Understanding the connections between different quantum information protocols has been proven fruitful for both theoretical insights and experimental applications. In this work, we investigate a specific link between nonlocal and prepare-and-measure scenarios, proposing a systematic way to translate bipartite Bell inequalities into dimensionally bounded prepare-and-measure tasks. We identify sufficient conditions under which the translation preserves the quantum bound and self-testing properties, enabling a wide range of certification protocols originally developed for the nonlocal setting to be adapted to the sequential framework of prepare-and-measure with a dimensional bound. While the dimensionality bound is not device independent, it still is a practical and experimentally reasonable assumption in many cases of interest. In some instances, we find new experimentally friendly certification protocols. In others, we demonstrate equivalences with already known prepare-and-measure protocols, where self-testing results were previously established using alternative mathematical methods. Our results unify different quantum correlation frameworks in specific scenarios and contribute to the ongoing research effort of studying the interplay between parallel and sequential protocols.
Understanding the connections between different quantum information protocols has been proven fruitful for both theoretical insights and experimental applications. In this work, we investigate a specific link between nonlocal and prepare-and-measure scenarios, proposing a systematic way to translate bipartite Bell inequalities into dimensionally bounded prepare-and-measure tasks. We identify sufficient conditions under which the translation preserves the quantum bound and self-testing properties, enabling a wide range of certification protocols originally developed for the nonlocal setting to be adapted to the sequential framework of prepare-and-measure with a dimensional bound. While the dimensionality bound is not device independent, it still is a practical and experimentally reasonable assumption in many cases of interest. In some instances, we find new experimentally friendly certification protocols. In others, we demonstrate equivalences with already known prepare-and-measure protocols, where self-testing results were previously established using alternative mathematical methods. Our results unify different quantum correlation frameworks in specific scenarios and contribute to the ongoing research effort of studying the interplay between parallel and sequential protocols.
Abstract We present a self-testing protocol in a constrained prepare-measure scenario, based on a communication game known as parity-oblivious multiplexing (POM) task. In this scenario, a parity-oblivious constraint is imposed on the preparations, allowing us to define a classical bound derived from a preparation noncontextual ontological model. We demonstrate that the optimal quantum value exceeds preparation noncontextual bound and therefore enables self-testing of the preparations and the measurement devices. Contrasting the prevailing consensus that the self-testing in prepare-measure scenario inevitably requires an upper bound on the dimension of the quantum system, we derive the optimal quantum success probability of the POM task devoid of assuming the dimension of the quantum system. Furthermore, by proving the existence of a unitary, we show that the optimal preparations and measurements in an unknown but finite dimensional Hilbert space, responsible for the observed input–output correlations, can be mapped, via a unitary, onto a known finite-dimensional quantum system. Our results thus pave the way for scalable, single system based certification protocols in the prepare-measure scenario.
A key aspect in quantum information is to understand the advantage offered by quantum systems over classical ones in communication tasks. In recent years, a fundamental approach to this problem has been developed, focusing on quantum correlations in prepare-and-measure scenarios. Inspired by the developments in Bell nonlocality and device-independent information processing, this line of research aims to characterize the possibilities and limits of quantum systems for communication, in particular to precisely capture the advantage they offer over classical systems. In addition to fundamental insights, these ideas also underpin the concept of semi-device-independent quantum information processing. Exploring trade-offs between security, performance and ease-of-implementation, this approach opens promising directions for novel quantum information processing technologies and devices. A number of protocols and proof-of-principle demonstrations have been reported in recent years, in particular for quantum randomness certification and key distribution. Here, we provide a comprehensive introduction to quantum prepare-and-measure correlations and semi-device independent applications.
Self-testing has been established as a major approach for quantum device certification based on experimental statistics with minimal assumptions. However, despite more than 20 years of research effort, most of the self-testing protocols are restricted to spatial scenarios (Bell scenarios), without many temporal generalizations known. Under the scenario of sequential measurements performed on a single quantum system, semi-definite optimization-based techniques have been applied to bound sequential measurement inequalities. Building upon this formalism, we show that the optimizer matrix that saturates such sequential inequalities is unique and, moreover, this uniqueness is robust to small deviations from the quantum bound. Furthermore, we consider a generalized scenario in the presence of quantum channels and highlight analogies to the structure of Bell and sequential inequalities using the pseudo-density matrix formalism. These analogies allow us to show a practical use of maximal violations of sequential inequalities in the form of certification of quantum channels up to isometries.
Bell inequalities reveal the fundamentally nonlocal character of quantum mechanics. In this regard, one of the interesting problems is to explore all possible Bell inequalities that demonstrate a gap between local and nonlocal quantum behaviour. This is useful for the geometric characterisation of the set of nonlocal correlations achievable within quantum theory. Moreover, it provides a systematic way to construct Bell inequalities that are tailored to specific quantum information processing tasks. This characterisation is well understood in the simplest (2,2,2) scenario, namely two parties performing two binary outcome measurements. However, beyond this setting, relatively few Bell inequalities are known, and the situation becomes particularly scarce in scenarios involving a greater number of outcomes. Here, we consider the (2,2,3) scenario, or two parties performing two three-outcome measurements, and characterise all Bell inequalities that can arise from the simplest sum-of-squares decomposition and are maximally violated by the maximally entangled state of local dimension three. We then utilise them to self-test this state, along with a class of three-outcome measurements.
Quantum correlations in Bell and prepare-and-measure experiments are central resources for probing nonclassicality and enabling device-based quantum information protocols. In the absence of shared public randomness (i.e., without run-to-run mixing), even qubit correlation sets are typically nonconvex, making standard convex characterizations inadequate. Here we derive qubit-specific constraints from uncertainty relations, yielding a state-independent consistency test for observed statistics in both prepare-and-measure and Bell scenarios. The test captures explicit nonconvex boundaries in representative correlation families and enables correlation-based device inference by constraining (and sometimes uniquely determining) unitary-invariant measurement parameters even away from extreme points. Moreover, incorporating the inferred qubit constraints as additional conditions in a moment-matrix relaxation strengthens separability tests and can certify entanglement even for Bell-local correlations within the independent-device model. These tools provide a practical route to characterize and leverage low-dimensional quantum devices, including certification, randomness generation, and entanglement verification.
An important problem in quantum information theory is that of bounding sets of correlations that arise from making local measurements on entangled states of arbitrary dimension. Currently, the best-known method to tackle this problem is the NPA hierarchy; an infinite sequence of semidefinite programs that provides increasingly tighter outer approximations to the desired set of correlations. In this work we consider a more general scenario in which one performs sequences of local measurements on an entangled state of arbitrary dimension. We show that a simple adaptation of the original NPA hierarchy provides an analogous hierarchy for this scenario, with comparable resource requirements and convergence properties. We then use the method to tackle some problems in device-independent quantum information. First, we show how one can robustly certify over 2.3 bits of device-independent local randomness from a two-quibt state using a sequence of measurements, going beyond the theoretical maximum of two bits that can be achieved with non-sequential measurements. Finally, we show tight upper bounds to two previously defined tasks in sequential Bell test scenarios.