Sharing quantum steering among multiple Alices and Bobs via a two-qubit Werner state

Abstract

Quantum steering, a type of quantum correlation with unique asymmetry, has important applications in asymmetric quantum information tasks. We consider a new quantum steering scenario in which one half of a two-qubit Werner state is sequentially measured by multiple Alices and the other half by multiple Bobs. We find that the maximum number of Alices who can share steering with a single Bob increases from 2 to 5 when the number of measurement settings N increases from 2 to 16. Furthermore, we find a counterintuitive phenomenon that for a fixed N, at most 2 Alices can share steering with 2 Bobs, while 4 or more Alices are allowed to share steering with a single Bob. We further analyze the robustness of the steering sharing by calculating the required purity of the initial Werner state, the lower bound of which varies from 0.503(1) to 0.979(5). Finally, we show that our both-sides sequential steering sharing scheme can be applied to control the steering ability, even the steering direction, if an initial asymmetric state or asymmetric measurement is adopted. Our work gives insights into the diversity of steering sharing and can be extended to study the problems such as genuine multipartite quantum steering when the sequential unsharp measurement is applied.

Activation of Einstein–Podolsky–Rosen steering sharing with unsharp nonlocal measurements

“…Until now, all researches aimed at improving the efficiency of EPR steering has been restricted to local measurements [25][26][27][28][29] , In the case of local measurements, each observer measures the qubit in the hand. Mathematically, each observer's measurement results can be obtained by measuring his or her respective reduced density matrices.…”

Einstein-Podolsky-Rosen steering of quantum phases in a cavity Bose-Einstein condensate with a single impurity

“…The Hamiltonian (37) indicates that the superradiant-phase Hamiltonian can act as two driving super-mode oscillators.…”

Experimental sharing of Bell nonlocality with projective measurements

“…They found that by adjusting the measurement sharpness, the former party can extract sufficient nonlocality and maintain enough entanglement, enabling sequential parties to share Bell nonlocality simultaneously [16]. Since then, unsharp measurement has been widely applied in sharing quantum correlations [17], such as standard Bell nonlocality [18][19][20][21][22][23], network nonlocality [24][25][26][27][28][29], steering [30][31][32][33][34][35][36][37][38][39], entanglement [40][41][42][43][44], coherence [45,46], and contextuality [47,48]. Moreover, it has been observed that these shared quantum correlations are closely connected to numerous quantum information tasks, including quantum random access code [49][50][51][52], randomness certification [53][54][55], self-testing [56,57] and revealing 'hidden' nonlocality [58].…”