We study the quantum channel between two localized first-quantized systems that communicate in $3+1$ 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.
We study the quantum channel between two localized first-quantized systems that communicate in 3+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.
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.
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.
Communication between a free-falling observer and an observer hovering above the Schwarzschild horizon of a black hole suffers from Unruh-Hawking noise, which degrades communication channels. Ignoring time dilation, which affects all channels equally, we show that for bosonic communication using single- and dual-rail encoding, the classical channel capacity reaches a finite value and the quantum coherent information tends to zero. We conclude that classical correlations still exist at infinite acceleration, whereas the quantum coherence is fully removed.
Abstract This study aims to investigate the distribution of distance-based quantum resources for fermionic fields in curved Schwarzschild spacetime (SST), as well as for bosonic fields in both flat Minkowski and curved SSTs. To achieve this, we will examine the quantum resources between an observer falling into a Schwarzschild black hole (SBH) and their stationary partner, who shares a Gisin state. Additionally, we will explore the quantum resources that arise when two uniformly accelerated detectors interact with bosonic fields in the Minkowski vacuum. Furthermore, we will investigate the interactions between these detectors and bosonic fields in the Hartle–Hawking and Boulware vacuums outside the SBH. At an infinite Hawking temperature, the quantum resources for the fermionic fields degrade; the rate of degradation is dependent on the distance between the observer and the event horizon, the fermionic frequency mode, and the Gisin state parameters. In the case of the bosonic fields, our results show that entanglement decreases monotonically, either towards zero or a constant value. Moreover, with increasing Unruh temperature, coherence and discord undergo sudden death followed by a sudden birth, and entanglement cannot be revived for a given initial state. Based on our findings, it appears that the Fermi–Dirac and Bose–Einstein statistics represent the primary differences in quantum resource distribution between the fermionic and bosonic cases. These findings may be essential for enhancing our understanding of the distribution of quantum resources in relativistic frameworks.
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.
Communication between a free-falling observer and an observer hovering above the Schwarzschild horizon of a black hole suffers from Unruh-Hawking noise, which degrades communication channel capacities. Ignoring time dilation, which affects all channels equally, we show that for bosonic communication using single and dual rail encoding the classical channel capacity reaches a finite value and the quantum channel capacity falls off exponentially. The latter defines an effective horizon, beyond which quantum communication becomes exponentially resource inefficient. The characteristic length scale associated with this quantum horizon depends on the mass of the black hole and the frequency of the communication channel.