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Scientific Reports

How the Relativistic Motion Affect Quantum Fisher Information and Bell Non-locality for Multipartite state

Chun Yu Huang, Wenchao Ma, Dong Wang, Liu Ye

Published Feb 1, 2017• 14 citations
Publisher

Abstract

Abstract In this work, the quantum fisher information (QFI) and Bell non-locality of a multipartite fermionic system are investigated. Unlike the currently existing research of QFI, we focus our attention on the differences between quantum fisher information and Bell non-locality under the relativistic framework. The results show that although the relativistic motion affects the strength of the non-locality, it does not change the physical structure of non-locality. However, unlike the case of non-locality, the relativistic motion not only influence the precision of the QFI Fϕ but also broke the symmetry of the function Fϕ. The results also show that for a special multipartite system, "Equation missing", the number of particles of a initial state do not affect the Fθ. Furthermore, we also find that Fθ is completely unaffected in non-inertial frame if there are inertial observers. Finally, in view of the decay behavior of QFI and non-locality under the non-inertial frame, we proposed a effective scheme to battle against Unruh effect.

DOI
10.1038/srep38456

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Abstract In this work, the quantum fisher information (QFI) and Bell non-locality of a multipartite fermionic system are investigated. Unlike the currently existing research of QFI, we focus our attention on the differences between quantum fisher information and Bell non-locality under the relativistic framework. The results show that although the relativistic motion affects the strength of the non-locality, it does not change the physical structure of non-locality. However, unlike the case of non-locality, the relativistic motion not only influence the precision of the QFI Fϕ but also broke the symmetry of the function Fϕ. The results also show that for a special multipartite system, "Equation missing", the number of particles of a initial state do not affect the Fθ. Furthermore, we also find that Fθ is completely unaffected in non-inertial frame if there are inertial observers. Finally, in view of the decay behavior of QFI and non-locality under the non-inertial frame, we proposed a effective scheme to battle against Unruh effect.
We investigate the performance of quantum Fisher information (QFI) under the Unruh-Hawking effect, where one of the observers (e.g., Rob) is uniformly accelerated with respect to other partners. In the context of relativistic quantum information theory, we demonstrate that quantum Fisher information, as an important measure of the information content of quantum states, has a rich and subtle physical structure compared with entanglement or Bell nonlocality. In this work, we mainly focus on the parametrized (and arbitrary) pure two-qubit states, where the weight parameter $\ensuremath{\theta}$ and phase parameter $\ensuremath{\phi}$ are naturally introduced. Intriguingly, we prove that QFI with respect to $\ensuremath{\theta}$ (${\mathcal{F}}_{\ensuremath{\theta}}$) remains unchanged for both scalar and Dirac fields. Meanwhile, we observe that QFI with respect to $\ensuremath{\phi}$ (${\mathcal{F}}_{\ensuremath{\phi}}$) decreases with the increase of acceleration rrr but remains finite in the limit of infinite acceleration. More importantly, our results show that the symmetry of ${\mathcal{F}}_{\ensuremath{\phi}}$ (with respect to $\ensuremath{\theta}=\ensuremath{\pi}/4$) has been broken by the influence of the Unruh effect for both cases.
We investigate the effect of the inertial and non-inertial segments of relativistic motion on the quantum Fisher information of (1+1) Dirac field modes confined to cavities. %For this purpose, a bipartite system comprising of Alice's and Rob's cavities with appropriate boundary conditions is prepared. For the purpose, we consider the situation that Rob's cavity, initially inertial, accelerates uniformly with respect to its proper time and then again becomes inertial while Alice's cavity remains inertial. The acceleration is assumed to be very small and its effects were analyzed in a perturbative regime. For analysis, we consider θθθ parameterized two-qubit pure entangled state and a Werner state. In contrast to the degradation of entanglement due to the relativistic motion between the cavities, the quantum Fisher information of the pure composite system Fθ\mathcal{F}_θFθ​ with respect to parameter θθθ is found to be invariant under the same conditions. However, in the case of the Werner state, the quantum Fisher information displays periodic degradation, due to the inertial and non-inertial segments of motion. Further, we investigate how this evolution process affects the quantum Fisher information distribution over the subsystems of Alice's and Rob's cavities. We find that the quantum Fisher information over the Rob's cavity shows the periodic degradation behavior depending upon the parameter θθθ as well as the uniform acceleration for both the two qubit pure state and Werner state. The quantum Fisher information over Alice's cavity remains invariant throughout the motion of Rob's cavity for the two qubit pure state whereas for Werner state it is affected by the mixing parameter of the Werner state.
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 $w=dy/d\ensuremath{\tau}$, 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.
We show that motion and gravity affect the precision of quantum clocks. We consider a localised quantum field as a fundamental model of a quantum clock moving in spacetime and show that its state is modified due to changes in acceleration. By computing the quantum Fisher information we determine how relativistic motion modifies the ultimate bound in the precision of the measurement of time. While in the absence of motion the squeezed vacuum is the ideal state for time estimation, we find that it is highly sensitive to the motion-induced degradation of the quantum Fisher information. We show that coherent states are generally more resilient to this degradation and that in the case of very low initial number of photons, the optimal precision can be even increased by motion. These results can be tested with current technology by using superconducting resonators with tunable boundary conditions.
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.
By using the non-Markovian master equation, we investigate the effect of the cavity and the environment on the quantum Fisher information (QFI) of an atom qubit system in a dissipation cavity. We obtain the formulae of QFI for two different initial states and analyze the effect of the atom–cavity coupling and the cavity–reservoir coupling on the QFI. The results show that the dynamic behavior of the QFI is obviously dependent on the initial atomic states, the atom–cavity coupling, and the cavity–reservoir coupling. The stronger the atom–cavity coupling, the quicker the QFI oscillates, and the slower the QFI decreases. In particular, the QFI will tend to be a stable value rather than zero if the atom–cavity coupling is large enough. On the other hand, the smaller the cavity–reservoir coupling, the stronger the non-Markovian effect, and the slower the QFI decays. In other words, choosing the best parameter can improve the accuracy of the parameter estimation. In addition, the physical explanation of the dynamic behavior of the QFI is given by means of the QFI flow.