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arXiv:2408.00518 · Journal of Physics A Mathematical and Theoretical

Transmission of quantum information through quantum fields in curved spacetimes

Michael Kasprzak, Erickson Tjoa

Published Feb 14, 2025• 9 citations
arXivHTMLPDF

Abstract

Abstract 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.

DOI
10.1088/1751-8121/adb66b

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Abstract 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.
We investigate the transmission of both classical and quantum information between two arbitrary observers in globally hyperbolic spacetimes using a quantum field as a communication channel. The field is supposed to be in some arbitrary quasifree state and no choice of representation of its canonical commutation relations is made. Both sender and receiver possess some localized two-level quantum system with which they can interact with the quantum field to prepare the input and receive the output of the channel, respectively. The interaction between the two-level systems and the quantum field is such that one can trace out the field degrees of freedom exactly and thus obtain the quantum channel in a nonperturbative way. We end the paper determining the unassisted as well as the entanglement-assisted classical and quantum channel capacities.
In this paper we provide a genuine relativistic quantum teleportation protocol the classical communication component of which makes use of relativistic causal propagation of a quantum field. Consequently, the quantum teleportation is fully relativistic by construction. Our scheme is based on the Unruh-DeWitt qubit detector model, where the quantum state being teleported is associated to an actual qubit rather than the field mode considered by Alsing and Milburn [P. M. Alsing and G. J. Milburn, Phys. Rev. Lett. 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 a fundamentally relativistic teleportation protocol in a relatively straightforward manner.
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Abstract The quantum channel between two particle detectors provides a prototype framework for the study of wireless quantum communication via relativistic quantum fields. In this article we calculate the classical channel capacity between two Unruh–DeWitt detectors arising from couplings within the perturbative regime. To this end, we identify the detector states which achieve maximal signal strength. We use these results to investigate the impact of relativistic effects on signaling between detectors in inertial and uniformly accelerated motion which communicate via a massless field in Minkowski spacetime.
We investigate the transmission of classical and quantum information between three observers in a general globally hyperbolic spacetime using a quantum scalar field as a communication channel. We build a model for a quantum broadcast channel in which one observer (sender) wishes to transmit (classical and quantum) information to two other observers (receivers). They possess some localized two-level quantum system (a qubit) that can interact with the quantum field in order to prepare an input or receive the output of this channel. The field is supposed to be in an arbitrary quasifree state, the three observers may be in arbitrary states of motion, and no choice of representation of the field canonical commutation relations is made. The interaction of the field and qubits is such that it allows us to obtain the map that describes this channel in a non-perturbative manner. We conclude by analyzing the rates at which information can be transmitted through this channel and by investigating relativistic causality effects on such rates.
We study the quantum channel between two localized first-quantized systems that communicate in 3+13+13+1 dimensional Schwarzschild spacetime via a quantum field. We analyze the information carrying capacity of direct and black hole-orbiting null geodesics as well as of the timelike contributions that arise because the strong Huygens principle does not hold on the Schwarzschild background. We find, in particular, that the nondirect-null and timelike contributions, which do not possess an analog on Minkowski spacetime, can dominate over the direct null contributions. We cover the cases of both geodesic and accelerated emitters. Technically, we apply tools previously designed for the study of wave propagation in curved spacetimes to a relativistic quantum information communication setup, first for generic spacetimes, and then for the case of Schwarzschild spacetime in particular.