Nonlocality of Symmetric States

Abstract

In this Letter we study the nonlocal properties of permutation symmetric states of n qubits. We show that all these states are nonlocal, via an extended version of the Hardy paradox and associated inequalities. Natural extensions of both the paradoxes and the inequalities are developed which relate different entanglement classes to different nonlocal features. Belonging to a given entanglement class will guarantee the violation of associated Bell inequalities which see the persistence of correlations to subsets of players, whereas there are states outside that class which do not violate.

Exploring laser-induced interlayer spin transfer by an all-optical method

“…Recently, it was realized that apart from local mechanisms, also the laser-induced transfer of spin polarized carriers over several to tens of nanometers can be a source of ultrafast magnetization dynamics [3]. This notion triggered fascinating new studies [4][5][6][7][8][9][10][11][12][13][14], but also led to intense scientific debate. It was experimentally demonstrated that laser-induced demagnetization can be enhanced by transfer of spins aligned antiparallel to the magnetization direction [4].…”

“…There is, however, one major disadvantage of using x rays to study magnetization dynamics: they require large scale facilities for fs electron slicing or x-ray free electron lasers [7,9,16,18]. Recently, other techniques have been introduced to measure element-specific magnetization dynamics, such as table-top higher harmonic generation [20,21] or the performance of MOKE at different frequencies in the visible spectrum [22].…”

Symmetric states: Their nonlocality and entanglement

“…The logical contradiction arises in a similar way as the original paradox. Similarly, the inequality now becomes [4,5,6]…”

“…It has been proven [6] that for all symmetric states except Dicke states, there exists a choice of |η i such that (6) to (8) are all satisfied, which also violates (9). Although Dicke states do not satisfy (6) to (8), it is also possible to choose measurement settings such that they violate (9) in a 2-setting/2-outcome experiment [6]. Indeed, is has recently been shown that all pure entangled states violate (9) [9].…”

“…It is known that two symmetric states having different degeneracies belong to different SLOCC classes [12], thus a symmetric state having degeneracy d guarantees the violation of Q n d (the converse, however, is not generally true). There are also "representative" states from different SLOCC classes such that the violation of Q n d is impossible while states with higher degeneracy can violate it [6,13].…”