Bridging the gap between general probabilistic theories and the device-independent framework for nonlocality and contextuality

Abstract

Characterizing quantum correlations in terms of information-theoretic principles is a popular chapter of quantum foundations. Traditionally, the principles used for this scope have been expressed in terms of conditional probability distributions, specifying the probability that a black box produces a certain output upon receiving a certain input. This approach is known as device-independent. Another major chapter of quantum foundations is the information-theoretic characterization of quantum theory as a whole, with its sets of states and measurements, and with its allowed dynamics. The different frameworks adopted for this scope are known under the umbrella term of general probabilistic theories. With only a few exceptions, the two research programmes on characterizing quantum correlations and characterizing quantum theory have so far proceeded on separate tracks, each one developing its own methods and its own agenda. Still, both programmes share the same basic goal: a new and better understanding of quantum mechanics in information-theoretic terms. This considered, it is quite striking that the connections between the two programmes are still largely undeveloped. This paper aims at bridging the gap, by presenting a "Rosetta stone" for the two frameworks and by illustrating how the two programmes can benefit each other.As a case study, we focus on two device-independent features known as Local Orthogonality (LO) and Consistent Exclusivity (CE). In a recent work [1], we showed that CE and LO can be derived from the basic idea that, at the fundamental level, measurements are repeatable and minimally disturbing. In this paper we provide a new, alternative derivation based on a different set of principles, revolving around the notion of pure orthogonal measurement -a mea-

Robust Self-Testing of Quantum Systems via Noncontextuality Inequalities

“…Lastly, in terms of applications, our results allows one to verify quantum systems locally under the following three assumptions characteristic of Kochen-Specker contextuality scenarios [10,12,13]. Assumption 1: The measurements are ideal [14,15] (i.e., they give the same outcome when performed consecutive times, they do not disturb compatible measurements, all their coarse-grainings admit realizations that satisfy these properties), Assumption 2: The measured system has no more memory than its information carrying capacity, each measurement device is only used once, and there is an unlimited supply of them. Assumption 3: The measurements obey the compatibility relations dictated by the odd cycle graph.…”

Almost Quantum Correlations are Inconsistent with Specker's Principle

“…As a final comment, the research scope that tackles the formulations of general physical theories beyond the quantum one has particularly focused on the definition of a subset of measurements, known as sharp measurements, which correspond to projective measurements in the case of quantum theory. There is still no consensus on how sharp measurements should be defined in a general theory [31,32]. In the following we argue that (i) any definition of sharp measurements in a theory that yields almost quantum correlations must violate Specker's principle, and (ii) any notion of sharpness in an almost quantum theory must deviate from the candidates proposed so far [31,32].…”

“…There is still no consensus on how sharp measurements should be defined in a general theory [31,32]. In the following we argue that (i) any definition of sharp measurements in a theory that yields almost quantum correlations must violate Specker's principle, and (ii) any notion of sharpness in an almost quantum theory must deviate from the candidates proposed so far [31,32].…”

“…For example, Corollary 2.1 sheds light on the notion of sharpness for general probabilistic theories that was proposed by Chiribella and Yuan [31,32]. The notion of sharpness there does imply Specker's principle, and as such no theory can give rise to the almost quantum models using only the sharp measurements in the sense of references [31,32].…”

Ruling out Higher-Order Interference from Purity Principles

“…It was shown to hold in Ref. [20], and expresses the possibility of constructing non-disturbing measurements [15,62,24]. Note that the pure transformation T is non-disturbing on ρ because it acts as the identity on ρ and on all states contained in it.…”