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arXiv:2202.12301 · Physical review. D/Physical review. D.

Channel capacity of relativistic quantum communication with rapid interaction

Erickson Tjoa, Kensuke Gallock‐Yoshimura

Published Apr 19, 2022• 27 citations
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Abstract

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 gapless detectors by Landulfo [Phys. Rev. D 93, 104019 (2016) ]. 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.

DOI
10.1103/physrevd.105.085011

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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 gapless detectors by Landulfo [Phys. Rev. D 93, 104019 (2016) ]. 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.
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.
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 nonperturbative 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 propose a model of communication employing two harmonic oscillator detectors interacting through a scalar field in a background Minkowski spacetime. In this way, the scalar field plays the role of a quantum channel, namely a bosonic Gaussian channel. The classical and quantum capacities of the communication channel are found, assuming that the detectors' spatial dimensions are negligible compared to their distance. In particular, we study the evolution in time of the classical capacity after the detectors-field interaction is switched on for various detectors' frequencies and coupling strengths with the field. As a result, we find a finite value of these parameters optimizing the communication of classical messages. Instead, a reliable communication of quantum messages turns out to be always inhibited.
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 consider the communication of classical and quantum information between two arbitrary observers in asymptotically flat spacetimes (possibly containing black holes) and investigate what the energy cost is for such information transmission. By means of localized two-level quantum systems, sender and receiver can use a quantum scalar field as a communication channel. As we have already shown in a previous paper, such a channel has nonvanishing classical capacity as well as entanglement-assisted classical and quantum capacities. Here we will show that the change in the expectation value of the energy of the system during the communication process can be separated in (i) a contribution coming from the particle creation due to the change of the spacetime, (ii) a contribution associated with the energy needed to switch on or off each qubit, and (iii) a term which comes from the communication process itself. For the quantum channel considered here, we show that the extra energy cost needed for communication vanishes. As a result, if one has already created a system of qubits for some specific task (e.g., quantum computation), one can also reliably convey information between its parts with no extra energy cost. We conclude the paper by illustrating the form of the channel capacities and energy contributions in two paradigmatic cases in Minkowski spacetime: (i) sender and receiver in inertial motion and (ii) sender in inertial motion while the receiver is uniformly accelerated.