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arXiv:2205.08725 · Physical review. D/Physical review. D.

Does relativistic motion always degrade quantum Fisher information?

Xiaobao Liu, Jiliang Jing, Zehua Tian, Weiping Yao

Published Jun 24, 2021• 22 citations
arXivHTMLPDF

Abstract

We investigate the ultimate estimation precision, characterized by the quantum Fisher information, of a two-level atom as a detector which is coupled to massless scalar field in the Minkowski vacuum. It has been shown that for an inertial detector moving with a constant velocity, its quantum Fisher information is completely unaffected by the velocity, however, it still decays over time due to the decoherence caused by the interaction between the atom and the field. In addition, for a uniformly accelerated detector ($w=0$) moving along spatially straight line, the accelerated motion will reduce the quantum Fisher information in the estimation of state parameters. However, when the detector trajectory is generated by a combination of the linear accelerated motion and a component of the four-velocity $w=dy/d\ensuremath{\tau}$, we find quite unlike the previous results that, for the nonrelativistic case ($w\ensuremath{\ll}1$), the acceleration could degrade the quantum Fisher information, while the four-velocity component will suppress the degradation of the quantum Fisher information, and thus could enhance the precision of parameters estimation. Furthermore, in the case for ultrarelativistic velocities $(w\ensuremath{\rightarrow}\ensuremath{\infty})$, although the detector still interacts with the environment, it behaves as if it were a closed system as a consequence of relativity correction associated to the velocity, and the quantum Fisher information in this case can be shielded from the effect of the external environment, and thus from the relativistic motion.

DOI
10.1103/physrevd.103.125025

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We investigate the ultimate estimation precision, characterized by the quantum Fisher information, of a two-level atom as a detector which is coupled to massless scalar field in the Minkowski vacuum. It has been shown that for an inertial detector moving with a constant velocity, its quantum Fisher information is completely unaffected by the velocity, however, it still decays over time due to the decoherence caused by the interaction between the atom and the field. In addition, for a uniformly accelerated detector (w=0w=0w=0) moving along spatially straight line, the accelerated motion will reduce the quantum Fisher information in the estimation of state parameters. However, when the detector trajectory is generated by a combination of the linear accelerated motion and a component of the four-velocity w=dy/d\ensuremathτw=dy/d\ensuremath{\tau}w=dy/d\ensuremathτ, we find quite unlike the previous results that, for the nonrelativistic case (w\ensuremath≪1w\ensuremath{\ll}1w\ensuremath≪1), the acceleration could degrade the quantum Fisher information, while the four-velocity component will suppress the degradation of the quantum Fisher information, and thus could enhance the precision of parameters estimation. Furthermore, in the case for ultrarelativistic velocities (w\ensuremath→\ensuremath∞)(w\ensuremath{\rightarrow}\ensuremath{\infty})(w\ensuremath→\ensuremath∞), although the detector still interacts with the environment, it behaves as if it were a closed system as a consequence of relativity correction associated to the velocity, and the quantum Fisher information in this case can be shielded from the effect of the external environment, and thus from the relativistic motion.
Abstract In this work, we devote to understand how boundaries can help improve parameter estimation against atomic decoherence and dissipation caused by relativistic motion. The system we considered is a two-level atom in uniform linear acceleration parallel to a planar wall in (3+1)-dimensional Minkowski spacetime, which is coupled to a massless scalar field with Dirichlet, Neumann or transparent boundary conditions at the wall. We find that the quantum Fisher information (QFI), which determines the ultimate estimation precision, depends on various factors, such as atomic motional trajectories, evolution time, atomic initial state, and the boundary condition. We identify the optimal estimation strategies that maximize the QFI through all the associated parameters, thus optimizing the estimation precision. Our results show that the QFI has different behaviors and even different magnitudes for different boundary cases. We also determine the boundary conditions that can effectively suppress the influence of atomic relativistic motion on the QFI. Our investigation may help advance the study of relativistic quantum information in cavity quantum electrodynamics.
In an open quantum system, we study the evolution of a two-level atom as a detector which interacts with given environments. For a uniformly accelerated two-level atom coupled to a massless scalar field in the Minkowski vacuum, when it evolves for a certain time, we find that there exists a peak value for the quantum Fisher information (QFI) of acceleration, which indicates that the optimal precision of estimation is achieved when choosing an appropriate acceleration aaa. QFI has different behaviors for different initial state parameters $\ensuremath{\theta}$ of the atom, displaying periodicity. However, the periodicity fades away with the evolution of time, which means that the initial state cannot affect the later stable quantum state. Furthermore, adding a boundary, we observe that the peak value of QFI increases when the atom is close to the boundary, which shows that QFI is protected by the boundary. Here, QFI fluctuates, and there may exist two peak values with a certain moment, which expands the detection range of the acceleration. Therefore, we can enhance the estimation precision of acceleration by choosing an appropriate position and acceleration aaa. The periodicity of QFI with respect to the initial state parameter $\ensuremath{\theta}$ lasts a longer time than the previous unbounded case, which indicates that the initial state is protected by the boundary. Finally, for a thermal bath with a boundary, QFI of temperature has no more than one peak value with a certain moment, which is different from QFI of acceleration with a boundary. The periodicity also lasts a longer time than unbounded case, which shows the initial quantum state of the atom is protected by the boundary for two cases.
In open quantum systems, we study the quantum Fisher information of acceleration for a uniformly accelerated two-level atom coupled to fluctuating electromagnetic fields in the Minkowski vacuum. With the time evolution, for the initial atom state parameter θ≠πθ\neqπθ=π, the quantum Fisher information can exist a maximum value and a local minimum value before reaching a stable value. In addition, in a short time, the quantum Fisher information varies with the initial state parameter, and the quantum Fisher information can take a maximum value at θ=0θ=0θ=0. The quantum Fisher information may exist two peak values at a certain moment. These features are different from the massless scalar fields case. With the time evolution, FmaxF_{max}Fmax​ firstly increases, then decreases, and finally, reaches the same value. However, FmaxF_{max}Fmax​ will arrive at a stable maximum value for the case of the massless scalar fields. Although the atom response to the vacuum fluctuation electromagnetic fields is different from the case of massless scalar fields, the quantum Fisher information eventually reaches a stable value.
Quantum metrology studies the ultimate limit of precision in estimating a physical quantity if quantum strategies are exploited. Here we investigate the evolution of a two-level atom as a detector which interacts with a massless scalar field using the master equation approach for open quantum system. We employ local quantum estimation theory to estimate the Unruh temperature when probed by a uniformly accelerated detector in the Minkowski vacuum. In particular, we evaluate the Fisher information (FI) for population measurement, maximize its value over all possible detector preparations and evolution times, and compare its behavior with that of the quantum Fisher information (QFI). We find that the optimal precision of estimation is achieved when the detector evolves for a long enough time. Furthermore, we find that in this case the FI for population measurement is independent of initial preparations of the detector and is exactly equal to the QFI, which means that population measurement is optimal. This result demonstrates that the achievement of the ultimate bound of precision imposed by quantum mechanics is possible. Finally, we note that the same configuration is also available to the maximum of the QFI itself.
A bstract In this work, we investigate the velocity effects on information degradation due to the Unruh effect in accelerated quantum systems (with finite interaction time). We consider a detector moving along a spatial trajectory within a two-dimensional plane, this trajectory is composed of uniform acceleration along one direction, combined with a constant four-velocity component in the plane orthogonal to the acceleration. The quantum systems studied were: accelerated single-qubit, quantum interferometric circuit, and which-path distinguishability circuit. Thus, for non-relativistic velocity regime, we obtained analytical expressions such as transition rates, quantum coherence, visibility, distinguishability, and the complementarity relation. On the other hand, for the ultra-relativistic velocity regime, we saw that the Unruh effect is suppressed and therefore the detector does not respond in this case. Our findings revealed that velocity effects imply mitigation of information degradation, this interesting behaviors happen because of the composite effect of both velocity and acceleration. The results obtained show that the addition of the non-relativistic, transverse and constant motion of an accelerated detector can play a protective role in quantumness in systems at high accelerations, although the effects are very small.
We study the quantum Fisher information (QFI) of acceleration, in the open quantum systems, for a two-level atom with the circular motion coupled to a massless scalar field in the Minkowski vacuum without and with a reflecting boundary in the ultra-relativistic limit. As we amplify a, the saturation time decreases for θ≠π, but first increases and then decreases for θ=π. Without a boundary, there exists a peak value of QFI with a certain time. The QFI varies with the initial state parameter θ, and firstly takes peak value in the ground state of the atom. The variation of QFI with respect to θ gradually fades away with the evolution of time. With a boundary, the detection range of acceleration has been expanded. The QFI firstly takes the maximum in the excited state of the atom. In addition, we study the QFI of temperature for a static atom immersed in a thermal bath without and with a boundary. The relation between the saturation time and T is similar to a. Without a boundary, the QFI of temperature is similar to that of acceleration. With a boundary, the QFI firstly takes peak value in the ground state of the atom, which is different from the behavior of acceleration. The results provide references for the detection of Unruh-like effect.