Certifying beyond quantumness of locally quantum no-signalling theories through quantum input Bell test

Abstract

Physical theories with local structure similar to quantum theory can allow beyond-quantum global states that are in agreement with unentangled Gleason's theorem. In a standard Bell experiment any such bipartite state produces correlations that are always quantum simulable. In this limited classical-input-classical-output Bell scenario, we show that there exist bipartite beyond-quantum states that produce correlations all of which are in-fact classically simulable. However, if the type of Bell scenario is generalized to consider quantum states as inputs, we then show that any such bipartite beyond-quantum state yields beyond-quantum input-output correlations. We also analyze the implication of this quantum input scenario while studying generic multipartite correlations obtained from local quantum theory but potentially allowing different global structure. Our study suggests the requirement of type sensitive information principles for isolating the quantum correlations from the beyond-quantum ones.Introduction.-Correlations among distant events established through the violation of Bell type inequalities confirm nonlocal behavior of the physical world [1][2][3][4]. Nonseparable multipartite quantum states yielding such correlations, in Schrödinger's words, are "...the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought" [5]. The advent of quantum information science identifies the power of such nonlocal correlations in numerous device independent protocols -cryptographic key distribution [6], randomness certification [7] and amplification [8], dimension witness [9] are few canonical examples. Cirel'son's result [10], however, establishes that the nonlocal strength of quantum correlations is limited compared to the general no-signaling (NS) ones [11] as depicted in the celebrated Clauser-Horne-Shimony-Holt (CHSH) inequality violation [12].

Classical analogue of quantum superdense coding and communication advantage of a single quantum

“…More recently, this scenario has been further generalized where Alice and Bob are given quantum inputs instead of classical random variables. [70][71][72].…”

Timelike correlations and quantum tensor product structure

“…In this work, we assume subsystems to be quantum and ask how the information processing capabilites of composite systems change when one uses different mathematical structures to describe composition. While Barnum,et al in [20] have shown that in the space-like scenario, bipartite maximal tensor product structure of local quantum systems cannot generate beyond quantum correlations, the authors in [22] have shown that in a generalized Bell scenario every beyond quantum state can produce beyond quantum correlations. In this work, we have used a different approach wherein timelike scenarios are considered instead of the traditional spacelike Bell scenarios.…”

“…While maximal composition involving more than two subsystems can yield stronger than quantum correlation in typical Bell scenario [21], recently in Ref. [22] it has been shown that even in bipartite case stronger than quantum correlations are possible if the typical classical input-classical output Bell scenario is generalized to quantum input-classical output semi-quantum scenario [23]. Although this quantum input scenario disallows all the compositions having beyond entangled states it requires trustworthy verifiers in producing some predetermined unentangled quantum inputs [22].…”

“…[22] it has been shown that even in bipartite case stronger than quantum correlations are possible if the typical classical input-classical output Bell scenario is generalized to quantum input-classical output semi-quantum scenario [23]. Although this quantum input scenario disallows all the compositions having beyond entangled states it requires trustworthy verifiers in producing some predetermined unentangled quantum inputs [22]. In a completely different approach, recently the authors in [24] have shown that the bipartite minimal composition can yield stronger than quantum correlation if timelike scenario is considered.…”