Steering Witness and Steering Criterion of Gaussian States

Ma, Ruifen; Tu, Yan; Wu, Dantong; Qi, Xiaofei

doi:10.3390/e24010062

Cited by 2 publications

(5 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…γ AB /γ A + iΩ NB ⩾ 0. Based also on the definition of the Schur complement in equation (10) we state that if a CM γ AB is non-steerable then there exists a CM σ B fulfilling equation (20), and it is the Schur complement γ AB /γ A . ⇐ Conversely, if the relation in equation ( 20) is fulfilled for some CM σ B , satisfying CMC σ B + iΩ NB ⩾ 0, then by the definition of the Schur complement in equation ( 10) it follows that there exists a positive semidefinite matrix P ⩾ 0 such that: σ B + P = γ AB /γ A .…”

Section: ) Is Alice To Bob Non-steerable By Gaussian Measurements If ...mentioning

confidence: 99%

“…This expression is invariant under local symplectic transformations at the CM level, and has a formal similarity to the logarithmic negativity [30], which for Gaussian states quantifies how much the partially transposed CM fails to fulfill CMC in equation (20). The quantification of Gaussian steerability takes a simpler form when the steered party, e.g.…”

Section: Detection Of Gaussian Steeringmentioning

confidence: 99%

“…An EW based on second moments is a real symmetric matrix Z ⩾ 0 such that Tr[Zγ s ] ⩾ 1 holds for all separable covariance matrices γ s , while Tr[Zγ] < 1 for some entangled CM γ [17]. An analogous definition holds also for steering witnesses (SWs) [20] due to the fact that the set of non-steerable covariance matrices is convex and closed. We introduce constraints fully characterizing the set of Gaussian SWs, which are shown to be stronger than analogous constraints on EWs.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Steering witnesses for unknown Gaussian quantum states

Mihaescu,

Kampermann,

Isar

et al. 2023

New J. Phys.

View full text Add to dashboard Cite

We define and fully characterize the witnesses based on second moments detecting steering in Gaussian states by means of Gaussian measurements. All such tests, which arise from linear combination of variances or second moments of canonical operators, are easily implemented in experiments. We propose also a set of linear constraints fully characterizing steering witnesses when the steered party has one bosonic mode, while in the general case the constraints restrict the set of tests detecting steering. Given an unknown quantum state we implement a semidefinite program providing the appropriate steering test with respect to the number of random measurements performed. Thus, it is a ‘repeat-until-success’ method allowing for steering detection with less measurements than in full tomography. We study the efficiency of steering detection for two-mode squeezed vacuum states, for two-mode general unknown states, and for three-mode continuous variable GHZ states. In addition, we discuss the robustness of this method to statistical errors.

show abstract

Section: ) Is Alice To Bob Non-steerable By Gaussian Measurements If ...mentioning

confidence: 99%

Section: Detection Of Gaussian Steeringmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Steering witnesses for unknown Gaussian quantum states

Mihaescu,

Kampermann,

Isar

et al. 2023

New J. Phys.

View full text Add to dashboard Cite

show abstract

“…Since then, the EPR steering theory has been rapidly developed. [15][16][17][18][19][20][21][22][23][24][25][26] Many studies of EPR steering theory were attributed to the solution of semidefinite programming (SDP). Skrzypczyk et al summarized the application of SDP in EPR steering.…”

Section: Introductionmentioning

confidence: 99%

“…[15] This is a powerful technique that can be used to study many problems related to steering, including steering detection, [18] steering quantification, [19] and cloning of steering. [27] A series of steering inequalities [20][21][22][23] and steering witnesses [24][25][26] have been proposed for quantifying steering.…”

Section: Introductionmentioning

confidence: 99%

Genuine Einstein–Podolsky–Rosen steering of generalized three-qubit states via unsharp measurements

Chen¹,

Guo²,

Wei³

et al. 2023

Chinese Phys. B

View full text Add to dashboard Cite

We aim to explore all possible scenarios of ($ 1 \rightarrow 2 $) (where one wing is untrusted and the other two wings are trusted) and ($ 2 \rightarrow 1 $) (where two wings are untrusted, and one wing is trusted) genuine tripartite EPR steering. The generalized Greenberger-Horne-Zeilinger (GHZ) state is shared between three spatially separated parties, Alice, Bob and Charlie. In both ($ 1 \rightarrow 2 $) and ($ 2 \rightarrow 1 $), we discuss the untrusted party and trusted party performing a sequence of unsharp measurements, respectively. For each scenario, we deduce an upper bound on the number of sequential observers who can demonstrate genuine EPR steering through the quantum violation of tripartite steering inequality. The results show that the maximum number of observers for the generalized GHZ states can be the same with that of the maximally GHZ state in a certain range of state parameters. Moreover, both the sharpness parameters range and the state parameters range in the scenario of ($ 1 \rightarrow 2 $) steering are larger than those in the scenario of ($ 2 \rightarrow 1 $) steering.

show abstract

Steering Witness and Steering Criterion of Gaussian States

Cited by 2 publications

References 30 publications

Steering witnesses for unknown Gaussian quantum states

Steering witnesses for unknown Gaussian quantum states

Genuine Einstein–Podolsky–Rosen steering of generalized three-qubit states via unsharp measurements

Contact Info

Product

Resources

About