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 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.

May 21, 201418 citations

Black holes as bosonic Gaussian channels

Kamil Brádler, Christoph Adami

We identify the quantum channels corresponding to the interaction of a Gaussian quantum state with an already formed Schwarzschild black hole. Using recent advances in the classification of one-mode bosonic Gaussian channels, we find that (with one exception) the black hole Gaussian channels lie in the nonentanglement breaking subset of the lossy channels $\mathcal{C}(\text{loss})$ , amplifying channels $\mathcal{C}(\mathrm{amp})$ and classical-noise channels ${\mathcal{B}}_{2}$ . We show that the channel parameters depend on the black hole mass and the properties of the potential barrier surrounding it. This classification enables us to calculate the classical and quantum capacity of the black hole and to estimate the quantum capacity where no tractable quantum capacity expression exists today. We discuss these findings in the light of the black hole quantum information loss problem.We identify the quantum channels corresponding to the interaction of a Gaussian quantum state with an already formed Schwarzschild black hole. Using recent advances in the classification of one-mode bosonic Gaussian channels, we find that (with one exception) the black hole Gaussian channels lie in the nonentanglement breaking subset of the lossy channels $\mathcal{C}(\text{loss})$, amplifying channels $\mathcal{C}(\mathrm{amp})$ and classical-noise channels ${\mathcal{B}}_{2}$. We show that the channel parameters depend on the black hole mass and the properties of the potential barrier surrounding it. This classification enables us to calculate the classical and quantum capacity of the black hole and to estimate the quantum capacity where no tractable quantum capacity expression exists today. We discuss these findings in the light of the black hole quantum information loss problem.

arXiv:1405.1097Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsJul 20, 201518 citations

A statistical model of information evaporation of perfectly reflecting black holes

László Gyöngyösi

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 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.

arXiv:1311.3598International Journal of Quantum InformationNov 1, 201410 citations

Effective horizons for quantum communication in a Schwarzschild spacetime

Dominic Hosler, Carsten van de Bruck, Pieter Kok

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.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.

Nov 7, 20110 citations

Black holes are almost optimal quantum cloners

Christoph Adami, Greg Ver Steeg

If black holes were able to clone quantum states, a number of paradoxes in black hole physics would disappear.However, the linearity of quantum mechanics forbids exact cloning of quantum states.Here we show that black holes indeed clone incoming quantum states with a fidelity that depends on the black hole's absorption coefficient, without violating the no-cloning theorem because the clones are only approximate.Perfectly reflecting black holes are optimal universal 'quantum cloning machines' and operate on the principle of stimulated emission, exactly as their quantum optical counterparts.In the limit of perfect absorption, the fidelity of clones is only equal to what can be obtained via quantum state estimation methods.But for any absorption probability less than one, the cloning fidelity is nearly optimal as long as ω ⩾ T 10, a common parameter for modest-sized black holes.If black holes were able to clone quantum states, a number of paradoxes in black hole physics would disappear.However, the linearity of quantum mechanics forbids exact cloning of quantum states.Here we show that black holes indeed clone incoming quantum states with a fidelity that depends on the black hole's absorption coefficient, without violating the no-cloning theorem because the clones are only approximate.Perfectly reflecting black holes are optimal universal 'quantum cloning machines' and operate on the principle of stimulated emission, exactly as their quantum optical counterparts.In the limit of perfect absorption, the fidelity of clones is only equal to what can be obtained via quantum state estimation methods.But for any absorption probability less than one, the cloning fidelity is nearly optimal as long as ω ⩾ T 10, a common parameter for modest-sized black holes.

arXiv:quant-ph/0601065Journal of Physics A Mathematical and TheoreticalMay 19, 201516 citations

Black Hole Information Transfer via Quantum Entanglement Protocol

Jincheng Zhang

This paper explores the feasibility of utilizing quantum entanglement to establish a novel protocol for information transfer within the confines of a black hole. The core concept centers on constructing a "quantum black hole information channel" – a system where entangled quantum states act as carriers of limited information, enabling precise measurements and analysis of the black hole's internal environment. Traditional methods for transmitting information across vast distances are hampered by quantum decoherence, necessitating a fundamentally different approach. This research investigates the potential of quantum entanglement to circumvent these limitations, offering a promising pathway to understanding the intricacies of black hole physics. The paper details the proposed protocol, its underlying mathematical framework, and preliminary analysis of its potential impact. The ultimate goal is to develop a practical framework for quantum information transfer, potentially offering insights into the fundamental properties of black holes.This paper explores the feasibility of utilizing quantum entanglement to establish a novel protocol for information transfer within the confines of a black hole. The core concept centers on constructing a "quantum black hole information channel" – a system where entangled quantum states act as carriers of limited information, enabling precise measurements and analysis of the black hole's internal environment. Traditional methods for transmitting information across vast distances are hampered by quantum decoherence, necessitating a fundamentally different approach. This research investigates the potential of quantum entanglement to circumvent these limitations, offering a promising pathway to understanding the intricacies of black hole physics. The paper details the proposed protocol, its underlying mathematical framework, and preliminary analysis of its potential impact. The ultimate goal is to develop a practical framework for quantum information transfer, potentially offering insights into the fundamental properties of black holes.

Sep 4, 20260 citations

\mathcal{C}(\text{loss})

, amplifying channels

\mathcal{C}(\mathrm{amp})

and classical-noise channels

{\mathcal{B}}_{2}

. We show that the channel parameters depend on the black hole mass and the properties of the potential barrier surrounding it. This classification enables us to calculate the classical and quantum capacity of the black hole and to estimate the quantum capacity where no tractable quantum capacity expression exists today. We discuss these findings in the light of the black hole quantum information loss problem.