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arXiv:2203.15417 · The European Physical Journal C

Black-box estimation of expanding parameter for de Sitter universe

Lulu Xiao, Cuihong Wen, Jiliang Jing, Jieci Wang

Published Aug 6, 2022• 5 citations
arXivHTMLPDF

Abstract

Abstract We study the black-box parameter estimation of expanding parameters and the dynamics of Gaussian interferometric power for the de Sitter space. We find that the state between separated open charts can be employed as a probe state for the black-box quantum metrology. This is nontrivial because the open charts are causally disconnected and classical information can not be exchanged between them according to the general relativity. It is shown that the mass of the scalar field remarkably affects the accuracy of the black-box parameter estimation in the de Sitter space, which is quite different from the flat space case where the mass parameter does not influence the precision of estimation. Quantum discord is found to be a key resource for the estimation of the expanding parameter when there is no entanglement between the initially uncorrelated open charts. It is demonstrated that the role of the probe state between different open charts is quite distinct because the curvature effect of the de sitter space damages quantum resources for the initially correlated probe states, while it generates quantum resources for the initially uncorrelated probe states.

DOI
10.1140/epjc/s10052-022-10633-1

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Abstract We study the black-box parameter estimation of expanding parameters and the dynamics of Gaussian interferometric power for the de Sitter space. We find that the state between separated open charts can be employed as a probe state for the black-box quantum metrology. This is nontrivial because the open charts are causally disconnected and classical information can not be exchanged between them according to the general relativity. It is shown that the mass of the scalar field remarkably affects the accuracy of the black-box parameter estimation in the de Sitter space, which is quite different from the flat space case where the mass parameter does not influence the precision of estimation. Quantum discord is found to be a key resource for the estimation of the expanding parameter when there is no entanglement between the initially uncorrelated open charts. It is demonstrated that the role of the probe state between different open charts is quite distinct because the curvature effect of the de sitter space damages quantum resources for the initially correlated probe states, while it generates quantum resources for the initially uncorrelated probe states.
We study the distribution of bipartite and tripartite quantum entanglement across causally disconnected regions (open charts) in de Sitter spacetime. We first consider a two-mode squeezed state shared between Alice and Bob, where the Gaussian channel models the effects of spacetime curvature. We employ Gaussian Rényi-2 entanglement as a witness for quantum entanglement, while Gaussian geometric discord is a measure of quantumness beyond entanglement, including entanglement. The Gaussian Rényi-2 classical correlations are used to quantify the correlations. Besides, we achieve tripartite entanglement among the open chart modes, quantified by residual Gaussian Rényi-2 entanglement. Our results demonstrate the generation of bipartite entanglement between spatially separated observers due to strong curvature. The impact of curvature on both classical and quantum correlations is shown to be particularly pronounced for conformal and massless scalar fields. Hence, residual Gaussian Rényi-2 entanglement is generated among the open chart modes due to the influence of de Sitter curvature for all nonzero squeezing values.
The Hilbert-Schmidt measure is a useful geometric tool used to investigate the properties on the manifold of mixed Gaussian states in multimode continuous variable quantum systems. In this work, we study the relationship between the scalar curvature and quantum entanglement across causally disconnected regions (open charts) in de Sitter spacetime. We first consider a two-mode squeezed state shared between Alice and Bob, where the Gaussian channel models the effects of spacetime curvature. We employ logarithmic negativity as a witness for quantum entanglement. We study the impact of the mass, parameter p and squeezing parameter on the scalar curvature and entanglement. We find an interesting interplay between scalar curvature and entanglement for certain values of the mass and parameter p . By varying p , we thus explore how information geometry and entanglement are influenced by both ultraviolet and infrared modes. Moreover, the relationship between scalar curvature and entanglement is discussed under the influence of various parameters characterizing the geometric system under consideration.
How precisely can we estimate cosmological parameters by performing a quantum measurement on a cosmological quantum state? In quantum estimation theory, the variance of an unbiased parameter estimator is bounded from below by the inverse of measurement-dependent Fisher information and ultimately by quantum Fisher information, which is the maximization of the former over all positive operator-valued measurements. Such bound is known as the quantum Cramer –Rao bound. We consider the evolution of a massless scalar field with Bunch–Davies vacuum in a spatially flat FLRW spacetime, which results in a two-mode squeezed vacuum out-state for each field wave number mode. We obtain the expressions of the quantum Fisher information as well as the Fisher informations associated to occupation number measurement and power spectrum measurement, and show the specific results of their evolution for pure de Sitter expansion and de Sitter expansion followed by a radiation-dominated phase as examples. We will discuss these results from the point of view of the quantum-to-classical transition of cosmological perturbations and show quantitatively how this transition and the residual quantum correlations affect the bound on the precision.
Abstract We propose a scheme for the quantum metrology of the Schwinger effect and the dynamics of Gaussian interference power (GIP). The ongoing reliability of the estimation strategy for the probe state prepared in particle–particle modes is demonstrated. Although the GIP sensitively depends on the strength of the external electric field and the transverse momentum, the advantage of quantum parameter estimation is still maintained even in the limit of an infinite electric field and zero transverse momentum. It is shown that the entanglement between the particle–particle modes provides a guarantee for obtaining higher precision for the black-box estimation. In contrast, for the probe state prepared in particle–antiparticle modes, the advantage of quantum parameter estimation can also be ensured even though there is no entanglement in the probe state. Put differently, some non-entanglement quantum correlations play the role of quantum resources in the estimation for particle–antiparticle modes.
We study the parameter estimation for excitations of Dirac fields in the expanding Robertson–Walker universe. We employ quantum metrology techniques to demonstrate the possibility for high precision estimation for the volume rate of the expanding universe. We show that the optimal precision of the estimation depends sensitively on the dimensionless mass m˜ and dimensionless momentum k˜ of the Dirac particles. The optimal precision for the ratio estimation peaks at some finite dimensionless mass m˜ and momentum k˜. We find that the precision of the estimation can be improved by choosing the probe state as an eigenvector of the hamiltonian. This occurs because the largest quantum Fisher information is obtained by performing projective measurements implemented by the projectors onto the eigenvectors of specific probe states.
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.