Detecting Einstein-Podolsky-Rosen steering through entanglement detection

Abstract

Quantum inseparabilities can be classified into three inequivalent forms: entanglement, Einstein-Podolsky-Rosen (EPR) steering, and Bell's nonlocality. Bell-nonlocal states form a strict subset of EPR steerable states which also form a strict subset of entangled states. Recently, EPR steerable states are shown to be fundamental resources for one-sided device-independent quantum information processing tasks and, hence, identification of EPR steerable states becomes important from foundational as well as informational theoretic perspectives. In the present study we propose a new criteria to detect whether a given two-qubit state is EPR steerable. From an arbitrary given two-qubit state, another two-qubit state is constructed in such a way that the given state is EPR steerable if the new constructed state is entangled. Hence, EPR steerability of an arbitrary two-qubit state can be detected by detecting entanglement of the newly constructed state. Apart from providing a distinctive way to detect EPR steering without using any steering inequality, the novel finding in the present study paves a new direction to avoid locality loophole in EPR steering tests and to reduce the "complexity cost" present in experimentally detecting EPR steering. We also generalise our criteria to detect EPR steering of higher dimensional quantum states. Finally, we illustrate our result by using our proposed technique to detect EPR steerability of various families of mixed states.

Detecting EPR steering via two classes of local measurements

“…From this criterion, we have that τ AB must be entangled. In addition, from that any qudit-qubit state ρ AB is EPR steering from Bob to Alice if the state τ AB = µρ AB + (1 − µ)ρ A ⊗ I 2 is entangled [37,38], we complete the proof. On the other hand, for a qubit-qudit state ρ AB in C 2 ⊗ C d shared by Alice and Bob, we can detect the EPR steering from Alice to Bob through the following theorem.…”

“…Recently, in [37,38], the authors focused on detecting arbitrary qubit-qudit state ρ AB and gave a criterion by detecting the entanglement of a new constructed state, µρ AB + (1 − µ) I 2 ⊗ ρ B , without using any steering inequality. Following the positive partial transposition criterion [39,40], the authors in [38] present a brief idea on how their result can be implemented in experiments for two-qubit states. Although such result consumes some resources, it provides a way of detecting EPR steering by avoiding steering inequalities.…”

Constraint Relation Between Steerability and Concurrence for Two‐Qubit States

“…Recently, steering has attracted extensive attentions and has revealed many advantages in quantum information applications. [ 4–9 ] Costa et al. proposed a measure of steering that is based on the maximal violation of the line steering inequality in two‐ and three‐measurement scenarios.…”

Experimental observation of Einstein-Podolsky-Rosen steering via entanglement detection

“…In this paper, we demonstrate the EPR steering in two directions via detecting entanglement in experiment, without using any steering inequality and measurement setting. To be specific, we experimentally construct two new states from a twoqubit target state on the basis of the recent theories of Das et al [35] and Chen et al [36], and observe the EPR steering by detecting the entanglements of the new states for the first time. The results verify that the entanglement of newly constructed states can be considered as a new kind of EPR steering witness for target states in experiment.…”

“…According to Refs. [35] and [36], the newly constructed states τ 1 AB (α, θ) and τ 2 AB (α, θ) for ρ AB (α, θ) can be given by…”