Influence of relativistic effects on satellite-based clock synchronization

Wang, Jieci; Tian, Zehua; Jing, Jiliang; Fan, Heng

doi:10.1103/physrevd.93.065008

Cited by 35 publications

(53 citation statements)

References 59 publications

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“…The relation between

a_{{normalΩ}_{A}}

and

a_{{normalΩ}_{B}}

was discussed in refs. [], and can be used to calculate the relation between the frequency distributions

F_{{normalΩ}_{K, 0}}^{false(K false)}

of the photons before and after the propagation

F_{Ω_{B, 0}}^{(B)} false(Ω_{B} false) = \sqrt[4]{\frac{f false(r_{B} false)}{f false(r_{A} false)}} F_{Ω_{A, 0}}^{(A)} (\sqrt{\frac{f (r_{B})}{f (r_{A})}} Ω_{B})

From Equation , we can see that the effect induced by the curved spacetime of the Earth cannot be simply corrected by a linear shift of frequencies. Therefore, it may be challenging to compensate the transformation induced by the curvature in realistic implementations.…”

Section: Light Wave Packets Propagating In the Curved Spacetimementioning

confidence: 99%

“…Indeed, such a nonlinear gravitational effect is found to influence the fidelity of the quantum channel between Alice and Bob . It is always possible to decompose the mode

{\bar{a}}^{'}

received by Bob in terms of the mode

a^{'}

prepared by Alice and an orthogonal mode

a_{⊥}^{'}

(i.e.,

[a^{'}, a_{⊥}^{' †}] = 0

)

{\overset{a}{true}}^{'} = Θ a^{'} + \sqrt{1 - {normalΘ}^{2}} a_{⊥}^{'}

where Θ is the wave packet overlap between the distributions

F_{Ω_{B, 0}}^{(B)} false(Ω_{B} false)

and

F_{Ω_{A, 0}}^{(A)} false(Ω_{B} false)

0true normalΘ : = \int_{0}^{+ \infty} d Ω_{B} F_{{normalΩ}_{B, 0}}^{false(B false) ★} ({normalΩ}_{B}) F_{{normalΩ}_{A, 0}}^{false(A false)} ({normalΩ}_{B})

and we have

Θ = 1

for a perfect channel.…”

Section: Light Wave Packets Propagating In the Curved Spacetimementioning

confidence: 99%

“…However, since

{normalΩ}_{0} ≫ σ

, it is possible to include negative frequencies without affecting the value of Θ. Using Equations and one finds that

Θ = \sqrt{\frac{2}{1 + {false(1 + δ false)}^{2}}} \frac{1}{1 + δ} e^{- \frac{δ^{2} {normalΩ}_{B, 0}^{2}}{4 false(1 + {false(1 + δ false)}^{2} false) σ^{2}}}

where the new parameter δ quantifying the shifting is defined by

δ = \sqrt[4]{\frac{f false(r_{A} false)}{f false(r_{B} false)}} - 1 = \sqrt{\frac{{normalΩ}_{B}}{{normalΩ}_{A}}} - 1

The expression for

\frac{{normalΩ}_{B}}{{normalΩ}_{A}}

in the equatorial plane of the Kerr spacetime has been shown in

\frac{Ω_{B}}{Ω_{A}} = \frac{1 + ε \frac{a}{r_{B}} \sqrt{\frac{M}{r_{B}}}}{C \sqrt{1 - 3 \frac{M}{r_{B}} + 2 ε \frac{a}{r_{B}} \sqrt{\frac{M}{r_{B}}}}}

where

C = {[1 - \frac{2 M}{r_{A}} false(1 + 2 a ω false) + false(r_{A}^{2} + a^{2} - \frac{2 M a^{2}}{r_{A}} false) ω^{2}]}^{- \frac{1}{2}}

is the normalization constant, ω is the Earth's equatorial angular velocity, and

ε = <...>

…”

Section: Light Wave Packets Propagating In the Curved Spacetimementioning

confidence: 99%

“…As discussed in refs. [], the influence of the Earth's gravitational effect can be modeled by a beam splitter with orthogonal modes

b_{1 ⊥}

and

b_{2 ⊥}

. The covariance matrix of the initial state is given by

{normalΣ}_{0}^{b_{1} b_{2} b_{1 ⊥} b_{2 ⊥}} = (\begin{matrix} \overset{σ}{true} (s) & 0 \\ 0 & I_{4} \end{matrix})

where I 4 denotes the 4 × 4 identity matrix and

\tilde{σ} false(s false)

is the covariance matrix of the two‐mode squeezed state

\tilde{σ} false(s false) = (\begin{matrix} prefixcosh (2 s) I_{2} & prefixsinh (2 s) σ_{z} \\ prefixsinh (2 s) σ_{z} & prefixcosh (2 s) I_{2} \end{matrix})

where

σ_{z}

is Pauli matrix and s is the squeezing parameter.…”

Section: The Influence Of Gravitational Effects On Quantum Steerabilimentioning

confidence: 99%

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Satellite‐Based Quantum Steering under the Influence of Spacetime Curvature of the Earth

2018

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Spacetime curvature of the Earth deforms wave packets of photons sent from the Earth to satellites, thus influencing the quantum state of light. We show that Gaussian steering of photon pairs, which are initially prepared in a two‐mode squeezed state, is affected by the curved spacetime background of the Earth. We demonstrate that quantum steerability of the state increases for a specific range of height h and then gradually approaches a finite value with further increasing height of the satellite's orbit. Comparing with the peak frequency parameter, the Gaussian steering changes more for different squeezing parameters, while the gravitational frequency effect leads to quantum steering asymmetry between the photon pairs. In addition, we find that the influence of spacetime curvature on the steering in the Kerr spacetime is very different from the non‐rotating case because special relativistic effects are involved.

show abstract

“…The relation between

a_{{normalΩ}_{A}}

and

a_{{normalΩ}_{B}}

was discussed in refs. [], and can be used to calculate the relation between the frequency distributions

F_{{normalΩ}_{K, 0}}^{false(K false)}

of the photons before and after the propagation

F_{Ω_{B, 0}}^{(B)} false(Ω_{B} false) = \sqrt[4]{\frac{f false(r_{B} false)}{f false(r_{A} false)}} F_{Ω_{A, 0}}^{(A)} (\sqrt{\frac{f (r_{B})}{f (r_{A})}} Ω_{B})

Section: Light Wave Packets Propagating In the Curved Spacetimementioning

confidence: 99%

“…Indeed, such a nonlinear gravitational effect is found to influence the fidelity of the quantum channel between Alice and Bob . It is always possible to decompose the mode

{\bar{a}}^{'}

received by Bob in terms of the mode

a^{'}

prepared by Alice and an orthogonal mode

a_{⊥}^{'}

(i.e.,

[a^{'}, a_{⊥}^{' †}] = 0

)

{\overset{a}{true}}^{'} = Θ a^{'} + \sqrt{1 - {normalΘ}^{2}} a_{⊥}^{'}

where Θ is the wave packet overlap between the distributions

F_{Ω_{B, 0}}^{(B)} false(Ω_{B} false)

and

F_{Ω_{A, 0}}^{(A)} false(Ω_{B} false)

0true normalΘ : = \int_{0}^{+ \infty} d Ω_{B} F_{{normalΩ}_{B, 0}}^{false(B false) ★} ({normalΩ}_{B}) F_{{normalΩ}_{A, 0}}^{false(A false)} ({normalΩ}_{B})

and we have

Θ = 1

for a perfect channel.…”

Section: Light Wave Packets Propagating In the Curved Spacetimementioning

confidence: 99%

“…However, since

{normalΩ}_{0} ≫ σ

, it is possible to include negative frequencies without affecting the value of Θ. Using Equations and one finds that

Θ = \sqrt{\frac{2}{1 + {false(1 + δ false)}^{2}}} \frac{1}{1 + δ} e^{- \frac{δ^{2} {normalΩ}_{B, 0}^{2}}{4 false(1 + {false(1 + δ false)}^{2} false) σ^{2}}}

where the new parameter δ quantifying the shifting is defined by

δ = \sqrt[4]{\frac{f false(r_{A} false)}{f false(r_{B} false)}} - 1 = \sqrt{\frac{{normalΩ}_{B}}{{normalΩ}_{A}}} - 1

The expression for

\frac{{normalΩ}_{B}}{{normalΩ}_{A}}

in the equatorial plane of the Kerr spacetime has been shown in

\frac{Ω_{B}}{Ω_{A}} = \frac{1 + ε \frac{a}{r_{B}} \sqrt{\frac{M}{r_{B}}}}{C \sqrt{1 - 3 \frac{M}{r_{B}} + 2 ε \frac{a}{r_{B}} \sqrt{\frac{M}{r_{B}}}}}

where

C = {[1 - \frac{2 M}{r_{A}} false(1 + 2 a ω false) + false(r_{A}^{2} + a^{2} - \frac{2 M a^{2}}{r_{A}} false) ω^{2}]}^{- \frac{1}{2}}

is the normalization constant, ω is the Earth's equatorial angular velocity, and

ε = <...>

…”

Section: Light Wave Packets Propagating In the Curved Spacetimementioning

confidence: 99%

“…As discussed in refs. [], the influence of the Earth's gravitational effect can be modeled by a beam splitter with orthogonal modes

b_{1 ⊥}

and

b_{2 ⊥}

. The covariance matrix of the initial state is given by

{normalΣ}_{0}^{b_{1} b_{2} b_{1 ⊥} b_{2 ⊥}} = (\begin{matrix} \overset{σ}{true} (s) & 0 \\ 0 & I_{4} \end{matrix})

where I 4 denotes the 4 × 4 identity matrix and

\tilde{σ} false(s false)

is the covariance matrix of the two‐mode squeezed state

\tilde{σ} false(s false) = (\begin{matrix} prefixcosh (2 s) I_{2} & prefixsinh (2 s) σ_{z} \\ prefixsinh (2 s) σ_{z} & prefixcosh (2 s) I_{2} \end{matrix})

where

σ_{z}

is Pauli matrix and s is the squeezing parameter.…”

Section: The Influence Of Gravitational Effects On Quantum Steerabilimentioning

confidence: 99%

See 2 more Smart Citations

Satellite‐Based Quantum Steering under the Influence of Spacetime Curvature of the Earth

2018

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show abstract

“…It was experimentally demonstrated that the gravitational frequency shift (GFS) effects have a remarkable influence on the precision of atomic clocks for a variation of 0.33m in height [34]. In addition, relativistic effects of the Earth notably affect satellite-based quantum information processing tasks [35][36][37] and quantum clock synchronization [38]. Quantum information also plays a prominent role in the study of the thermodynamics and information loss problem [40,41] of black holes.…”

Section: Introductionmentioning

confidence: 99%

Gaussian quantum steering and its asymmetry in curved spacetime

et al. 2016

Self Cite

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We study Gaussian quantum steering and its asymmetry in the background of a Schwarzschild black hole. We present a Gaussian channel description of quantum state evolution under the influence of the Hawking radiation. We find that thermal noise introduced by Hawking effect will destroy the steerability between an inertial observer Alice and an accelerated observer Bob who hovers outside the event horizon, while it generates steerability between Bob and a hypothetical observer anti-Bob inside the event horizon. Unlike entanglement behaviors in curved spacetime, here the steering from Alice to Bob suffers from a "sudden death" and the steering from anti-Bob to Bob experiences a "sudden birth" with increasing Hawking temperature. We also find that the Gaussian steering is always asymmetric and the maximum steering asymmetry cannot exceed ln 2, which means the state never evolves to an extremal asymmetry state. Furthermore, we obtain the parameter settings that maximize steering asymmetry and find that (i) s = arccosh() is the critical point of steering asymmetry, and (ii) the attainment of maximal steering asymmetry indicates the transition between one-way steerability and both-way steerability for the two-mode Gaussian state under the influence of Hawking radiation.

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Multipartite Quantum Coherence and Distribution under the Unruh Effect

Ding

Shi

et al. 2018

Annalen der Physik

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Quantum coherence of the tripartite W state and Greenberger-Horne-Zeilinger (GHZ) state under the Unruh effect are explored based on the model of a two-level detector qubit coupled to a massless scalar field. The results reveal that Unruh thermal noise really destroys tripartite quantum resources. It is worth mentioning that the quantum coherence of the GHZ state reaches zero in the infinite acceleration limit, but that of the W-state always remains nonzero. Coherence of the GHZ state displays a sudden death as the coupling parameter grows, while coherence freezing can be witnessed for the W state. It can be concluded that the W state is more robust than the GHZ state against Unruh radiation. Moreover, the related investigation can be expanded to N-qubit quantum systems and the corresponding analytical solution is obtained. It indicates that the larger number W-type entangled qubit can be as a better quantum resource for quantum information tasks under the Unruh effect.

show abstract

Influence of relativistic effects on satellite-based clock synchronization

Cited by 35 publications

References 59 publications

Satellite‐Based Quantum Steering under the Influence of Spacetime Curvature of the Earth

Satellite‐Based Quantum Steering under the Influence of Spacetime Curvature of the Earth

Gaussian quantum steering and its asymmetry in curved spacetime

Multipartite Quantum Coherence and Distribution under the Unruh Effect

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