Programme

P.31 -- Poster, NCTP-43

Date: Tuesday, 31 July 2018

Time: 08:30 - 10:00

Numerical determination of Einstein-Podolsky-Rosen steering for two-qubit states

T. Ha Duong (1, 2), N. Duc Le (3), H. Chau Nguyen (4), and Huy-Viet Nguyen (5)

(1) Graduate University of Science and Technology, VAST (2) Thai Nguyen University of Education (3)University of Science and Technology of Hanoi, VAST (4) University of Siegen, Germany (5) Institute of Physics, VAST

Einstein-Podolsky-Rosen (EPR) steering, together with Bell nonlocality and entanglement (nonseparability), are basic notions of quantum nonlocality. In a typical EPR steering experiment, Alice and Bob share a bipartite quantum system which can be at an arbitrary distance apart. Alice, by performing a measurement on her side, steers Bob’s system into the corresponding conditional ensemble, thus can predict the outcome of Bob’s measurements prior to his performance. Bob, however, is not convinced that Alice can do so if he can explain Alice’s prediction with a local model [more precisely, local hidden state model (LHS)] for his side. In this case, the state is said to be unsteerable. It is well established that steerability forms a distinct class of quantum nonlocality which is a subset of the entanglement class and a superset of the Bell nolocal one. Despite of intense research since the work of EPR in 1935 until recent years, the question of whether a given quantum state can be used to demonstrate the EPR steering remains open, even for the simplest case of two qubits. Recently, a geometrical approach [Nguyen et al., Phys. Rev. A 94, 012114 (2016)], where steerability of a quantum state with respect to a given LHS model is characterized by the so-called principal radius of the capacity of the LHS model, has been developed. In this approach, a state is steerable if and only if the principal radii of all possible LHS models are less than 1. Thus, the steerability problem is transformed into the determination the optimal LHS model that has the largest principal radius. In this work, we report our numerical implementation for the calculation of the principal radius of a two-qubit state with a given LHS model. We benchmark our implementation for the cases of the Werner state and T-states where analytic solutions are available. Our work is the first step towards the determination of the optimal LHS model.

Presenter: Duong Thi Ha