Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1306.3144 · Physical Review A

Parameter estimation using NOON states over a relativistic quantum channel

Dominic Hosler, Pieter Kok

Published Nov 13, 2013• 42 citations
arXivHTMLPDF

Abstract

We study the effect of the acceleration of the observer on a parameter estimation protocol using NOON states. An inertial observer, Alice, prepares a NOON state in Unruh modes of the quantum field, and sends it to an accelerated observer, Rob. We calculate the quantum Fisher information of the state received by Rob. We find the counterintuitive result that the single-rail encoding outperforms the dual rail. The NOON states have an optimal $N$ for the maximum information extractable by Rob, given his acceleration. This optimal $N$ decreases with increasing acceleration.

DOI
10.1103/physreva.88.052112

Related papers

Fundamental limitations to information transfer in accelerated frames

Eduardo Martín-Martínez, Dominic Hosler, Miguel Montero

We study communication between an inertial observer and one of two causally disconnected counteraccelerating observers. We will restrict the quantum channel considering inertial-to-accelerated bipartite classical and quantum communication over different sets of Unruh modes (single-rail or dual-rail encoding). We find that the coherent information (and therefore the amount of entanglement that can be generated via state merging protocol) in this strongly restricted channel presents some interesting monogamy properties between the inertial and only one of the accelerated observers if we take a fixed choice of the Unruh mode used in the channel. The optimization of the controllable parameters is also studied and we find that they deviate from the values usually employed in the literature.

arXiv:1204.6271•Physical Review A•Dec 7, 2012•24 citations

Weak measurement effect on optimal estimation with lower and upper bound on relativistic metrology

Hossein Rangani Jahromi

We address the quantum estimation of parameters encoded into the initial state of two modes of a Dirac field described by relatively accelerated parties. By using the quantum Fisher information (QFI), we investigate how the weak measurements performed before and after the accelerating observer, affect the optimal estimation of information encoded into the weight and phase parameters of the initial state shared between the parties. Studying the QFI, associated with weight parameter [Formula: see text], we find that the acceleration at which the optimal estimation occurs may be controlled by weak measurements. Moreover, it is shown that the post-measurement plays the role of a quantum key for manifestation of the Unruh effect. On the other hand, investigating the phase estimation optimization and assuming that there is no control over the initial state, we show that the weak measurements may be utilized to match the optimal [Formula: see text] to its predetermined value. Moreover, in addition to determination of a lower bound on the QFI with the local quantum uncertainty (LQU), we unveil an important upper bound on the precision of phase estimation in our relativistic scenario, given by the maximal steered coherence (MSC). We also obtain a compact expression of the MSC for general X states.

arXiv:1807.09362•International Journal of Modern Physics D•Aug 13, 2019•9 citations

Quantum Fisher information in noninertial frames

Yao Yao, Xing Mao Xiao, Li Ge +2 more

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 $r$ 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.

arXiv:1401.0596•Physical Review A•Apr 30, 2014•110 citations

Estimation of teleported and gained parameters in a non-inertial frame

N Metwally

Abstract Quantum Fisher information is introduced as a measure of estimating the teleported information between two users, one of which is uniformly accelerated. We show that the final teleported state depends on the initial parameters, in addition to the gained parameters during the teleportation process. The estimation degree of these parameters depends on the value of the acceleration, the used single mode approximation (within/beyond), the type of encoded information (classic/quantum) in the teleported state, and the entanglement of the initial communication channel. The estimation degree of the parameters can be maximized if the partners teleport classical information.

arXiv:1611.03460•Laser Physics Letters•Feb 13, 2017•32 citations

Unruh acceleration effect on the precision of parameter estimation

NASSER METWALLY

The dynamics of Fisher information for an accelerated system initially prepared in the $X$-state is discussed. An analytical solution, which consists of three parts: classical, the average over all pure states and a mixture of pure states is derived for the general state and for Werner state. It is shown that, the Unruh acceleration has a depleting effect on the Fisher information. This depletion depends on the degree of entanglement of the initial state settings. For the $X$-state, for some intervals of Unruh acceleration, the Fisher information remains constant, irrespective to the Unruh acceleration. In general, the possibility of estimating the state's parameters decreases as the acceleration increases. However, the precision of estimation can be maximized for certain values of the Unruh acceleration. We also investigate the contribution of the different parts of the Fisher information on the dynamics of the total Fisher information.

arXiv:1609.02092•Sep 7, 2016•2 citations

Quantum Fisher information of fermionic cavity modes in an accelerated motion

Zahid Hussain Shamsi, DaiGyoung Kim, Younghun Kwon

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.

arXiv:1409.6847•Sep 24, 2014•1 citation
We study the effect of the acceleration of the observer on a parameter estimation protocol using NOON states. An inertial observer, Alice, prepares a NOON state in Unruh modes of the quantum field, and sends it to an accelerated observer, Rob. We calculate the quantum Fisher information of the state received by Rob. We find the counterintuitive result that the single-rail encoding outperforms the dual rail. The NOON states have an optimal NNN for the maximum information extractable by Rob, given his acceleration. This optimal NNN decreases with increasing acceleration.
We study communication between an inertial observer and one of two causally disconnected counteraccelerating observers. We will restrict the quantum channel considering inertial-to-accelerated bipartite classical and quantum communication over different sets of Unruh modes (single-rail or dual-rail encoding). We find that the coherent information (and therefore the amount of entanglement that can be generated via state merging protocol) in this strongly restricted channel presents some interesting monogamy properties between the inertial and only one of the accelerated observers if we take a fixed choice of the Unruh mode used in the channel. The optimization of the controllable parameters is also studied and we find that they deviate from the values usually employed in the literature.
We address the quantum estimation of parameters encoded into the initial state of two modes of a Dirac field described by relatively accelerated parties. By using the quantum Fisher information (QFI), we investigate how the weak measurements performed before and after the accelerating observer, affect the optimal estimation of information encoded into the weight and phase parameters of the initial state shared between the parties. Studying the QFI, associated with weight parameter [Formula: see text], we find that the acceleration at which the optimal estimation occurs may be controlled by weak measurements. Moreover, it is shown that the post-measurement plays the role of a quantum key for manifestation of the Unruh effect. On the other hand, investigating the phase estimation optimization and assuming that there is no control over the initial state, we show that the weak measurements may be utilized to match the optimal [Formula: see text] to its predetermined value. Moreover, in addition to determination of a lower bound on the QFI with the local quantum uncertainty (LQU), we unveil an important upper bound on the precision of phase estimation in our relativistic scenario, given by the maximal steered coherence (MSC). We also obtain a compact expression of the MSC for general X states.
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.
Abstract Quantum Fisher information is introduced as a measure of estimating the teleported information between two users, one of which is uniformly accelerated. We show that the final teleported state depends on the initial parameters, in addition to the gained parameters during the teleportation process. The estimation degree of these parameters depends on the value of the acceleration, the used single mode approximation (within/beyond), the type of encoded information (classic/quantum) in the teleported state, and the entanglement of the initial communication channel. The estimation degree of the parameters can be maximized if the partners teleport classical information.
The dynamics of Fisher information for an accelerated system initially prepared in the XXX-state is discussed. An analytical solution, which consists of three parts: classical, the average over all pure states and a mixture of pure states is derived for the general state and for Werner state. It is shown that, the Unruh acceleration has a depleting effect on the Fisher information. This depletion depends on the degree of entanglement of the initial state settings. For the XXX-state, for some intervals of Unruh acceleration, the Fisher information remains constant, irrespective to the Unruh acceleration. In general, the possibility of estimating the state's parameters decreases as the acceleration increases. However, the precision of estimation can be maximized for certain values of the Unruh acceleration. We also investigate the contribution of the different parts of the Fisher information on the dynamics of the total Fisher information.
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.