, although the performance of all methods depends on the dataset, encoding strategy, measured observables, and hardware conditions. These findings support generalized Hamiltonian PQFMs as a promising route toward near-term quantum utility. less

We formulate a local geometric criterion for weak cosmic censorship in black hole overcharging and overspinning thought experiments. Under the null convergence and generic conditions, matter injection turns a horizon cross section into a closed trapped surface. Any final spacetime unable to accommodate this surface is ruled out. This trapped surface criterion excludes superextremal Reissner-Nordström, Reissner-Nordström-de Sitter, and Kerr-Newman final states, as well as Weyl-class naked singularities. Our criterion does not rely on asymptotic charges or on an extremal condition characterizing naked singularities. less

For general max-k-XORSAT with $k \geq 3$, no polynomial-time algorithm can do substantially better than random guessing on worst-case instances unless $\mathsf{P} = \mathsf{NP}$: approximating beyond the random-assignment value of $1/2$ is $\mathsf{NP}$-hard. The picture changes when each variable appears in at most $D$ constraints. In that bounded-degree setting, polynomial-time algorithms can provably beat the random baseline by an additive amount of order $1/\sqrt{D}$. For Boolean instances, this scaling is known to be optimal: the matching hardness result is due to Trevisan, while the corresponding algorithmic guarantee was established by Barak et al. Whether the same holds over general finite fields, and what it implies for quantum algorithms, has not been established. We make this connection explicit and extend the hardness to max-E$k$-LINSAT$(q,r)$ with bounded degree $D$ and over arbitrary finite fields $\mathbb{F}_q$, proving that it is $\mathsf{NP}$-hard to exceed $r/q + \mathcal{O}_{q,r}(1/\sqrt{D})$. These results provide the complexity-theoretic benchmark for the bounded-degree instances targeted by decoded quantum interferometry (DQI), QAOA, and classical heuristics. Any quantum advantage on bounded-degree instances is therefore confined to the constant prefactor. We further show that in the context of DQI and on $(k,D)$-regular instances, this prefactor is sensitive to the nature of the decoder: DQI with classical decoders faces an information-theoretic $1/\sqrt{D \log D}$ barrier that prevents it from matching the hardness scaling, while DQI with quantum decoders is compatible with the $1/\sqrt{D}$ scaling -- identifying quantum decoding as the key ingredient for matching the complexity-theoretic scaling with DQI. less

Full tomography of an unknown quantum evolution is resource-intensive and often unnecessary when the goal is only to predict selected properties. This motivates the study of classical shadow estimation of unitary channels (CSEU), a task in which one queries an unknown $d$-dimensional unitary $U$ and stores classical data that can later be used to predict expectation values $\mathrm{tr}[O \cdot UρU^\dagger]$ up to additive error $\varepsilon$ for arbitrary input states $ρ$ and observables $O$. We propose a parallel, non-adaptive CSEU protocol using $\mathcal{O}(d\varepsilon^{-1})$ queries when the input states or observables have constant rank. This achieves Heisenberg scaling with respect to $\varepsilon$ and is query-optimal, as we prove a matching $Ω(d\varepsilon^{-1})$ lower bound that remains valid even with stronger access to the unknown unitary. Our query-optimal CSEU protocol provides a versatile and powerful tool for quantum learning theory, pushing the performance limits of several fundamental learning tasks, including unitary channel tomography, Hamiltonian learning, boundary-regime quantum channel tomography, Pauli transfer matrix learning, inverse-free amplitude estimation, pure-state property estimation, and shallow-circuit learning. Remarkably, we show that optimal unitary channel tomography can be achieved using only parallel queries, closing the gap between the best achievable efficiency of parallel and sequential tomography protocols. Together, these applications establish our framework as a fundamental tool for learning properties of quantum processes, particularly for certain key tasks that require high precision. less

This paper develops an epistemological constraint on quantum gravity grounded in the empirical meaning of general relativity. The central claim is that a complete recovery of general relativity requires an effective metric, a continuum limit, or Einstein-like dynamics together with the physical conditions under which relational geometrical quantities can be objectively determined. These conditions concern the dynamical stability of measuring devices and reference systems, causal accessibility among physical systems, record formation, and invariance under admissible descriptions. In classical general relativity, they are usually implicit in the use of clocks, rods, light signals, freely falling bodies, detectors, and gauge-invariant observables. In quantum gravity, however, they become non-trivial because spacetime geometry may be emergent, effective, thermodynamic, relational, or frame-dependent. This claim is developed through four cases: Rindler horizons and the Unruh effect, black-hole thermodynamics and Jacobson's equation-of-state derivation, gravitational-wave detection, and Weyl and conformal gravity. The latter is discussed as a critical limiting case in which conformal invariance raises a sharp question about whether scale-dependent measurements of space and time can be physically fixed. Implications for quantum gravity are also discussed using emergent gravity and quantum reference frames as examples. The perspective developed in the study suggests a general epistemological constraint on quantum gravity: any viable approach must recover the physical possibility of objective geometrical measurement together with geometry itself. less

We study the ability of the upcoming Laser Interferometer Space Antenna (LISA) to constrain gas torques acting on extreme-mass-ratio inspirals (EMRIs) when these are embedded in accretion disks, using recently developed relativistic models for the binary-disk interaction. Using a fully Bayesian setup, we find that, contrary to previous forecasts based on Newtonian results, these observations can provide simultaneous estimates of the disk surface density and the accretion rate (or, equivalently, its total luminosity) without the need for an electromagnetic counterpart. Our analysis also indicates that simpler measurement constraints based on the linear-signal (Fisher matrix) approximation are not valid for these systems. For typical EMRI observations, the torque amplitude can be constrained to within ~10%, strengthening the prospect of probing accretion physics at (sub)microparsec scales, deep in the strong-field gravity regime and complementing electromagnetic observations. This also strengthens LISA's ability to help answering questions such as how massive black holes grow and coevolve with their host galaxies and, by helping to identify the EMRI's host galaxy through cross-correlation with AGN catalogues, to improve the use of these sources as (dark) sirens for cosmology. less

Gravitational wave (GW) observations provide an unprecedented laboratory for testing general relativity (GR) in the strong-field, highly dynamic, and relativistic regimes. Within the parameterized post-Newtonian (PN) formalisms, waveform generation tests have conventionally been limited to constraining inspiral coefficients up to the 3.5PN order. Leveraging the recent theoretical breakthrough that extended the analytical compact binary phasing to the 4.5PN order, we present the first observational constraints on these higher-order effects. Our analysis utilizes two exceptional events detected by the LIGO-Virgo-KAGRA (LVK) network: GW250114\_082203, which boasts the highest signal-to-noise ratio (SNR) recorded to date, and GW230627\_015337, which features a uniquely prolonged inspiral phase and the highest inspiral phase SNR to date. By performing Bayesian inference on the dimensionless deviation parameters ($δφ_i$) associated with the 4PN and 4.5PN coefficients, we find that our results are fully consistent with the predictions of GR. While the current 90\% credible intervals for the four deviation parameters are of order $\mathcal{O}(1) \text{-} \mathcal{O}(10)$, the general relativistic null values ($δ\hatφ_a= 0$) are entirely encapsulated within the bounds. This investigation establishes the first empirical baseline for 4PN and 4.5PN inspiral tests of GR, paving the way for high-precision null tests of GR with current and next-generation GW detectors. less

The detection of high-frequency gravitational waves (HFGWs) above 10 kHz provides a crucial probe of exotic astrophysical phenomena and new physics. We report the first search for HFGWs via their conversion to electromagnetic radiation through the inverse Gertsenshtein effect in Earth's magnetic field, utilizing radio telescopes including the Very Large Array (VLA) and the Atacama Large Millimeter/submillimeter Array (ALMA). Since no statistically significant signal is observed, we obtain new upper limits on the characteristic strain across the 1 GHz -- 1 THz band, with the most stringent constraint reaching $h_c \lesssim 10^{-18}$, improving upon existing bounds by up to three orders of magnitude. These results significantly advance the exploration of uncharted parameter space for exotic gravitational-wave sources, paving the way for future discoveries with next-generation facilities such as the Square Kilometre Array (SKA). less