Erickson Tjoa

In this work, we introduce an ansatz for continuous matrix-product operators for quantum field theory. We show that (1) they admit a closed-form expression in terms of finite number of matrix-valued functions without reference to any lattice parameter; (2) they are obtained as a suitable continuum limit of matrix-product operators; and (3) they preserve the entanglement area law directly in the continuum, and in particular they map a continuous matrix-product state (cMPS) to another cMPS. As an application, we use this ansatz to construct several families of continuous matrix-product unitaries beyond quantum cellular automata.

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.

In this work we make the connection between the Unruh–DeWitt (UDW) particle detector model applied to quantum field theory in curved spacetimes and the rigorous construction of the spin-boson (SB) model. With some modifications, we show that existing results about the existence of a SB ground state can be adapted to the UDW model. In the most relevant scenario involving massless scalar fields in (3+1)-dimensional globally hyperbolic spacetimes, where the UDW 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 (IR) 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 IR bosons in the SB models, and paves the way for more rigorous study of entanglement and communication in the UDW framework involving multiple detectors.

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.

In this work we first collect and generalize several existing nonperturbative 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 nonperturbative models to include a very large class of Gaussian states of the quantum field, that includes an arbitrary combination of coherent and squeezing operations (i.e., Gaussian operations) on the field. We show that all physical results involving the nonvacuum 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 nonperturbative models it is possible to perform exact computation of the Rényi 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.

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.

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.