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arXiv:1409.6847

Quantum Fisher information of fermionic cavity modes in an accelerated motion

Zahid Hussain Shamsi, DaiGyoung Kim, Younghun Kwon

Published Sep 24, 2014• 1 citation
arXivHTMLPDF

Abstract

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 $θ$ 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 $\mathcal{F}_θ$ with respect to parameter $θ$ 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 $θ$ 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.

DOI
10.48550/arxiv.1409.6847

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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.
Although quantum coherence is a well known phenomenon in quantum information theory and quantum optics, it has been investigated from the resource theory perspective only recently. Furthermore, quantum coherence has important implications in relativistic quantum information where the degradation of entanglement can be attributed to decoherence. In this paper, we investigate the quantum coherence of 1+1 Dirac field modes localized in a cavity as observed by two relatively accelerated observers. The acceleration is assigned very small values and its effects are investigated in a perturbative regime. For this purpose, we use α parameterized two-qubit pure entangled state and a Werner state. We find that coherence shows a periodic degradation due to accelerated motion. However, this degradation can be balanced by adjusting the durations of uniform and accelerated motion. Moreover, it is found that dynamics of quantum coherence closely resembles that of entanglement under the same settings. This similarity confirms the recent attempts to relate the resource theories of coherence and entanglement in a relativistic regime.
A central aim of relativistic quantum information (RQI) is the investigation of quantum information tasks and resources taking into account the relativistic aspects of nature. More precisely, it is of fundamental interest to understand how the storage, manipulation, and transmission of information utilizing quantum systems are influenced by the fact that these processes take place in a relativistic spacetime. In particular, many studies in RQI have been focused on the effects of non-uniform motion on entanglement, the main resource of quantum information protocols. Early investigations in this direction were performed in highly idealized settings that prompted questions as to the practical accessibility of these results. To overcome these limitations it is necessary to consider quantum systems that are in principle accessible to localized observers. In this thesis we present such a model, the rigid relativistic cavity, and its extensions, focusing on the effects of motion on entanglement and applications such as quantum teleportation. We study cavities in (1+1) dimensions undergoing non-uniform motion, consisting of segments of uniform acceleration and inertial motion of arbitrary duration that allow the involved velocities to become relativistic. The transitions between segments can be sharp or smooth and higher dimensions can be incorporated. The primary focus lies in the Bogoliubov transformations of the quantum fields, real scalar fields or Dirac fields, confined to the cavities. The Bogoliubov transformations change the particle content and the occupation of the energy levels of the cavity. We show how these effects generate entanglement between the modes of the quantum fields inside a single cavity for various initial states. The entanglement between several cavities, on the other hand, is degraded by the non-uniform motion, influencing the fidelity of tasks such as teleportation.
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.
In this work we mainly focus on two main aspects of interest within the field of Relativistic Quantum Information. We first expand on the current knowledge of the effects of relativity on entanglement between global field modes. Within this aspect, we focus on two topics: we address and revise the single mode approximation commonly used in the literature. We study the nonlocal correlations of charged bosonic field modes and the degradation of entanglement initially present in maximally entangled states as a function of acceleration, when one observer is accelerated. In the second part of this work we introduce, develop and exploit a method for confining quantum fields within one (or two) cavities and analyzing the effects of motion of one cavity on the entanglement initially present between cavity field modes. One cavity is always allowed to undergo arbitrary trajectories composed of segments of inertial motion and uniform acceleration. We investigate how entanglement is degraded, conserved and created as a function of the parameters describing the motion and we provide the analytical tools to understand how these effects occur. We conclude this work by analyzing the effects of the change of spatial topology on the nonlocal correlations present in the Hawking-Unruh radiation in the topological geon analogue of black hole spacetimes.
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.
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.