Abstract The prepare-and-measure theory is a new type of quantum paradox that reveals the incompatibility between classical theory and quantum mechanics in terms of the dimensionality of physical systems. Just as the Horodecki criterion can determine whether given quantum states are capable of exhibiting Bell nonclassicality, a similar criterion is needed for the prepare-and-measure theory to determine whether given quantum states can exhibit the prepare-and-measure nonclassicality. Recently, Poderini et al [Phys. Rev. Research 2, 043 106 (2020)] presented such a criterion for the prepare-and-measure nonclassicality. In this work, we experimentally validate this criterion—52 different sets of quantum states are prepared and tested one by one using this criterion to determine whether they can exhibit the prepare-and-measure nonclassicality, and the experimental results are in good agreement with the theoretical expectations. The criterion experimentally verified here has the potential to be widely used in future research on the prepare-and-measure nonclassicality.
Abstract The prepare-and-measure theory is a new type of quantum paradox that reveals the incompatibility between classical theory and quantum mechanics in terms of the dimensionality of physical systems. Just as the Horodecki criterion can determine whether given quantum states are capable of exhibiting Bell nonclassicality, a similar criterion is needed for the prepare-and-measure theory to determine whether given quantum states can exhibit the prepare-and-measure nonclassicality. Recently, Poderini et al [Phys. Rev. Research 2, 043 106 (2020)] presented such a criterion for the prepare-and-measure nonclassicality. In this work, we experimentally validate this criterion—52 different sets of quantum states are prepared and tested one by one using this criterion to determine whether they can exhibit the prepare-and-measure nonclassicality, and the experimental results are in good agreement with the theoretical expectations. The criterion experimentally verified here has the potential to be widely used in future research on the prepare-and-measure nonclassicality.
Preparing and measuring physical systems are the operational building blocks of any physical experiment, and to describe them is the first purpose of any physical theory.Remarkably, even when only uncharacterized preparation and measurement devices are present, it is sometimes possible to distinguish between the behaviors of quantum and classical systems from only observational data.Certifying the physical origin of measurement statistics in the prepare and measure scenario is of primal importance for developing quantum networks, distributing quantum keys, and certifying randomness, to mention a few applications, but, surprisingly, no general methods to do so are known.We progress on this problem by crafting a general, sufficient condition to certify that a given set of preparations can only generate classical statistics, for any number of generalized measurements.As an application, we employ the method to demonstrate nonclassicality activation in the prepare and measure scenario, also considering its application in random access codes.Following that, we adapt our method to certify, again through a sufficient condition, whether a given set of measurements can never give rise to nonclassical behaviors, irrespective of what preparations they may act upon.This, in turn, allows us to find a large set of incompatible measurements that cannot be used to demonstrate nonclassicality, thus showing incompatibility is not sufficient for nonclassicality in the prepare and measure scenario.
Consideration of the classic measurement paradox of quantum mechanics raises the question: What is the relationship between acceptable theories of the physical world at different levels? It is suggested that it is similar to the relationship between maps of different types and that, while theories at different levels need not be derivable from one another, they must at least be mutually consistent in their predictions. The relationship between quantum mechanics, in its standard interpretation, and classical physics fails this test. Existing attempts to resolve the measurement paradox are briefly reviewed, and it is suggested that one avenue has been insufficiently explored; namely, the possibility that the complexity of a physical system may itself be a relevant variable which may introdu;ce new physical principles. Possible reasons for this lacuna are discussed, and it is pointed out that some of the relevant questions are now within the reach of an experimental test.
We theoretically introduce and experimentally demonstrate the realization of a nonclassicality test that allows for arbitrarily low detection efficiency without invoking an extra assumption of independence of the devices. Our test and its implementation is set in a prepare-and-measure scenario with an upper limit on the classical communication capacity of the channel through which the systems are communicated. The essence for our test is the use of two preparation and two measurement devices, which are randomly paired in each round. Our work opens the possibility for experimental realizations of nonclassicality tests with off-the-shelf technology.
Prepare-and-measure scenarios are among the simplest and most widely used settings for quantum communication. A sender prepares a physical system in one of several possible states, which a receiver then measures. Despite this simple structure, these scenarios offer a rich framework for exploring the differences between classical and quantum communication, revealing quantum advantages, and developing protocols for quantum cryptography and device certification. In this tutorial, we give a ground-up introduction to prepare-and-measure scenarios and the methods used to study them. We introduce different frameworks for constraining and characterising communication, with an emphasis on semi-device-independent approaches to quantum information. We also cover modern convex-optimisation techniques for characterising the correlations achievable in these scenarios and illustrate how these tools can be applied in practice. Our aim is to give newcomers the conceptual and technical foundations needed to approach the current literature and apply prepare-and-measure methods in their own research. We conclude with a discussion of open problems and directions for future work.
Starting from arbitrary sets of quantum states and measurements, referred to as the prepare-and-measure scenario, an operationally noncontextual ontological model of the quantum statistics associated with the prepare-and-measure scenario is constructed. The operationally noncontextual ontological model coincides with standard Spekkens noncontextual ontological models for tomographically complete scenarios, while covering the non-tomographically complete case with a new notion of a reduced space, which we motivate following the guiding principles of noncontextuality. A mathematical criterion, called unit separability , is formulated as the relevant classicality criterion – the name is inspired by the usual notion of quantum state separability. Using this criterion, we derive a new upper bound on the cardinality of the ontic space. Then, we recast the unit separability criterion as a (possibly infinite) set of linear constraints, from which we obtain two separate hierarchies of algorithmic tests to witness the non-classicality or certify the classicality of a scenario. Finally, we reformulate our results in the framework of generalized probabilistic theories and discuss the implications for simplex-embeddability in such theories.
In this letter, we propose and experimentally test a quantumness criterion for single systems. The criterion is based on the violation of an already reported classical inequality. This inequality is expressed in terms of joint probabilities that we identify as realizations of preparation-and-measurement schemes. Our analysis points out that superposition is the key notion to grasp the quantum nature of physical systems. We verify our criterion in an all-optical experimental setup with heralded single photons generated via spontaneous parametric down conversion and use exclusively projective preparations and projective measurements.