Eur. Phys. J. D (2019) 73: 66
https://doi.org/10.1140/epjd/e2019-90184-3

Regular Article

Several trade off features of quantum steering in distributed scenario

¹ Centre for Astroparticle Physics and Space Science (CAPSS), Bose Institute, Block EN, Sector V, Salt Lake, 700091 Kolkata, India
² Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong, P.R. China
³ Optics and Quantum Information Group, The Institute of Mathematical Sciences, HBNI, C.I.T Campus, Taramani, 600113 Chennai, India
⁴ Department of Mathematics, Heritage Institute of Technology, 700107 Kolkata, India
⁵ Department of Mathematics, South Malda College, Malda, West Bengal, India
⁶ Department of Mathematics, Government Girls’ General Degree College, Ekbalpore, 700023 Kolkata, India

^a e-mail: nirmanganguly@gmail.com

Received: 18 April 2018
Received in final form: 17 January 2019
Published online: 2 April 2019

Abstract

In the present work we address the question of how bipartite steering violation takes place among multi-partite systems (where each sub-system have Hilbert space dimension restricted to two) based on the maximal violations of the bipartite steering inequality of the reduced pairwise qubit systems. We have derived a trade-off relation which is satisfied by those pair wise bipartite maximal steering violations, which physically can be understood as providing restrictions on the distribution of steering among sub systems. For a three-qubit system, it is impossible that all pairs of qubits violate the steering inequality, and once a pair of qubits violates the steering inequality maximally, the other two pairs of qubits must both obey the steering inequality. We also present a complementarity relation between genuine entanglement present in a tripartite state and maximum bipartite steering violation by its reduced states.