arXiv subjects

Erickson Tjoa

Publications and source records attributed to Erickson Tjoa.

At least 19 recordsLinked to original sources

arXiv2026

Gaussian-augmented bosonic matrix-product states: theory and applications

We propose and analyze the structure of a family of bosonic quantum many-body states that have the following features: (i) they include all pure Gaussian states and finite-dimensional matrix-product states as subclasses; (ii) their expectation values can be efficiently computed, allowing them to be used, among other things, for variational calculations; (iii) they admit exact parent Hamiltonians expressed as simple functions of the bosonic creation and annihilation operators.

quant-ph↗

arXiv2026

Multi-agent Autoformalization of Tensor Network Theory

We build a team of specialized large language-model agents and present an agent-driven workflow for research-level formalization in theoretical physics, with the autoformalization of the fundamental theorem of matrix-product states as a demonstration. The agents, coordinated through a structured mathematical blueprint and periodic human review, orchestrated and executed the full formalization autonomously. For some statements, the agents were able to explore new proof routes that are not part of the standard literature. Along the way the agents produced extensive tensor-network and quantum-information libraries not previously available in Mathlib, Lean's mathematical library. As a physical application, the formalization also extends towards symmetry-protected topological phases in one dimension. We find that the main bottleneck in large-scale autoformalization is enforcing mathematical intent and we provide a detailed study of the full process and various subtleties involved. We release the codebase as the library \href{https://github.com/LionSR/TNLean}{TNLean}, together with a \nChapters{}-chapter \href{https://lionsr.github.io/TNLean/blueprint/}{blueprint} of the formalization effort.

quant-ph↗

arXiv2025

Continuous matrix product operators for quantum fields

In this work we introduce an ansatz for continuous matrix product operators for quantum field theory. We show that (i) they admit a closed-form expression in terms of finite number of matrix-valued functions without reference to any lattice parameter; (ii) they are obtained as a suitable continuum limit of matrix product operators; (iii) they preserve the entanglement area law directly in the continuum, and in particular they map continuous matrix product states (cMPS) to another cMPS. As an application, we use this ansatz to construct several families of continuous matrix product unitaries beyond quantum cellular automata.

quant-ph↗

arXiv2025

Bipartite and tripartite entanglement in pure dephasing relativistic spin-boson model

We study nonperturbatively the entanglement generation between two and three emitters in an exactly solvable relativistic variant of the spin-boson model, equivalent to the time-independent formulation of the Unruh-DeWitt detector model. We show that (i) (highly) entangled states of the two emitters require interactions very deep into the light cone, (ii) the mass of the field can generically improve the entanglement generation, (iii) while it is possible to find regimes with genuine Greenberger-Horne-Zeilinger-like tripartite entanglement, it is difficult find regimes where tripartite entanglement can be easily shown to be significant or classified. Result (iii), in particular, suggests that probing the multipartite entanglement of a relativistic quantum field nonperturbatively requires either different probe-based techniques or variants of the Unruh-DeWitt model. Along the way, we provide the regularity conditions for the $N$-emitter model to have well-defined ground states in the Fock space.

quant-ph↗

arXiv2024

Transmission of quantum information through quantum fields in curved spacetimes

We construct a relativistic quantum communication channel between two localized qubit systems, mediated by a relativistic quantum field, that can achieve the theoretical maximum for the quantum capacity in arbitrary curved spacetimes using the Unruh-DeWitt detector formalism. Using techniques from algebraic quantum field theory, we express the quantum capacity of the quantum communication channel purely in terms of the correlation functions of the field and the causal propagator for the wave equation. Consequently, the resulting quantum channel, and hence the quantum capacity, are by construction manifestly covariant, respect the causal structure of spacetime, and are independent of the details of the background geometry, topology, and the choice of Hilbert space (quasifree) representations of the field.

quant-ph↗

arXiv2024

Particle detectors under chronological hazard

We analyze how the presence of closed timelike curves (CTCs) characterizing a time machine can be discerned by placing a local particle detector in a region of spacetime which is causally disconnected from the CTCs. Our study shows that not only can the detector tell if there are CTCs, but also that the detector can separate topological from geometrical information and distinguish periodic spacetimes without CTCs (like the Einstein cylinder), curvature, and spacetimes with topological identifications that enable time-machines.

quant-ph↗

arXiv2024

The Unruh-DeWitt model and its joint interacting Hilbert space

In this work we make the connection between the Unruh-DeWitt particle detector model applied to quantum field theory in curved spacetimes and the rigorous construction of the spin-boson model. With some modifications, we show that existing results about the existence of a spin-boson ground state can be adapted to the Unruh-DeWitt model. In the most relevant scenario involving massless scalar fields in (3+1)-dimensional globally hyperbolic spacetimes, where the Unruh-DeWitt model describes a simplified model of light-matter interaction, we argue that common choices of the spacetime smearing functions regulate the ultraviolet behaviour of the model but can still exhibit infrared divergences. In particular, this implies the well-known expectation that the joint interacting Hilbert space of the model cannot be described by the tensor product of a two-dimensional complex Hilbert space and the Fock space of the vacuum representation. We discuss the conditions under which this problem does not arise and the relevance of the operator-algebraic approach for better understanding of particle detector models and their applications. Our work clarifies the connection between obstructions due to Haag's theorem and infrared bosons in the spin-boson models, and paves the way for more rigorous study of entanglement and communication in the UDW framework involving multiple detectors.

quant-ph↗

arXiv2023

Unruh phenomena and thermalization for qudit detectors

We study Unruh phenomena for a qudit detector coupled to a quantized scalar field, comparing its response to that of a standard qubit-based Unruh-DeWitt detector. We show that there are limitations to the utility of the detailed balance condition as an indicator for Unruh thermality of higher-dimensional qudit detector models. This can be traced to the fact that a qudit has multiple possible transition channels between its energy levels, in contrast to the 2-level qubit model. We illustrate these limitations using two types of qutrit detector models based on the spin-1 representations of $SU(2)$ and the non-Hermitian generalization of the Pauli observables (the Heisenberg-Weyl operators).

quant-ph↗

arXiv2023

Wigner function for quantum field theory via spacetime tiling

We present a construction of the Wigner function for a bosonic quantum field theory that has well-defined ultraviolet (UV) and infrared (IR) properties. Our construction uses the local mode formalism in algebraic quantum field theory that is valid in any globally hyperbolic curved spacetimes, i.e., without invoking the path integral formalism. The idea is to build $N$ quantum harmonic oscillators degrees of freedom from $2N$ smeared field operators and use them to "tile" a Cauchy surface of the spacetime manifold. The smallest support of the smearing functions that define each local mode define the UV scale and the number of modes local modes fix the IR scale. This construction can be viewed as a form of "covariant discretization" of the quantum field in curved spacetimes, since the tiling of the Cauchy surface does not depend on any choice of coordinate systems or foliation.

quant-ph↗

arXiv2023

Fuzzy spacetime: fundamental limits of quantum-optical holographic bulk reconstruction

In this Essay we construct a concrete, non-perturbative realization of metric reconstruction using quantum-optical model of particle detectors in relativistic quantum information. The non-perturbative approach allows us to realize a version of "short-distance physics corresponds to poor statistics" idea by Kempf which occurs way above the Planck scale before one reaches the quantum-gravitational regime. In particular, the "fuzziness" of spacetime that arise from operational measurement protocols can be given a holographic dual interpretation using bulk-to-boundary correspondence between scalar correlators in asymptotically flat spacetimes. The holographic interpretation necessitates imperfect metric reconstruction even in principle due to the universality of future null infinity.

gr-qc↗

arXiv2022

Effective master equations for two accelerated qubits

We revisit the problem involving two constantly accelerating Unruh-DeWitt detectors using Open Effective Field Theory methods. We study the time evolution of the joint detector state using a Markovian approximation which differs from the standard one taken in the literature. We show that this Markovian limit already implies the complete positivity of the dynamical evolution map without invoking the rotating wave approximation (RWA), in contrast to standard derivations of open system master equations. By calculating explicitly the domain of validity of this Markovian approximation, we argue that the lack of complete positivity in the usual microscopic derivation stems from the (subtle) fact that the Redfield equation is used outside its domain of validity. We give two well-known cases studied in the literature that violate the validity of the Markovian approximation: (i) the ``stacked trajectory'' limit (when detector trajectories are taken to be on top of one another), and (ii) large gap-to-acceleration ratio. Since Markovian dynamics with or without RWA can lead to different qualitative predictions for entanglement dynamics, our work emphasizes the need to properly track the regime of validity of all approximations.

quant-ph↗

arXiv2022

Non-perturbative simple-generated interactions with a quantum field for arbitrary Gaussian states

In this work we first collect and generalize several existing non-perturbative models for the interaction between a single two-level qubit detector and a relativistic quantum scalar field in arbitrary curved spacetimes, where the time evolution is given by simple-generated unitaries, i.e., those generated by Schmidt rank-1 interaction Hamiltonians. We then extend the relativistic quantum channel associated to these non-perturbative models to include a very large class of Gaussian states of the quantum field, that includes an arbitrary combinations of coherent and squeezing operations (i.e., Gaussian operations) on the field. We show that all physical results involving the non-vacuum Gaussian states can be rephrased in terms of interaction with the vacuum state but with Gaussian operators applied to the field operators via the adjoint channel, effectively giving a "Fourier transformed" interpretation of the Gaussian operations in terms of the causal propagators in spacetime. Furthermore, we show that in these non-perturbative models it is possible to perform exact computation of the R\'enyi entropy and hence, via the replica trick, the von Neumann entropy for the field state after the interaction with the detector, without making any assumptions about the purity of the joint initial states of the detector and the field. This gives us a three-parameter family of "generalized cat states" of the field whose entropies are finite and exactly computable.

quant-ph↗

arXiv2022

Quantum teleportation with relativistic communication from first principles

In this work we provide a genuine relativistic quantum teleportation protocol whose classical communication component makes use of relativistic causal propagation of a quantum field. Consequently, the quantum teleportation is fully relativistic by construction. Our scheme is based on Unruh-DeWitt qubit detector model, where the quantum state being teleported is associated to an actual qubit rather than a field mode considered by Alsing and Milburn [PRL 91, 180404 (2003)]. We show that the existing works in (relativistic) quantum information, including good definitions of one-shot and asymptotic channel capacities, as well as algebraic formulation of quantum field theory, already provide us with all the necessary ingredients to construct fundamentally relativistic teleportation protocol in relatively straightforward manner.

quant-ph↗

arXiv2022

Fermi two-atom problem: non-perturbative approach via relativistic quantum information and algebraic quantum field theory

In this work we revisit the famous Fermi two-atom problem, which concerns how relativistic causality impacts atomic transition probabilities, using the tools from relativistic quantum information (RQI) and algebraic quantum field theory (AQFT). The problem has sparked different analyses from many directions and angles since the proposed solution by Buchholz and Yngvason (1994). Some of these analyses employ various approximations, heuristics, perturbative methods, which tends to render some of the otherwise useful insights somewhat obscured. It is also noted that they are all studied in flat spacetime. We show that current tools in relativistic quantum information, combined with algebraic approach to quantum field theory, are now powerful enough to provide fuller and cleaner analysis of the Fermi two-atom problem for arbitrary curved spacetimes in a completely non-perturbative manner. Our result gives the original solution of Buchholz and Yngvason a very operational reinterpretation in terms of qubits interacting with a quantum field, and allows for various natural generalizations and inclusion of detector-based local measurement for the quantum field (Phys. Rev. D 105, 065003).

quant-ph↗

arXiv2022

Modest holography and bulk reconstruction in asymptotically flat spacetimes

In this work we present a "modest" holographic reconstruction of the bulk geometry in asymptotically flat spacetime using the two-point correlators of boundary quantum field theory (QFT) in asymptotically flat spacetime. The boundary QFT lives on the null boundary of the spacetime, namely null infinity and/or the Killing horizons. The bulk reconstruction relies on two unrelated results: (i) there is a bulk-to-boundary type correspondence between free quantum fields living in the bulk manifold and free quantum fields living on its null boundary, and (ii) one can construct the metric by making use of the Hadamard expansion of the field living in the bulk. This holographic reconstruction is "modest" in that the fields used are non-interacting and not strong-weak holographic duality in the sense of AdS/CFT, but it works for generic asymptotically flat spacetime subject to some reasonably mild conditions.

gr-qc↗

arXiv2022

Holographic reconstruction of asymptotically flat spacetimes

We present a "holographic" reconstruction of bulk spacetime geometry using correlation functions of a massless field living at the "future boundary" of the spacetime, namely future null infinity $\mathscr{I}^+$. It is holographic in the sense that there exists a one-to-one correspondence between correlation functions of a massless field in four-dimensional spacetime $\mathcal{M}$ and those of another massless field living in three-dimensional null boundary $\mathscr{I}^+$. The idea is to first reconstruct the bulk metric $g_{\mu\nu}$ by "inverting" the bulk correlation functions and re-express the latter in terms of boundary correlators via the correspondence. This effectively allows asymptotic observers close to $\mathscr{I}^+$ to reconstruct the deep interior of the spacetime using only correlation functions localized near $\mathscr{I}^+$.

hep-th↗

arXiv2022

Channel capacity of relativistic quantum communication with rapid interaction

In this work we study nonperturbatively the transmission of classical and quantum information in globally hyperbolic spacetimes, where the communication channel is between two qubit detectors interacting with a quantized massless scalar field via delta-coupling interaction. This interaction approximates very rapid detector-field interaction, effectively occurring at a single instant in time for each detector. We show that when both detectors interact via delta-coupling, one can arrange and tune the detectors so that the channel capacity is (at least) as good as the quantum channel constructed nonperturbatively using \textit{gapless detectors} by Landulfo [PRD 93, 104019]. Furthermore, we prove that this channel capacity is in fact optimal, i.e., both nonperturbative methods give essentially the same channel capacity, thus there is a sense in which the two methods can be regarded as equivalent as far as relativistic quantum communication is concerned.

quant-ph↗

arXiv2022

Unruh-DeWitt detector in dimensionally-reduced static spherically symmetric spacetimes

We study the dynamics of an Unruh-DeWitt detector interacting with a massless scalar field in an arbitrary static spherically symmetric spacetimes whose metric is characterised by a single metric function $f(r)$. In order to obtain clean physical insights, we employ the derivative coupling variant of the Unruh-DeWitt model in (1+1) dimensions where powerful conformal techniques enable closed-form expressions for the vacuum two-point functions. Due to the generality of the formalism, we will be able to study a very general class of static spherically symmetric (SSS) background. We pick three examples to illustrate our method: (1) non-singular Hayward black holes, (2) the recently discovered $D\to 4$ limit of Gauss-Bonnet black holes, and (3) the "black bounce" metric that interpolates Schwarzschild black holes and traversable wormholes. We also show that the derivative coupling Wightman function associated with the generalized Hartle-Hawking vacuum satisfies the KMS property with the well-known temperature $f'(r_\text{H})/(4\pi)$, where $r_\text{H}$ is the horizon radius.

gr-qc↗