Contextual Advantage for State Discrimination

Abstract

Finding quantitative aspects of quantum phenomena which cannot be explained by any classical model has foundational importance for understanding the boundary between classical and quantum theory. It also has practical significance for identifying information processing tasks for which those phenomena provide a quantum advantage. Using the framework of generalized noncontextuality as our notion of classicality, we find one such nonclassical feature within the phenomenology of quantum minimum error state discrimination. Namely, we identify quantitative limits on the success probability for minimum error state discrimination in any experiment described by a noncontextual ontological model. These constraints constitute noncontextuality inequalities that are violated by quantum theory, and this violation implies a quantum advantage for state discrimination relative to noncontextual models. Furthermore, our noncontextuality inequalities are robust to noise and are operationally formulated, so that any experimental violation of the inequalities is a witness of contextuality, independently of the validity of quantum theory. Along the way, we introduce new methods for analyzing noncontextuality scenarios, and demonstrate a tight connection between our minimum error state discrimination scenario and a Bell scenario.1 Such models are ψ-epistemic, in the terminology of Ref. [17].

Geometry of joint reality: Device-independent steering and operational completeness

“…Finally, it is worth noting that results obtained using the assumption of preparation noncontextuality [7,[17][18][19][20][21][22][23] can, in many cases, be strengthened to obtain similar results using the weaker assumption of operational completeness (particularly for the case of outcome deterministic ontological models). In this sense preparation noncontextuality can often be replaced by operational completeness.…”

“…Section IV is motivated by previous work that relates the joint reality of physical observables to the assumption of "preparation noncontextuality" [7,[17][18][19][20], i.e., to the requirement that operationally equivalent preparations have the same underlying distributions of any ontic variables. Preparation noncontextuality is, unlike Bell inequality and Kochen-Specker arguments, sufficient to rule out the joint reality of qubit observables [18,19], and has a number of interesting implications [7,[17][18][19][20][21][22][23]. In Sec.…”

State independent contextuality advances one-way communication

“…at least one of its neighbor is assigned the same color. Thus, p x y p x min min , is equal to the minimum number of vertices which are not properly colored when maximum d colors are used to color all the vertices in G, obtaining the bound given by (19). , Corollary 1.…”

“…Many attempts have been made to answer this question in multiple directions. For instance, it is shown that many aspects of quantum computation reveal contextuality [10][11][12]; contextual correlations are also valuable in several information processing [13][14][15][16][17][18][19] and originate novel applications of nonlocal correlations [20][21][22][23][24][25]. While the necessity of quantum contextuality in information processing is one side of the picture, a relevant question to address is whether every proof of SIC has any direct inference to quantum advantage in operational tasks.…”

Updating the Born rule

“…for a completely positive map  A describing the first measurement, is typically introduced as an independent axiom in the theory. 2 In some works, a distinction is made between operational and ontological versions of non-contextuality [33][34][35], where the latter are used to rule out hidden-variable models. Although the expression 'measurement non-contextuality' was introduced in the ontological setting [33], we here use it in the operational sense (corresponding to the simple expression 'non-contextuality' used in [6,30]).…”