Hardy’s argument and successive spin-smeasurements

Abstract

We consider a hidden-variable theoretic description of successive measurements of non commuting spin observables on a input spin-s state. In this scenario, the hidden-variable theory leads to a Hardy-type argument that quantum predictions violate it. We show that the maximum probability of success of Hardy's argument in quantum theory is ( 1 2 ) 4s , which is more than in the spatial case.

Quantum Correlations Require Multipartite Information Principles

“…Celebrated examples of these principles are information causality [4] or non-trivial communication complexity [2,5]. While the use of these information concepts has been successfully applied to some specific scenarios [6][7][8][9][10], proving, or disproving, the validity of a principle for quantum correlations is extremely challenging. On the one hand, it is rather difficult to derive the Hilbert space structure needed for quantum correlations from information quantities.…”

The Hardy's nonlocality argument

“…It can also be checked that for the above set, the nonzero probability ( 11) is 25% which is also the maximum success probability of this argument for qubit systems [71,72]. The experimental verification of the above fact followed soon after in [73].…”

“…These inequalities get violated in quantum mechanics and thereby give rise to the notion of entanglement in time which has been a topic of current research interest [68,67,71,72,74,73,75,77,78,79]. These inequalities have been studied to probe the similarities and differences between spatial and temporal correlations in quantum mechanics to learn more about the relation between the structure of space and time and the abstract formalism of quantum theory [68].…”

“…Interestingly, the original argument of Hardy, which establishes the incompatibility of quantum theory with the notion of local-realism, can also be used to reveal this timenonlocal feature of quantum states [71,72,73]. To see this we consider a single two-level physical system on which an observer (Alice) chooses to measure one of two observables A or A ′ at time t 1 , whereas at a later time t 2 , another observer (Bob) [80] measures either of the two observables B and B ′ .…”

Persistence of Hardy's nonlocality in time

“…These inequalities get violated in Quantum Mechanics and thereby give rise to the notion of entanglement in time which has been a topic of current research interest [3,4,[8][9][10][11][12]. Interestingly, the original argument of Hardy, which establishes the incompatibility of Quantum Theory with the notion of local-realism [13,14], can also be used to reveal this time-nonlocal feature of quantum states [8][9][10]. Recently, Hardy's argument was studied in the case of two observable settings at each time of measurement [8,9].…”