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

Abstract

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.

The Generalized OTOC from Supersymmetric Quantum Mechanics—Study of Random Fluctuations from Eigenstate Representation of Correlation Functions

“…Very recently, in Reference [110][111][112][113][114], the authors have studied various relevant measures for an entangled open quantum system. The study of OTOCs for such type of entangled systems [115][116][117][118] will be quite relevant for understanding the rtime disorder averaging phenomena and chaos for such an entangled OQS.…”

Four-mode squeezed states in de Sitter space: A study with two field interacting quantum system

“…Additional terms (31) In order to construct the additional term S (r 1 , r 2 , θ 1 , θ 2 ) of the total squeezed operator we will use the Baker-Campbell-Hausdorff formula. Let us consider S given in Eq (32) and Eq (33).…”

“…To get the full squeezed operator for our case whose form is mentioned in Eq (31), we multiply the usual free squeezed operators from both the fields with the the BCH expansion given in Eq (37). The total squeezed operator for two scalar fields in de Sitter background space after applying the Baker-Campbell-Hausdorff will become:…”

“…From an application perspective the squeezed states of light are being used for various applications in quantum computing [14,15] and quantum cryptography [16] because these non-classical states of light can perform as an elementary resource in quantum information processing for the continuous variable systems. These states are also now being used in gravitational wave physics [17][18][19] to enhance the sensitivity of gravitational wave detectors [20][21][22][23], such as the LIGO [24] and to improve measurement techniques in quantum metrology [25][26][27][28][29][30][31]. For a more broad class of application of squeezed states see [32][33][34][35][36][37][38][39][40][41][42][43][44].…”

Four‐mode Squeezed States in de Sitter Space: A Study With Two Field Interacting Quantum System

“…These states are also now being used in gravitational wave physics [ 17–19 ] to enhance the sensitivity of gravitational wave detectors, [ 20–23 ] such as the LIGO [ 24 ] and to improve measurement techniques in quantum metrology. [ 25–31 ] For a more broad class of application of squeezed states see [32–44].…”