Recently a quantum portrait of black holes was suggested according to which a macroscopic black hole is a Bose--Einstein condensate of soft gravitons stuck at the critical point of a quantum phase transition. We explain why quantum criticality and instability are the key for an efficient generation of entanglement and consequently of the scrambling of information. By studying a simple Bose--Einstein prototype, we show that the scrambling time, which is set by the quantum break time of the system, goes as $\mathrm{log}\text{ }N$ for $N$ the number of quantum constituents or equivalently the black hole entropy.
Recently a quantum portrait of black holes was suggested according to which a macroscopic black hole is a Bose--Einstein condensate of soft gravitons stuck at the critical point of a quantum phase transition. We explain why quantum criticality and instability are the key for an efficient generation of entanglement and consequently of the scrambling of information. By studying a simple Bose--Einstein prototype, we show that the scrambling time, which is set by the quantum break time of the system, goes as logN for N the number of quantum constituents or equivalently the black hole entropy.
It has recently been suggested that black holes may be described as condensates of weakly interacting gravitons at a critical point, exhibiting strong quantum effects. In this paper, we study a model system of attractive bosons in one spatial dimension which is known to undergo a quantum phase transition. We demonstrate explicitly that indeed quantum effects are important at the critical point, even if the number of particles is macroscopic. Most prominently, we evaluate the entropy of entanglement between different momentum modes and observe it to become maximal at the critical point. Furthermore, we explicitly see that the leading entanglement is between long-wavelength modes and is hence a feature independent of ultraviolet physics. If applicable to black holes, our findings substantiate the conjectured breakdown of semiclassical physics even for large black holes. This can resolve long-standing mysteries, such as the information paradox and the no-hair theorem.
We establish a fundamental connection between quantum criticality of a many-body system, such as Bose-Einstein condensates, and its capacity of information-storage and processing. For deriving the effective theory of modes in the vicinity of the quantum critical point, we develop a new method by mapping a Bose-Einstein condensate of N-particles onto a sigma model with a continuous global (pseudo)symmetry that mixes bosons of different momenta. The Bogolyubov modes of the condensate are mapped onto the Goldstone modes of the sigma model, which become gapless at the critical point. These gapless Goldstone modes are the quantum carriers of information and entropy. Analyzing their effective theory, we observe information-processing properties strikingly similar to the ones predicted by the black hole portrait. The energy cost per qubit of information-storage vanishes in the large-N limit and the total information-storage capacity increases with N either exponentially or as a power law. The longevity of information-storage also increases with N, whereas the scrambling time in the over-critical regime is controlled by the Lyapunov exponent and scales logarithmically with N. This connection reveals that the origin of black hole information storage lies in the quantum criticality of the graviton Bose-gas, and that much simpler systems that can be manufactured in table-top experiments can exhibit very similar information-processing dynamics.
Recent ideas about understanding physics of black hole information-processing in terms of quantum criticality allow us to implement black hole mechanisms of quantum computing within critical Bose-Einstein systems. The generic feature, uncovered both by analytic and numeric studies, is the emergence at the critical point of gapless weakly-interacting modes, which act as qubits for information-storage at a very low energy cost. These modes can be effectively described in terms of either Bogoliubov or Goldstone degrees of freedom. The ground-state at the critical point is maximally entangled and far from being classical. We confirm this near-critical behavior by a new analytic method. We compute growth of entanglement and show its consistency with black hole type behavior. On the other hand, in the over-critical regime the system develops a Lyapunov exponent and scrambles quantum information very fast. By, manipulating the system parameters externally, we can put it in and out of various regimes and in this way control the sequence of information storage and processing. By using gapless Bogoliubov modes as control qubits we design some simple logic gates.
Collective quantum effects have traditionally not received much attention in high energy physics. Recently, however, a model for black hole physics was put forward, in which black holes are described as Bose-condensates of gravitons close to a critical point. In a different line of research, estimates of high-energy collisions in the electro-weak theory have hinted that scattering processes with multiple Higgs or vector Bosons in the final state might be in reach for future particle colliders. In both scenarios, collective quantum effects may be crucial for understanding the physics. In the first part of this thesis, we address the black hole condensate picture of Dvali and Gomez. We study a Bosonic many-body system (attractive Lieb-Liniger) which exhibits a quantum phase transition and was proposed as a model for the graviton condensate. We demonstrate that, even for macroscopic particle number, quantum effects are prominent at the critical point. This becomes especially clear in the entanglement of different momentum modes and in the quantum discord between two successive density measurements. We point out that the leading contribution to these phenomena arises from long-wavelength modes and is therefore insensitive to ultra-violet physics. For black holes in the graviton condensate picture, these findings imply a breakdown of the semiclassical description and may be the key to resolving the long-standing information problem. We then turn our attention to the question of information processing in black holes. Inspired by the properties of three-dimensional attractive Bose condensates, we propose a concrete mechanism for fast scrambling in graviton-condensate black holes. To bolster our claims, we perform simulations of the Lieb-Liniger model in an appropriate regime that reveal entanglement-generation in logarithmic time. We also point out that the idea of instability and possibly chaos as the origin of fast quantum breaking and scrambling may also be relevant for other models of black holes. In the second part of this thesis, we use techniques of integrability (Bethe ansatz) to address the phase transition of the attractive Lieb-Liniger model analytically. We derive the continuum limit of the Bethe equations and solve it for the ground state at arbitrary coupling. We establish an exact equivalence between the Bethe-ansatz description in the large-particle-number limit and the large-N saddle point of Euclidean two dimensional U(N) Yang-Mills theory quantized on a sphere. The transition between the homogeneous and solitonic phases of the Lieb-Liniger model is thus dual to the Douglas-Kazakov confinement-deconfinement transition. In the last part, we consider scattering amplitudes involving many particles. In a simple integral-model, we study in detail the breakdown of perturbation theory and emphasize that the pure tree-level approximation fails earlier, parametrically. We then demonstrate, in three different (integral and quantum mechanical) model systems, that the physical high multiplicity amplitudes can be predicted on the basis of leading-order information from (non-perturbative) saddle points. In the non-Borel summable cases, one non-perturbative saddle contribution alone dominates the amplitudes. We highlight that high-multiplicity amplitudes may thus be a fruitful application for the methods of resurgence theory.
In a previous series of papers it was proposed that black holes can be understood as Bose-Einstein condensates at the critical point of a quantum phase transition. Therefore other bosonic systems with quantum criticalities, such as the Lieb-Liniger model with attractive interactions, could possibly be used as toy models for black holes. Even such simple models are hard to analyse, as mean field theory usually breaks down at the critical point. Very few analytic results are known. In this paper we present a method of studying such systems at quantum critical points analytically. We will be able to find explicit expressions for the low energy spectrum of the Lieb-Liniger model and thereby to confirm the expected black hole like properties of such systems. This opens up an exciting possibility of constructing and studying black hole like systems in the laboratory.
Analyzing some well established facts, we give a model‐independent parameterization of black hole quantum computing in terms of a set of macro and micro quantities and their relations. These include the relations between the extraordinarily‐small energy gap of black hole qubits and important time‐scales of information‐processing, such as, scrambling time and Page's time. We then show, confirming and extending previous results, that other systems of nature with identical quantum informatics features are attractive Bose‐Einstein systems at the critical point of quantum phase transition. Here we establish a complete isomorphy between the quantum computational properties of these two systems. In particular, we show that the quantum hair of a critical condensate is strikingly similar to the quantum hair of a black hole. Irrespectively whether one takes the similarity between the two systems as a remarkable coincidence or as a sign of a deeper underlying connection, the following is evident. Black holes are not unique in their way of quantum information processing and we can manufacture black hole based quantum computers in labs by taking advantage of quantum criticality.