Gaussian quantum steering and its asymmetry in curved spacetime

Wang, Jieci; Cao, Haixin; Jing, Jiliang; Fan, Heng

doi:10.1103/physrevd.93.125011

Cited by 55 publications

(46 citation statements)

References 56 publications

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“…In this section we introduce the quantum field theory and the Hawking radiation of a bosonic field in the background of an asymptotically flat black hole. We are going to show how the thermal radiation induced by the Hawking effect can be described by a Gaussian channel . We consider a massless bosonic field Φ, which satisfies the Klein‐Gordon(K‐G) equation

\begin{matrix} true \\ right \frac{1}{\sqrt{- g}} \frac{\partial}{\partial x^{μ}} ((), \sqrt{- g}, g^{μ ν}, \frac{\partial Φ}{\partial x^{ν}}) = 0, \end{matrix}

in a general spacetime.…”

Section: Gaussian Channel Description Of Hawking Effect For An Asymptmentioning

confidence: 99%

“…Here κ is the surface gravity of the asymptotically flat black hole which relates the Hawking temperature T by

T = κ / 2 π

. By employing the Bogliubov transformation between the Unruh modes and the Schwarzschild modes, the Unruh vacuum is found to be

0true {| 0_{Ω} ⟩}_{U} = \frac{1}{prefixcosh r_{Ω}^{2}} \sum_{n, m = 0}^{\infty} prefixtanh r_{Ω}^{n + m} {| m n m^{'} n^{'} ⟩}_{Ω},

where

| m n m^{'} n^{'} ⟩ = {false| m_{normalΩ} false⟩}_{o u t}^{+} {false| n_{- Ω} false⟩}_{i n}^{-} {false| m_{- Ω}^{'} false⟩}_{o u t}^{-} {false| n_{normalΩ}^{'} false⟩}_{i n}^{+}

, and the superscripts

{+, -}

on the kets is used to indicate the particle and antiparticle modes, respectively. In Eq.…”

Section: Gaussian Channel Description Of Hawking Effect For An Asymptmentioning

confidence: 99%

“…Therefore, the effect of Hawking radiation can be described by a two‐mode squeezing operator

{\overset{U}{true}}_{o u t, i n} false(r_{Ω} false)

acting on the input state

false| ψ_{0} false⟩

\begin{matrix} true \\ right ρ_{o u t} & = & left {tr}_{i n} {{\hat{U}}_{o u t, i n} (r_{normalΩ}) ([, {(| ψ_{0} ⟩ false⟨ ψ_{0} false|)}_{o u t}) \\ left (] \otimes {(false| 0 false⟩ false⟨ 0 false|)}_{i n}) {\hat{U}}_{o u t, i n}^{†} (r_{normalΩ})}, \end{matrix}

where the squeezing operator has the form

{\overset{U}{true}}_{o u t, i n} false(r_{Ω} false) = e^{r_{normalΩ} false({\hat{b}}_{normalΩ, out}^{†} {\hat{b}}_{normalΩ, in}^{†} - {\hat{a}}_{normalΩ, out} {\hat{a}}_{normalΩ, in} false)}

and we rewrite

r_{Ω}

as r hereafter. In this paper we work in the phase space, then we employ a symplectic phase‐space representation

S_{B, \bar{B}} false(r false)

for the two‐mode squeezing transformation, which is …”

Section: Gaussian Channel Description Of Hawking Effect For An Asymptmentioning

confidence: 99%

“…Unlike entanglement, quantum steering is a type of quantum correlation depending on the direction of measurement, which makes the symmetric property of steering a crucial issue. For Gaussian states, it was recently found that the 1 → 1 steering is asymmetric both in the flat spacetime and the curved spacetime . We wonder if the asymmetry of steering will pass to the monogamy of steering in the curved spacetime.…”

Section: Dynamics Of Monogamy Deficit and Monogamy Asymmetry For Quanmentioning

confidence: 99%

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Monogamy of Einstein‐Podolsky‐Rosen Steering in the Background of an Asymptotically Flat Black Hole

2017

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We study the behavior of monogamy deficit and monogamy asymmetry for Einstein-Podolsky-Rosen steering of Gaussian states under the influence of the Hawking effect. We demonstrate that the monogamy of quantum steering shows an extreme scenario in the curved spacetime: the first part of a tripartite system cannot individually steer two other parties, but it can steer the collectivity of the remaining two parties.We also find that the monogamy deficit of Gaussian steering, a quantifier of genuine tripartite steering, are generated due to the influence of the Hawking thermal bath. Our results elucidate the structure of quantum steering in tripartite quantum systems in curved spacetime.

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\begin{matrix} true \\ right \frac{1}{\sqrt{- g}} \frac{\partial}{\partial x^{μ}} ((), \sqrt{- g}, g^{μ ν}, \frac{\partial Φ}{\partial x^{ν}}) = 0, \end{matrix}

in a general spacetime.…”

Section: Gaussian Channel Description Of Hawking Effect For An Asymptmentioning

confidence: 99%

“…Here κ is the surface gravity of the asymptotically flat black hole which relates the Hawking temperature T by

T = κ / 2 π

. By employing the Bogliubov transformation between the Unruh modes and the Schwarzschild modes, the Unruh vacuum is found to be

0true {| 0_{Ω} ⟩}_{U} = \frac{1}{prefixcosh r_{Ω}^{2}} \sum_{n, m = 0}^{\infty} prefixtanh r_{Ω}^{n + m} {| m n m^{'} n^{'} ⟩}_{Ω},

where

| m n m^{'} n^{'} ⟩ = {false| m_{normalΩ} false⟩}_{o u t}^{+} {false| n_{- Ω} false⟩}_{i n}^{-} {false| m_{- Ω}^{'} false⟩}_{o u t}^{-} {false| n_{normalΩ}^{'} false⟩}_{i n}^{+}

, and the superscripts

{+, -}

on the kets is used to indicate the particle and antiparticle modes, respectively. In Eq.…”

Section: Gaussian Channel Description Of Hawking Effect For An Asymptmentioning

confidence: 99%

“…Therefore, the effect of Hawking radiation can be described by a two‐mode squeezing operator

{\overset{U}{true}}_{o u t, i n} false(r_{Ω} false)

acting on the input state

false| ψ_{0} false⟩

\begin{matrix} true \\ right ρ_{o u t} & = & left {tr}_{i n} {{\hat{U}}_{o u t, i n} (r_{normalΩ}) ([, {(| ψ_{0} ⟩ false⟨ ψ_{0} false|)}_{o u t}) \\ left (] \otimes {(false| 0 false⟩ false⟨ 0 false|)}_{i n}) {\hat{U}}_{o u t, i n}^{†} (r_{normalΩ})}, \end{matrix}

where the squeezing operator has the form

{\overset{U}{true}}_{o u t, i n} false(r_{Ω} false) = e^{r_{normalΩ} false({\hat{b}}_{normalΩ, out}^{†} {\hat{b}}_{normalΩ, in}^{†} - {\hat{a}}_{normalΩ, out} {\hat{a}}_{normalΩ, in} false)}

and we rewrite

r_{Ω}

as r hereafter. In this paper we work in the phase space, then we employ a symplectic phase‐space representation

S_{B, \bar{B}} false(r false)

for the two‐mode squeezing transformation, which is …”

Section: Gaussian Channel Description Of Hawking Effect For An Asymptmentioning

confidence: 99%

Section: Dynamics Of Monogamy Deficit and Monogamy Asymmetry For Quanmentioning

confidence: 99%

See 2 more Smart Citations

Monogamy of Einstein‐Podolsky‐Rosen Steering in the Background of an Asymptotically Flat Black Hole

2017

Self Cite

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show abstract

“…The definition of quantum entanglement and quantum steering are both employed in the studies of quantum correlations. [10][11][12][13] The definition of steering can be traced back to the previous work by Schrödinger. [10][11][12][13] The definition of steering can be traced back to the previous work by Schrödinger.…”

Section: Introductionmentioning

confidence: 99%

Generation of One‐Way Gaussian Steering by Gaussian Channel and Converting One‐Way Gaussian Steering by Beamsplitters

et al. 2017

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Gaussian steering is used to characterize the intrinsic quantum correlation of Gaussian states under Gaussian measurement. Here we study the generation of one‐way Gaussian steering and the conversion of one‐way Gaussian steering. It is found that one‐way Gaussian steering could be generated by using Gaussian channels, either the Gaussian lossy channel or the Gaussian amplification channel. Exploiting the one‐way Gaussian steering in a two‐partite quantum system consists of two subsystems marked with A and B, one‐way Gaussian steering (steering from A to B) can be converted to the other one‐way Gaussian steering (steering from B to A) using linear optics, and vice versa.

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Dynamical Measurement's Uncertainty in the Curved Space‐Time

2019

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The dynamical characteristics of measurement's uncertainty are investigated under two modes of Dirac field in the Garfinkle-Horowitz-Strominger dilation space-time. It shows that the Hawking effect induced by the thermal field would result in an expansion of the entropic uncertainty with increasing dilation-parameter value, as the systemic quantum coherence reduces, reflecting that the Hawking effect could undermine the systemic coherence. Meanwhile, the intrinsic relationship between the uncertainty and quantum coherence is obtained, and it is revealed that the uncertainty's bound is anti-correlated with the system's quantum coherence. Furthermore, it is illustrated that the systemic mixedness is correlated with the uncertainty to a large extent. Via the information flow theory, various correlations including quantum and classical aspects, which can be used to form a physical explanation on the relationship between the uncertainty and quantum coherence, are also analyzed. Additionally, this investigation is extended to the case of multi-component measurement, and the applications of the entropic uncertainty relation are illustrated on entanglement criterion and quantum channel capacity. Lastly, it is declared that the measurement uncertainty can be quantitatively suppressed through optimal quantum weak measurement. These investigations might pave an avenue to understand the measurement's uncertainty in the curved space-time.

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Gaussian quantum steering and its asymmetry in curved spacetime

Cited by 55 publications

References 56 publications

Monogamy of Einstein‐Podolsky‐Rosen Steering in the Background of an Asymptotically Flat Black Hole

Monogamy of Einstein‐Podolsky‐Rosen Steering in the Background of an Asymptotically Flat Black Hole

Generation of One‐Way Gaussian Steering by Gaussian Channel and Converting One‐Way Gaussian Steering by Beamsplitters

Dynamical Measurement's Uncertainty in the Curved Space‐Time

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