Towards a Fisher-Information Description of Complexity in de Sitter Universe

Chen, Chong-Bin; Shu, Fu-Wen

doi:10.3390/universe5120221

Cited by 5 publications

(6 citation statements)

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“…This conjecture was demonstrated in Ref. [28]. However, machine learning is also related to the tensor network through renormalization in condensed matter physics [31] and possibly has significant holographic meaning [32,33].…”

Section: Qsat K − S Atmentioning

confidence: 86%

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Quantum bit threads of MERA tensor network in large c limit *

Chen

Shu

2020

Chinese Phys. C

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The Ryu-Takayanagi (RT) formula plays a large role in the current theory of gauge-gravity duality and emergent geometry phenomena. The recent reinterpretation of this formula in terms of a set of “bit threads” is an interesting effort in understanding holography. In this study, we investigate a quantum generalization of the “bit threads” based on a tensor network, with particular focus on the multi-scale entanglement renormalization ansatz (MERA). We demonstrate that, in the large c limit, isometries of the MERA can be regarded as “sources” (or “sinks”) of the information flow, which extensively modifies the original picture of bit threads by introducing a new variable ρ: density of the isometries. In this modified picture of information flow, the isometries can be viewed as generators of the flow. The strong subadditivity and related properties of the entanglement entropy are also obtained in this new picture. The large c limit implies that classical gravity can emerge from the information flow.

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Section: Qsat K − S Atmentioning

confidence: 86%

“…χ → ∞ Fortunately, recent work from Hastingss [28] demonstrated that this conjecture is "asymptotically" true in the limit as . Hence, the ratio of the QMF to the QMC χ QMF(G, χ, O) χ converges to one as tends to infinity.…”

Section: Large C Limitmentioning

confidence: 98%

Quantum bit threads of MERA tensor network in large c limit *

Chen

Shu

2020

Chinese Phys. C

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“…Hence, Quantum Metrology not only refines precision measurement but it also provides fresh avenues of probes which are otherwise inaccessible. The technique of fisher information has previously been used in various different models for studying the dynamics of systems in curved spacetime [18][19][20] The precision of parameter estimation is measured by Fisher information [22]. In the field of parameter estimation, the prime focus is to give an estimate of the values of the unknown physical parameters labelling a quantum mechanical model and to enhance the precision of resolution.…”

Section: Introductionmentioning

confidence: 99%

QMetrology from QCosmology: Study with entangled two qubit open quantum system in De Sitter space

et al. 2021

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In this paper, our prime objective is to apply the techniques of parameter estimation theory and the concept of Quantum Metrology in the form of Fisher Information to investigate the role of certain physical quantities in the open quantum dynamics of a two entangled qubit system under the Markovian approximation. There exist various physical parameters which characterize such system, but can not be treated as any quantum mechanical observable. It becomes imperative to do a detailed parameter estimation analysis to determine the physically consistent parameter space of such quantities. We apply both Classical Fisher Information (CFI) and Quantum Fisher Information (QFI) to correctly estimate these parameters, which play significant role to describe the out-of-equilibrium and the long range quantum entanglement phenomena of open quantum system. Quantum Metrology, compared to classical parameter estimation theory, plays a two-fold superior role, improving the precision and accuracy of parameter estimation. Additionally, in this paper we present a new avenue in terms of Quantum Metrology, which beats the classical parameter estimation. We also present an interesting result of revival of out-of-equilibrium feature at the late time scales, arising due to the long range quantum entanglement at early time scale and provide a physical interpretation for the same in terms of Bell's Inequality Violation in early time scale giving rise to non-locality.

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“…In addition, increasing evidences show that it may play a crucial role in the understanding the nature of space-time [6,7]. In particular, as implied by the holographic entanglement entropy [8,9], there is a fundamental connection between quantum information theory and gravitational physics [10][11][12][13][14][15][16][17][18]. The quantum complexity is another significant concept of the connection and thus has attracted a lot of attention in the past few years.…”

Section: Introductionmentioning

confidence: 99%

Holographic complexity for nonlinearly charged Lifshitz black holes

Zhu,

Shu,

2020

Preprint

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Using "complexity=action" proposal we study the late time growth rate of holographic complexity for nonlinear charged Lifshitz black hole with a single horizon or two horizons. As a toy model, we consider two kinds of such black holes: nonlinear charged Lifshitz black hole and nonlinear logarithmic charged Lifshitz black hole. We find that for the black hole with two horizons, the action growth bound is satisfied. But for the black hole with a single horizon, whether the Lloyd bound is violated depends on the specific value of dimensionless coupling constants β 1 , β 2 , spacetime dimension D and dynamical exponent z.

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Towards a Fisher-Information Description of Complexity in de Sitter Universe

Cited by 5 publications

References 50 publications

Quantum bit threads of MERA tensor network in large c limit *

Quantum bit threads of MERA tensor network in large c limit *

QMetrology from QCosmology: Study with entangled two qubit open quantum system in De Sitter space

Holographic complexity for nonlinearly charged Lifshitz black holes

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