Quantum steering

Abstract

Quantum correlations between two parties are essential for the argument of Einstein, Podolsky, and Rosen in favour of the incompleteness of quantum mechanics. Schrödinger noted that an essential point is the fact that one party can influence the wave function of the other party by performing suitable measurements. He called this phenomenon quantum steering and studied its properties, but only in the last years this kind of quantum correlation attracted significant interest in quantum information theory. In this paper we review the theory of quantum steering. We first present the basic concepts of steering and local hidden state models and their relation to entanglement and Bell nonlocality. Then, we describe the various criteria to characterize steerability and structural results on the phenomenon. A detailed discussion is given on the connections between steering and incompatibility of quantum measurements. Finally, we review applications of steering in quantum information processing and further related topics. 34 J. Quantum teleportation 34 K. Resource theory of steering 35 L. Post-quantum steering 36 M. Historical aspects of steering 36 1. Discussions between Schrödinger and Einstein 36 2. The two papers by Schrödinger 37 3. Impact of these papers 38 VI. Conclusion 38 References 39 arXiv:1903.06663v2 [quant-ph]

Measurement incompatibility and steering are necessary and sufficient for operational contextuality

“…These two features of quantum theory are thoroughly researched, see e.g. Refs [10][11][12][13] and Refs [14,15] respectively. We estab- * A. T. and R. U. contributed equally to this work.…”

Nonlocality, quantum correlations, and violations of classical realism in the dynamics of two noninteracting quantum walkers

“…For the problem of two noninteracting walkers, with spins prepared in the singlet state, we showed that genuine fourpartite entanglement is created throughout the walk, monotonically increasing with time [Eq. (27)], at the expense of two-spin correlations [Eq. (44)].…”

“…This work aims at advancing the above-delineated framework by dissecting a given two-particle quantum walk with respect to its potentialities in producing several types of quantumness, in particular quantum nonlocality, general quantum correlations, and violations of realism. We analytically assess the behaviors (over time and asymptotically) of some wellestablished notions, such as entanglement and genuine multipartite entanglement [22], quantum discord [23,24], symmetrical quantum discord [25], Einstein-Podolsky-Rosen (EPR) steering [26,27], Bell nonlocality [28,29], realism-based nonlocality [30], and irreality [31]. While the global state evolves unitarily, thus conserving its initial degree of purity, we find that most of the aforementioned quantumnesses decrease with time between the bipartitions of the system, with some eventual occurences of sudden deaths.…”

Quantum steering of Bell-diagonal states with generalized measurements

“…Characterization of quantum steering has been studied, many connections to different areas of quantum information were found and applications were established, for a recent review see Ref. [9].…”