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arXiv:2109.13896 · Physical review. D/Physical review. D.

Relativistic quantum communication: Energy cost and channel capacities

Ian Bernardes Barcellos, André G. S. Landulfo

Published Nov 22, 2021• 17 citations
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Abstract

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.

DOI
10.1103/physrevd.104.105018

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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.
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 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.
Information and energy are concepts central to our understanding of nature. Their relevance, in physics, ranges from fundamental physics, e.g., in black hole physics, all the way to future quantum computing technology. This thesis investigates how information and energy propagate in quantum fields. The main result is that in massless fields the propagation of information can decouple from the propagation of energy partially and, under special circumstances, even completely. \n \nIt has been known that in general curved spacetimes, and also in odd-dimensional Minkowski space, signals can propagate slower than light even in a massless field. Here it is shown that the energy-to-information ratio of these classical timelike signals can approach zero. The extreme case is marked by two-dimensional Minkowski space. In this case, timelike signals reach arbitrarily far into the future lightcone, without diluting, and they carry no energy at all. Instead, the energy cost associated with the detection of energyless signals has to be provided by the receiver, much as in a collect call. \n \nTechnically, sender and receiver are modelled as basic first-quantized systems coupling locally to the relativistic quantum field, i.e., as Unruh-DeWitt particle detectors. This gives rise to a standard quantum channel from the sender to the receiver. Thus, the tools of quantum information can be applied to investigate the combined impact of relativistic and quantum effects on the propagation of information. \n \nIn the perturbative regime, signals analogous to phase modulation are shown to over- come signals analogous to amplitude modulation: It is shown that the sender has to prepare superpositions of eigenstates, to achieve signalling effects at leading order. Signals from pure energy eigenstates are subdominant, and only appear in next-to-leading order. The classical channel capacities resulting from optimal signalling states are calculated. \n \nAnalyzing the energy injected into the field by the sender, it is shown that signals reach further in spacetime than the energy radiated by the sender, both for timelike, as well as for lightlike signals. Instead, the energy budget is balanced by the energy that the receiver has to provide when decoupling the detector from the field. This switching cost is particularly sensitive to timelike signals. \n \nTimelike signals are also demonstrated to occur between harmonic oscillators coupling to the field inside a cavity. This model could be instrumental for future research, because it can be treated non-perturbatively using Gaussian methods. \n \nSuch numerical calculations only take into account a finite number of field modes. It is shown that relativistic properties of the field can still be resolved reliably, because the number of necessary modes scales with the desired accuracy, namely following a power law.
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.
A communication protocol with nonzero quantum capacity is found when the two communicating parts are particle detector models in ( 3 + 1 )-dimensional spacetime. In particular, as detectors, we consider two harmonic oscillators interacting with a scalar field, whose evolution is generalized for whatever background spacetime and whatever spacetime smearing of the detectors. We then specialize to Minkowski spacetime and an initial Minkowski vacuum, considering a rapid interaction between the field and the two detectors, studying the case where the receiver is static and the sender is moving. The possibility to have a quantum capacity greater than zero stems from a relative acceleration between the detectors. Indeed, no reliable quantum communication is possible when the two detectors are static or moving inertially with respect to each other, but a reliable quantum communication can be achieved between a uniformly accelerated sender and an inertial receiver. Published by the American Physical Society 2024
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.