The Einstein–Podolsky–Rosen (EPR) paper

Debarshi Das, Souradeep Sasmal, Sovik Roy

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 have been 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 paper, we propose a criterion 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 present paper also provides an alternative way to avoid locality loopholes in EPR steering tests and to reduce the ``complexity cost'' present in experimentally detecting EPR steering. We also generalize 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.

F. J. Duarte

Wen‐Yang Sun, Dong Wang, Liu Ye

Abstract In this letter, the dynamic behavior of Einstein–Podolsky–Rosen (EPR) steering and the redistribution of EPR steering under a relativistic framework are investigated. Specifically, we explore the scenario that particle A held by Alice is in a flat space–time and another particle B held by Bob entangled with A is in a non-inertial framework. The results show that EPR steering from Alice to Bob is dramatically destroyed by the Unruh effect caused by the acceleration of Bob. Besides, EPR steering possess asymmetry, and EPR steering asymmetry increases with growing intensity of the Unruh effect, implying that the Unruh effect can bring about EPR steering asymmetry. Furthermore, the reduced physically accessible EPR steering from Alice to Bob is distributed to the physically inaccessible EPR steering (from Alice to anti-Bob or from Bob to anti-Bob). Notably, unlike entanglement and quantum discord, only one of the EPR steering from Alice to anti-Bob and Bob to anti-Bob experiences a sudden birth with increase in the acceleration parameter, which means that they cannot simultaneously survive. That is, the monogamous relationship of EPR steering is still tenable in such a scenario. Consequently, we believe that EPR steering could also serve as an important information resource within long-distance quantum secure communication under the relativistic framework.

S. Chaturvedi, Narasimhaiengar Mukunda, R. Simon

Claus Kiefer

Huaixin Cao, Zhihua Guo

Bell nonlocality and Einstein-Podolsky-Rosen (EPR) steering are every important quantum correlations of a composite quantum system. Bell nonlocality of a bipartite state is a quantum correlation demonstrated by some local quantum measurements, while EPR steering is another form of quantum correlations, observed firstly by Schrodinger in the context of famous EPR paradox. In this paper, we give some remarks on Bell nonlocality and EPR steering of bipartite states, including mathematical definitions and characterizations of these two quantum correlations, the convexity and closedness of the set of all Bell local states and the set of all EPR unsteerable states. We also derive a EPR-steering criteria, with which the EPR steerability of the maximally entangled states are checked.