Focus on device independent quantum information

Abstract

The field of quantum information is born out of a sequence of surprising discoveries in the 1980s, all building on the same deep insight: the counter-intuitive quantum properties of particles such as photons or electrons can be put to task in order to accomplish certain computational, cryptographic, and information-theoretic tasks impossible to realize by purely classical means. A famous example is the cryptographic problem of key distribution, for which Bennett and Brassard devised the first quantum protocol in 1984 [6] and whose security relies on the no-cloning principle of quantum mechanics. Another example is the computational problem of factoring large numbers, for which Shor devised the first efficient quantum algorithm in 1994 [32] by exploiting the possibility for quantum systems to evolve in superpositions of exponentially many different states.In this early history, and until very recently, the violation of Bell inequalities was simply seen as yet another feature distinguishing the quantum processing of information from a classical one. It provided one of the initial motivations for developing a better understanding of entangled states; it was recognized as a key factor responsible for the quantum advantage in communication complexity protocols; it was frequently used in experiments to demonstrate oneʼs ability to generate and manipulate entanglement. It also played an important conceptual role, as it established that the predictions of quantum theory, including its claimed information processing advantages, could not be naively reproduced by a classical theory. But overall the manifestation of quantum non-locality was just another way to evidence the weirdness of quantum theory, on par with the nocloning principle or the uncertainty of quantum measurements in having little consequence for practical applications.In very recent years, however, the violation of Bell inequalities has acquired a special status that is starting to revolutionize our understanding of the information-theoretic possibilities of quantum information. Indeed, not only are the properties of quantum states and measurements leading to the violation of Bell inequalities unique in the sense of having no classical explanation, but they also often uniquely single out the quantum system itself. More precisely, given a black-box device that is verifiably violating a Bell inequality, quantum theory allows for a virtually unique way in which this can be accomplished. Furthermore, for the many tasks for which quantum information provides an advantage, there often turns out to be a protocol whose advantage essentially amounts to the sufficiently large violation of a certain Bell inequality.Taken together, these two phenomena lead to the following observation: it is possible to devise quantum information protocols whose correctness can be certified even when they are run with untrusted quantum devices, on which no a priori assumptions are made. Hence the name 'device-independence' (DI) to refer to such protocols. The implications of this are pr...

Measurement incompatibility and steering are necessary and sufficient for operational contextuality

“…Consider now the case of steering. For simplicity, let Alice and Bob share the noisy singlet state 1]. What is the critical value of v = v n so that Bob can steer Alice using n projective measurements?…”

Geometry of the quantum set on no-signaling faces

“…Notice that the nonzero probability in the condition (14) does not belong to the set of free-variable probabilities. To sum up, conditions (14)- (19) basically give all Hardy nonlocal points contained in the NL simplex that we consider. For instance, the PR box (a vertex of the NL simplex and a Hardy nonlocal point) satisfies all the conditions (14)- (19).…”

“…[51] that for a given set of measurements there is a unique pure state achieving such correlations. Therefore, since all possible Hardy nonlocality arguments given by conditions (14)- (19) have quantum solutions, we know that every seven-dimensional nonlocal facet of the NL simplex contains nonlocal quantum correlations.…”

The type-independent resource theory of local operations and shared randomness

“…However, when a resource has a quantum output, one requires a well-characterized quantum measurement to probe that output and consequently the resource [25]. In such a case, the test of nonclassicality is said to be device-dependent, while in adversarial scenarios such as cryptography, the terminology of trust is also used [26]. The same idea applies to a quantum input, which must be probed using a well-characterized quantum state preparation device.…”