Optimal estimation of parameters for scalar field in an expanding spacetime exhibiting Lorentz invariance violation

Abstract

We address the optimal estimation of quantum parameters, in the framework of local quantum estimation theory, for a massive scalar quantum field in the expanding Robertson-Walker universe exhibiting Lorentz invariance violation (LIV). The information about the history of the expanding spacetime in the presence of LIV can be extracted by taking measurements on the entangled state of particle modes. We find that, in the estimation of cosmological parameters, the ultimate bounds to the precision of the Lorentz-invariant massive scalar field can be improved due to the effects of LIV under some appropriate conditions. We also show that, in the Lorentz-invariant massive scalar field and massless scalar field due to LIV backgrounds, the optimal precision can be achieved by choosing the particles with some suitable LIV, cosmological and field parameters. Moreover, in the estimation of LIV parameter during the spacetime expansion, we prove that the appropriate momentum mode of field particles and larger cosmological parameters can provide us a better precision. Particularly, the optimal precision of the parameters estimation can be obtained by performing projective measurements implemented by the projectors onto the eigenvectors of specific probe states.

Quantum correlation between a qubit and a relativistic boson in an expanding spacetime

“…Let us consider a two-dimensional Robertson-Walker spacetime with the line element described by the metric [35][36][37]…”

“…where b in,k is the bosonic annihilation operator acting on the state in the asymptotic past, and b out,k and b † out,−k are the bosonic annihilation and antibosonic creation operators acting on the states in the asymptotic future. This allows us to write the in-vacuum state as [35][36][37][38]…”

“…The analysis highlight the role of polarization of particles and compare the polarization results with those obtainable without accounting for it. Mohammadzadeh et al studied entropy production due to Lorentz invariance violation (LIV) in an expanding spacetime [46], and Liu et al used the optimal estimation of parameters for scalar fields to extract information in expanding Universe exhibiting LIV [37]. The extracted information about the past existence of LIV might be useful in recovering the quantum structure of gravity.…”

Probing cosmic string spacetime through parameter estimation

“…Quantum metrology which aims to achieve higher precision than the classical ways by using quantum tech-niques, has been paid a lot of attention recently [31][32][33][34]. There are considerable interests in applying quantum metrological techniques in relativistic settings, specifically, to relativistic quantum fields [35][36][37][38][39]. One of the purpose is to explore, in the relativistic quantum regimes, how the relativistic effects on quantum system affect the precision of certain measurements [40][41][42][43][44].…”

Optimal parameter estimation of open quantum systems*

“…Quantum precise measurement has become a new research hotpot in recent years. [1,2] It plays an important role in acquisition and transmission of quantum information, and has formed a new interdisciplinary-quantum metrology. [3] Precision of classical parameter estimation is limited by the quantum limit (or shot-noise limit).…”