arXiv subjects

Stephen D. H. Hsu

Publications and source records attributed to Stephen D. H. Hsu.

At least 19 recordsLinked to original sources

arXiv2026

Quantum State of the Asymptotic Gravity Field from BRST Quantization

We derive the quantum state of the asymptotic linearized gravity field of a compact energy source, using BRST quantization. Barnich has previously derived the quantum state of the U(1) field in QED using the Gauss law constraint. The role of Gauss's law is now played by the linearized Hamiltonian and momentum constraints in gravity. For a static mass source, only the scalar Hamiltonian constraint is shifted. The quantum state corresponding to the static Newton field originates in the non-radiative scalar constraint sector, not in the propagating transverse-traceless graviton sector. We discuss implications for holography and for black hole information: 1. the exact quantum state of the compact source is encoded in the asymptotic quantum state of its gravity field 2. Hawking amplitudes are dependent, via the gravity state outside the horizon, on the black hole internal state.

hep-th↗

arXiv2026

Embedded AI Companion System on Edge Devices

Computational resource constraints on edge devices make it difficult to develop a fully embedded AI companion system with a satisfactory user experience. AI companion and memory systems detailed in existing literature cannot be directly used in such an environment due to lack of compute resources and latency concerns. In this paper, we propose a memory paradigm that alternates between active and inactive phases: during phases of user activity, the system performs low-latency, real-time dialog using lightweight retrieval over existing memories and context; whereas during phases of user inactivity, it conducts more computationally intensive extraction, consolidation, and maintenance of memories across full conversation sessions. This design minimizes latency while maintaining long-term personalization under the tight constraints of embedded hardware. We also introduce an AI Companion benchmark designed to holistically evaluate the AI Companion across both its conversational quality and memory capabilities. In our experiments, we found that our system (using a very weak model: Qwen2.5-7B-Instruct quantized int4) outperforms the equivalent raw LLM without memory across most metrics, and performs comparably to GPT-3.5 with 16k context window.

cs.AI↗

arXiv2025

Leading order effective operators in quantum gravity

We explore the nature of higher dimensional operators generated by quantum gravity. Calculating the tree-level and one-loop effective operators generated by graviton exchange between fields of the standard model and those of a hidden sector, we show that the leading order operators generated by quantum gravity are non-local dimension 6 operators. Dimension 5 operators are not generated by perturbative (weak field) effects, although they might be generated by strong field effects such as Planck-scale fluctuations in spacetime. We investigate the consequences of our findings for models of ultralight scalar dark matter.

hep-th↗

arXiv2025

Relativistic Covariance and Nonlinear Quantum Mechanics: Tomonaga-Schwinger Analysis

We use the Tomonaga-Schwinger (TS) formulation of quantum field theory to determine when state-dependent additions to the local Hamiltonian density (i.e., modifications to linear Schrodinger evolution) violate relativistic covariance. We derive new operator integrability conditions required for foliation independence, including the Frechet derivative terms that arise from state-dependence. Nonlinear modifications of quantum mechanics affect operator relations at spacelike separation, leading to violation of the integrability conditions.

hep-th↗

arXiv2024

Black Hole Information, Replica Wormholes, and Macroscopic Entanglement

In this invited review, we discuss the evaporation of a black hole, with emphasis on the resulting macroscopically distinct patterns of Hawking radiation. The density matrix of this radiation can approach a pure final state in the form of a highly entangled macroscopic superposition state. We note that this exact property is exhibited in replica wormhole calculations, and also in quantum hair effects on Hawking radiation amplitudes. Finally, we revisit the information paradox (Mathur's theorem and firewalls), showing that it can be resolved by macroscopic entanglement.

hep-th↗

arXiv2024

Replica Wormholes and Quantum Hair

We discuss recent applications of Euclidean path integrals to the black hole information problem. In calculations with replica wormholes as the next-to-leading order correction to the Gibbons-Hawking saddlepoint, the radiation density matrix approaches a pure state at late times, following the Page curve. We compare unitary evaporation of black holes (in real time), mediated by calculable quantum hair effects, with the replica wormhole results. Both replica wormhole and quantum hair approaches imply that radiation states are macroscopic superpositions of spacetime backgrounds, invalidating firewall and monogamy of entanglement constructions. Importantly, identification of modes inside the horizon with radiation modes (i.e., large scale nonlocality across the horizon) is not required to provide a physical picture of unitary evaporation. Radiation modes can encode the interior information while still remaining independent degrees of freedom.

hep-th↗

arXiv2023

Quantum Hair During Gravitational Collapse

We consider quantum gravitational corrections to the Oppenheimer-Snyder metric describing time-dependent dust ball collapse. The interior metric also describes Friedmann-Lemaitre-Robertson-Walker cosmology and our results are interpreted in that context. The exterior corrections are an example of quantum hair, and are shown to persist throughout the collapse. Our results show the quantum hair survives throughout the horizon formation and that the internal state of the resulting black hole is accessible to outside observers.

hep-th↗

arXiv2023

Quantum Gravitational Corrections to Particle Creation by Black Holes

We calculate quantum gravitational corrections to the amplitude for the emission of a Hawking particle by a black hole. We show explicitly how the amplitudes depend on quantum corrections to the exterior metric (quantum hair). This reveals the mechanism by which information escapes the black hole. The quantum state of the black hole is reflected in the quantum state of the exterior metric, which in turn influences the emission of Hawking quanta.

hep-th↗

arXiv2022

Decoherence and Quantum Measurement: The Missing Lecture

We give an elementary account of quantum measurement and related topics from the modern perspective of decoherence. The discussion should be comprehensible to students who have completed a basic course in quantum mechanics with exposure to concepts such as Hilbert space, density matrices, and von Neumann projection (``wavefunction collapse'').

quant-ph↗

arXiv2022

Quantum Hair in Electrodynamics and Gravity

We demonstrate the existence of quantum hair in electrodynamics and gravity using effective action techniques. In the case of electrodynamics we use the Euler-Heisenberg effective action while in the case of quantum gravity we use the unique effective action. We give a general formulation of these effects which applies to both theories and discuss analogies and differences between them. Furthermore, we present a QED analog to black hole evaporation. Spontaneous pair production in the external field of a ball of charge is analogous to Hawking radiation from black holes. Assuming spherical symmetry, the Gauss law prevents the external field from depending on the density profile of the ball. Quantum corrections violate these expectations, showing that quantum radiation can encode classically forbidden information about the source.

hep-th↗

arXiv2022

Quantum Hair from Gravity

We explore the relationship between the quantum state of a compact matter source and of its asymptotic graviton field. For a matter source in an energy eigenstate, the graviton state is determined at leading order by the energy eigenvalue. Insofar as there are no accidental energy degeneracies there is a one to one map between graviton states on the boundary of spacetime and the matter source states. A typical semiclassical matter source results in an entangled asymptotic graviton state. We exhibit a purely quantum gravitational effect which causes the subleading asymptotic behavior of the graviton state to depend on the internal structure of the source. These observations establish the existence of ubiquitous quantum hair due to gravitational effects.

hep-th↗

arXiv2022

A Brief History of Hawking's Information Paradox

In this invited review, we describe Hawking's information paradox and a recently proposed resolution of it. Explicit calculations demonstrate the existence of quantum hair on black holes, meaning that the quantum state of the external graviton field depends on the internal state of the black hole. Simple quantum mechanics then implies that Hawking radiation amplitudes depend on the internal state, resulting in a pure final radiation state that preserves unitarity and, importantly, violates a factorization assumption which is central to the original paradox. Black hole information is encoded in entangled macroscopic superposition states of the radiation.

hep-th↗

arXiv2022

Quantum Hair and Black Hole Information

It has been shown that the quantum state of the graviton field outside a black hole horizon carries information about the internal state of the hole. We explain how this allows unitary evaporation: the final radiation state is a complex superposition which depends linearly on the initial black hole state. Under time reversal, the radiation state evolves back to the original black hole quantum state. Formulations of the information paradox on a fixed semiclassical geometry describe only a small subset of the evaporation Hilbert space, and do not exclude overall unitarity.

hep-th↗

arXiv2021

Fundamental Limit on Angular Measurements and Rotations from Quantum Mechanics and General Relativity

We show that the precision of an angular measurement or rotation (e.g., on the orientation of a qubit or spin state) is limited by fundamental constraints arising from quantum mechanics and general relativity (gravitational collapse). The limiting precision is $r^{-1}$ in Planck units, where $r$ is the physical extent of the (possibly macroscopic) device used to manipulate the spin state. This fundamental limitation means that spin states $S_1$ and $S_2$ cannot be experimentally distinguished from each other if they differ by a sufficiently small rotation. Experiments cannot exclude the possibility that the space of quantum state vectors (i.e., Hilbert space) is fundamentally discrete, rather than continuous. We discuss the implications for finitism: does physics require infinity or a continuum?

quant-ph↗

arXiv2021

Macroscopic Superposition States in Isolated Quantum Systems

For any choice of initial state and weak assumptions about the Hamiltonian, large isolated quantum systems undergoing Schrodinger evolution spend most of their time in macroscopic superposition states. The result follows from von Neumann's 1929 Quantum Ergodic Theorem. As a specific example, we consider a box containing a solid ball and some gas molecules. Regardless of the initial state, the system will evolve into a quantum superposition of states with the ball in macroscopically different positions. Thus, despite their seeming fragility, macroscopic superposition states are ubiquitous consequences of quantum evolution. We discuss the connection to many worlds quantum mechanics.

quant-ph↗

arXiv2021

From Genotype to Phenotype: polygenic prediction of complex human traits

Decoding the genome confers the capability to predict characteristics of the organism(phenotype) from DNA (genotype). We describe the present status and future prospects of genomic prediction of complex traits in humans. Some highly heritable complex phenotypes such as height and other quantitative traits can already be predicted with reasonable accuracy from DNA alone. For many diseases, including important common conditions such as coronary artery disease, breast cancer, type I and II diabetes, individuals with outlier polygenic scores (e.g., top few percent) have been shown to have 5 or even 10 times higher risk than average. Several psychiatric conditions such as schizophrenia and autism also fall into this category. We discuss related topics such as the genetic architecture of complex traits, sibling validation of polygenic scores, and applications to adult health, in vitro fertilization (embryo selection), and genetic engineering.

q-bio.GN↗

arXiv2020

Discrete Hilbert Space, the Born Rule, and Quantum Gravity

Quantum gravitational effects suggest a minimal length, or spacetime interval, of order the Planck length. This in turn suggests that Hilbert space itself may be discrete rather than continuous. One implication is that quantum states with norm below some very small threshold do not exist. The exclusion of what Everett referred to as maverick branches is necessary for the emergence of the Born Rule in no collapse quantum mechanics. We discuss this in the context of quantum gravity, showing that discrete models (such as simplicial or lattice quantum gravity) indeed suggest a discrete Hilbert space with minimum norm. These considerations are related to the ultimate level of fine-graining found in decoherent histories (of spacetime geometry plus matter fields) produced by quantum gravity.

gr-qc↗

arXiv2020

Theta terms and asymptotic behavior of gauge potentials in (3+1) dimensions

We describe paths in the configuration space of (3+1) dimensional QED whose relative quantum phase (or relative phase in the functional integral) depends on the value of the theta angle. The final configurations on the two paths are related by a gauge transformation but differ in magnetic helicity or Chern-Simons number. Such configurations must exhibit gauge potentials that fall off no faster than 1/r in some region of finite solid angle, although they need not have net magnetic charge (i.e., are not magnetic monopoles). The relative phase is proportional to theta times the difference in Chern-Simons number. We briefly discuss some possible implications for QCD and the strong CP problem.

hep-th↗