Einstein-Podolsky-Rosen Steering Inequalities and Applications

Abstract

Einstein-Podolsky-Rosen (EPR) steering is very important quantum correlation of a composite quantum system. It is an intermediate type of nonlocal correlation between entanglement and Bell nonlocality. In this paper, based on introducing definitions and characterizations of EPR steering, some EPR steering inequalities are derived. With these inequalities, the steerability of the maximally entangled state is checked and some conditions for the steerability of the X-states are obtained. IntroductionGenerally, quantum correlations means the correlations between subsystems of a composite quantum system, including Bell nonlocality, steerability, entanglement and quantum discord.Einstein-Podolsky-Rosen (EPR) steering was first observed by Schrodinger [1] in the context of famous Einstein-Podolsky-Rosen (EPR) paradox [2][3][4][5]. It was realized that EPR steering, as a form of bipartite quantum correlation, is an intermediate between entanglement and Bell nonlocality. Wiseman et al. [6] shown the inequivalence between entanglement, steering, and nonlocality when considering the projective measurements. Then, Quintino et al. [7] further considered the general measurements and proved that these three quantum relations are inequivalent. Interestingly, steering can be characterized by a simple quantum information processing task, namely, entanglement verification with an untrusted party [6][7][8][9][10]. In addition, steering has been found useful in several applications, such as one-sided device-independent quantum key distribution [11]; subchannel discrimination [12]; temporal steering and security of quantum key distribution with mutually unbiased bases against individual attacks [13]; temporal steering in four dimensions with applications to coupled qubits and magnetoreception [14]; no-cloning of quantum steering [15]; and spatio-temporal steering for testing nonclassical correlations in quantum networks [16]. Recently, detection and characterization of steering have attracted increasing attention [3,6,8,[17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]. Many of the standard Bell inequalities (e.g., CHSH ) are not effective for detection of quantum correlations which allow for steering, because for a wide range of such correlations they are not violated. Various steering inequalities have been derived, such as linear steering inequalities [33][34][35]; inequalities based on multiplicative variances [3,17,33]; entropy uncertainty relations [36,37]; fine-grained uncertainty relations [38], temporal steering inequality [39]. Besides, Zukowski et al. [40] presented some Bell-like inequalities which have lower bounds for non-steering correlations than for local causal models. These inequalities involve all possible measurement settings at each side. Based on the data-processing inequality for an extended Rényi relative entropy, Zhu et al. [41] introduced a family of steering inequalities, which detect steering much more efficiently than those inequalities known before. Chen et al. [42] showed that Bell nonlo...

Quantum steering in two-forked tree-shaped networks

“…Similarly, it follows from equation (14) in [39] that a n-layer tree-shaped network state ρ is the non-(2 n − 2)-local will imply that it is…”

“…The phenomenon of quantum steering had attracted more attentions because it provides advantages for a number of applications including one-sided device-independent quantum key distribution [4][5][6], subchannel discrimination [7], and quantum teleportation [8]. Varied methods had been put forward to detect quantum steering, such as linear and nonlinear inequalities [9][10][11][12][13][14], uncertainty relations [15][16][17], the moment matrix approach [18], and the all-versus-nothing method [19]. Furthermore, He and Reid introduced the concept of multipartite steering and put forward the corresponding criteria [20].…”

Improvement in quantum communication using quantum switch

“…Steering is useful for different information-theoretic tasks [28]. There exist several steering inequalities each of which detects the steerability of a bipartite quantum state [29][30][31][32]. One such steering inequality using two measurement settings, we are writing below which was originally studied in [29,30,32].…”

Some Measurement-Based Characterizations of Separability of Bipartite States

“…As an intermediary property between Bell nonlocality and entanglement, EPR steering was first observed by Schrödinger [2] in the context of the well-known EPR paradox [1,[20][21][22]. It is also is an important resources in quantum information and then has been recently discussed, please refer to [17,[23][24][25][26][27][28][29][30][31]. Especially, mathematical definitions of Bell nonlocality and EPR steerability of bipartite states were proposed and their characterizations were given in [17] by Cao and Guo. Although entanglement was first recognized as the characteristic trait of quantum mechanics [1], its role has been debated since it does not capture all the quantum features of a quantum system [32][33][34].…”