Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1507.02948 · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Nambu-Goldstone effective theory of information at quantum criticality

Gia Dvali, Andre Franca, César Gómez, Nico Wintergerst

Published Dec 1, 2015• 35 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevd.92.125002

Related papers

Black Hole Type Quantum Computing in Critical Bose-Einstein Systems

Gia Dvali, Mischa Panchenko

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.

arXiv:1507.08952•Jul 31, 2015•15 citations

Finding critical states of enhanced memory capacity in attractive cold bosons

Gia Dvali, Marco Michel, Sebastian Zell

We discuss a class of quantum theories which exhibit a sharply increased memory storage capacity due to emergent gapless degrees of freedom. Their realization, both theoretical and experimental, is of great interest. On the one hand, such systems are motivated from a quantum information point of view. On the other hand, they can provide a framework for simulating systems with enhanced capacity of pattern storage, such as black holes and neural networks. In this paper, we develop an analytic method that enables us to find critical states with increased storage capabilities in a generic system of cold bosons with weak attractive interactions. The enhancement of memory capacity arises when the occupation number N of certain modes reaches a critical level. Such modes, via negative energy couplings, assist others in becoming effectively gapless. This leads to degenerate microstates labeled by the occupation numbers of the nearly-gapless modes. In the limit of large N , they become exactly gapless and their decoherence time diverges. In this way, a system becomes an ideal storer of quantum information. We demonstrate our method on a prototype model of N attractive cold bosons contained in a one-dimensional box with Dirichlet boundary conditions. Although we limit ourselves to a truncated system, we observe a rich structure of quantum phases with a critical point of enhanced memory capacity.

arXiv:1805.10292•EPJ Quantum Technology•Mar 25, 2019•24 citations

Scrambling in the black hole portrait

Gia Dvali, Daniel Flassig, César Gómez +2 more

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.

arXiv:1307.3458•Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Dec 26, 2013•98 citations

Black holes and quantumness on macroscopic scales

Daniel Flassig, Alexander Pritzel, Nico Wintergerst

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.

arXiv:1212.3344•Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Apr 2, 2013•50 citations

Bounds on quantum information storage and retrieval

Gia Dvali

We present certain universal bounds on the capacity of quantum information storage and on the time scale of its retrieval for a generic quantum field theoretic system. The capacity, quantified by the microstate entropy, is bounded from above by the surface area of the object measured in units of a Goldstone decay constant. The Goldstone bosons are universally present due to the spontaneous breaking of Poincare and internal symmetries by the information-storing object. Applied to a black hole, the bound reproduces the Bekenstein-Hawking entropy. However, the relation goes beyond gravity. The minimal time-scale required for retrieving the quantum information from a system is equal to its volume measured in units of the same Goldstone scale. For a black hole, this reproduces the Page time as well as the quantum break-time. Again, the expression for the information retrieval time is very general and is shared by non-gravitational saturated states in gauge theories including QCD. All such objects exhibit universal signatures such as the emission of ultra-soft radiation. Similar bounds apply to non-relativistic many-body systems. This article is part of the theme issue 'Quantum technologies in particle physics'.

arXiv:2107.10616•Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences•Dec 20, 2021•13 citations

Bosonic Quantum Conditional Mutual Information and Bose-Einstein Condensation

Anupam Ghosh

This article aims to introduce the bosonic asymmetric quantum conditional mutual information (QCMI), $I_{B}(A; B|C)$, as a rigorously defined information-theoretic quantity for continuous-variable (bosonic) systems. After defining $I_{B}(A; B|C)$ through quantum instruments on infinite-dimensional Fock spaces, we prove that Bose-Einstein condensation (BEC) induces a logarithmic divergence $ I_{B}(A; B|C) \geq α\log_2 (N_{0}^C+1)$, which further establishes $I_{B}(A; B|C)$ as a quantum-information order parameter for BEC with power-law scaling near the critical point. We provide the complete five-step proof of this result, connecting measurement back-action, off-diagonal long-range order, and Jensen's inequality. In the condensed phase, the effective causal propagation velocity is set by the Bogoliubov sound speed $c_s$ in the long-wavelength limit, and vanishes continuously at the superfluid--Mott-insulator transition. Applications to composite bosons, the BEC--BCS crossover, and a quantum-gas-microscope measurement protocol are presented. Finally, we demonstrate how the reduced bosonic QCMI serves as a finite-size scaling probe analogous to the Binder cumulant.

quant-pharXiv:2610.16626•Oct 13, 2026•0 citations
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 NNN-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-NNN limit and the total information-storage capacity increases with NNN either exponentially or as a power law. The longevity of information-storage also increases with NNN, whereas the scrambling time in the over-critical regime is controlled by the Lyapunov exponent and scales logarithmically with NNN. 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.
We discuss a class of quantum theories which exhibit a sharply increased memory storage capacity due to emergent gapless degrees of freedom. Their realization, both theoretical and experimental, is of great interest. On the one hand, such systems are motivated from a quantum information point of view. On the other hand, they can provide a framework for simulating systems with enhanced capacity of pattern storage, such as black holes and neural networks. In this paper, we develop an analytic method that enables us to find critical states with increased storage capabilities in a generic system of cold bosons with weak attractive interactions. The enhancement of memory capacity arises when the occupation number N of certain modes reaches a critical level. Such modes, via negative energy couplings, assist others in becoming effectively gapless. This leads to degenerate microstates labeled by the occupation numbers of the nearly-gapless modes. In the limit of large N , they become exactly gapless and their decoherence time diverges. In this way, a system becomes an ideal storer of quantum information. We demonstrate our method on a prototype model of N attractive cold bosons contained in a one-dimensional box with Dirichlet boundary conditions. Although we limit ourselves to a truncated system, we observe a rich structure of quantum phases with a critical point of enhanced memory capacity.
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 log N\mathrm{log}\text{ }Nlog N for NNN 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 present certain universal bounds on the capacity of quantum information storage and on the time scale of its retrieval for a generic quantum field theoretic system. The capacity, quantified by the microstate entropy, is bounded from above by the surface area of the object measured in units of a Goldstone decay constant. The Goldstone bosons are universally present due to the spontaneous breaking of Poincare and internal symmetries by the information-storing object. Applied to a black hole, the bound reproduces the Bekenstein-Hawking entropy. However, the relation goes beyond gravity. The minimal time-scale required for retrieving the quantum information from a system is equal to its volume measured in units of the same Goldstone scale. For a black hole, this reproduces the Page time as well as the quantum break-time. Again, the expression for the information retrieval time is very general and is shared by non-gravitational saturated states in gauge theories including QCD. All such objects exhibit universal signatures such as the emission of ultra-soft radiation. Similar bounds apply to non-relativistic many-body systems. This article is part of the theme issue 'Quantum technologies in particle physics'.
This article aims to introduce the bosonic asymmetric quantum conditional mutual information (QCMI), IB(A;B∣C)I_{B}(A; B|C)IB​(A;B∣C), as a rigorously defined information-theoretic quantity for continuous-variable (bosonic) systems. After defining IB(A;B∣C)I_{B}(A; B|C)IB​(A;B∣C) through quantum instruments on infinite-dimensional Fock spaces, we prove that Bose-Einstein condensation (BEC) induces a logarithmic divergence $ I_{B}(A; B|C) \geq α\log_2 (N_{0}^C+1)$, which further establishes IB(A;B∣C)I_{B}(A; B|C)IB​(A;B∣C) as a quantum-information order parameter for BEC with power-law scaling near the critical point. We provide the complete five-step proof of this result, connecting measurement back-action, off-diagonal long-range order, and Jensen's inequality. In the condensed phase, the effective causal propagation velocity is set by the Bogoliubov sound speed csc_scs​ in the long-wavelength limit, and vanishes continuously at the superfluid--Mott-insulator transition. Applications to composite bosons, the BEC--BCS crossover, and a quantum-gas-microscope measurement protocol are presented. Finally, we demonstrate how the reduced bosonic QCMI serves as a finite-size scaling probe analogous to the Binder cumulant.