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arXiv:2103.07374 · Physical review. D/Physical review. D.

Quantum communication through a partially reflecting accelerating mirror

Michael R. R. Good, Alessio Lapponi, Orlando Luongo, Stefano Mancini

Published Nov 29, 2021• 24 citations
arXivHTMLPDF

Abstract

Motivated by the fact that the null shell of a collapsing black hole can be described by a perfectly reflecting accelerating mirror, we investigate an extension of this model to mirror semitransparency and derive a general implicit expression for the corresponding Bogolyubov coefficients. Then, we turn this into an explicit analytical form by focusing on mirrors that are accelerated via an impulsive force. From the so-obtained Bogolyubov coefficients we derive the particle production. Finally, we realize the field coming from the left-past spacetime region, passing through the semitransparent moving mirror and ending up to the right-future spacetime region as undergoing the action of a Gaussian quantum channel. We study the transmission and noisy generation properties of this channel, relating them to the Bogolyubov coefficients of the mirror's motion, through which we evaluate capacities in transmitting classical and quantum information.

DOI
10.1103/physrevd.104.105020

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Motivated by the fact that the null shell of a collapsing black hole can be described by a perfectly reflecting accelerating mirror, we investigate an extension of this model to mirror semitransparency and derive a general implicit expression for the corresponding Bogolyubov coefficients. Then, we turn this into an explicit analytical form by focusing on mirrors that are accelerated via an impulsive force. From the so-obtained Bogolyubov coefficients we derive the particle production. Finally, we realize the field coming from the left-past spacetime region, passing through the semitransparent moving mirror and ending up to the right-future spacetime region as undergoing the action of a Gaussian quantum channel. We study the transmission and noisy generation properties of this channel, relating them to the Bogolyubov coefficients of the mirror's motion, through which we evaluate capacities in transmitting classical and quantum information.
We study the properties of the quantum information transmission channel that emerges from the quantum dynamics of particles interacting with a black hole horizon. We calculate the quantum channel capacity in two limiting cases where a single-letter capacity is known to exist: the limit of perfectly reflecting and perfectly absorbing black holes. We find that the perfectly reflecting black hole channel is closely related to the Unruh channel and that its capacity is non-vanishing, allowing for the perfect reconstruction of quantum information outside of the black hole horizon. We also find that the complementary channel (transmitting entanglement behind the horizon) is entanglement-breaking in this case, with vanishing capacity. We then calculate the quantum capacity of the black hole channel in the limit of a perfectly absorbing black hole and find that this capacity vanishes, while the capacity of the complementary channel is non-vanishing instead. Rather than inviting a new crisis for quantum physics, this finding instead is in accordance with the quantum no-cloning theorem, because it guarantees that there are no space-like surfaces that contain both the sender’s quantum state and the receiver’s reconstructed quantum state.
Light reflection on a mirror can be thought as a simple physical effect. However if this happens when the mirror moves a rich scenario opens up. Here we aim at analyzing it from a quantum communication perspective. In particular, we study the kind of quantum channel that arises from (Gaussian) light reflection upon an accelerating mirror. Two competing mechanisms emerge in such a context, namely photons production by the mirror's motion and interference between modes. As consequence we find out a quantum amplifier channel and quantum lossy channel respectively below and above a threshold frequency (that depends on parameters determining mirror's acceleration). Exactly at the threshold frequency the channel behaves like a purely classical additive channel, while it becomes purely erasure for large frequencies. In addition the time behavior of the channel is analyzed by employing wave packets expansion of the light field.
We study the properties of the quantum information transmission channel that emerges from the quantum dynamics of particles interacting with a black hole horizon. We calculate the quantum channel capacity in two limiting cases where a single-letter capacity is known to exist: the limit of perfectly reflecting and perfectly absorbing black holes. We find that the perfectly reflecting black hole channel is closely related to the Unruh channel and that its capacity is non-vanishing, allowing for the perfect reconstruction of quantum information outside of the black hole horizon. We also find that the complementary channel (transmitting entanglement behind the horizon) is entanglement-breaking in this case, with vanishing capacity. We then calculate the quantum capacity of the black hole channel in the limit of a perfectly absorbing black hole and find that this capacity vanishes, while the capacity of the complementary channel is non-vanishing instead. Rather than inviting a new crisis for quantum physics, this finding instead is in accordance with the quantum no-cloning theorem, because it guarantees that there are no space-like surfaces that contain both the sender's quantum state and the receiver's reconstructed quantum state.
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 provide a statistical communication model for the phenomenon of quantum information evaporation from black holes (BHs). A BH behaves as a reflecting quantum channel in a very special regime, which allows for a receiver to perfectly recover the absorbed quantum information. The quantum channel of a perfectly reflecting (PR) BH is the probabilistically weighted sum of infinitely many qubit cloning channels. In this work, we reveal the statistical communication background of the information evaporation process of PR BHs. We show that the density of the cloned quantum particles in function of the PR BH's mass approximates a Chi-square distribution, while the stimulated emission process is characterized by zero-mean, circular symmetric complex Gaussian random variables. The results lead to the existence of Rayleigh random distributed coefficients in the probability density evolution, which confirms the presence of Rayleigh fading (a special type of random fluctuation) in the statistical communication model of BH information evaporation.
We present an analytic flat-spacetime accelerating boundary analog of Hawking-type emission that possesses infinite asymptotic acceleration (and radial acceleration in the black hole analog) but finite total radiated energy (and zero surface gravity in the black hole analog). We perform a unified study of its scattering symmetry, horizon formation, asymptotically extreme acceleration, finite total radiated energy, and the distinction between local energy flux and global particle production within a single closed-form model. The particle spectrum, energy spectrum, and equivalent spacetime metric are derived, revealing an interesting mix of normal and extremal black hole properties.