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Register a new userCorrelations in entanglement-assisted prepare-and-measure scenarios
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We investigate the correlations that can arise between Alice and Bob in prepare-and-measure communication scenarios where the source (Alice) and the measurement device (Bob) can share prior entanglement. The paradigmatic example of such a scenario is the quantum dense coding protocol, where the communication capacity of a qudit can be doubled if a two-qudit entangled state is shared between Alice and Bob. We provide examples of correlations that actually require more general protocols based on higher-dimensional entangled states. This motivates us to investigate the set of correlations that can be obtained from communicating either a classical or a quantum $d$-dimensional system in the presence of an unlimited amount of entanglement. We show how such correlations can be characterized by a hierarchy of semidefinite programming relaxations by reducing the problem to a non-commutative polynomial optimization problem. We also introduce an alternative relaxation hierarchy based on the notion of informationally-restricted quantum correlations, which, though it represents a strict (non-converging) relaxation scheme, is less computationally demanding. As an application, we introduce device-independent tests of the dimension of classical and quantum systems that, in contrast to previous results, do not make the implicit assumption that Alice and Bob share no entanglement. We also establish several relations between communication with and without entanglement as resources for creating correlations.
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Entanglement and quantum communication are paradigmatic resources in quantum information science leading to correlations between systems that have no classical analogue. Correlations due to entanglement when communication is absent have for long been studied in Bell scenarios. Correlations due to quantum communication when entanglement is absent have been studied extensively in prepare-and-measure scenarios in the last decade. Here, following up on a recent companion paper [arXiv:2103.10748], we set out to understand and investigate correlations in scenarios that involve both entanglement and communication, focusing on entanglement-assisted prepare-and-measure scenarios. We establish several elementary relations between standard classical and quantum communication and their entanglement-assisted counterparts. In particular, while it was already known that bits or qubits assisted by two-qubit entanglement between the sender and receiver constitute a stronger resource than bare bits or qubits, we show that higher-dimensional entanglement further enhance the power of bits or qubits. We also provide a characterisation of generalised dense coding protocols, a natural subset of entanglement-assisted quantum communication protocols, finding that they can be understood as standard quantum communication protocols in real-valued Hilbert space. Though such dense coding protocols can convey up to two bits of information, we provide evidence, perhaps counter-intuitively, that resources with a small information capacity, such as a bare qutrits, can sometimes produce stronger correlations. Along the way we leave several conjectures and conclude with a list of interesting open problems.
We report an experimental demonstration of effective entanglement in a prepare&measure type of quantum key distribution protocol. Coherent polarization states and heterodyne measurement to characterize the transmitted quantum states are used, thus enabling us to reconstruct directly their Q-function. By evaluating the excess noise of the states, we experimentally demonstrate that they fulfill a non-separability criterion previously presented by Rigas et al. [J. Rigas, O. Guhne, N. Lutkenhaus, Phys. Rev. A 73, 012341 (2006)]. For a restricted eavesdropping scenario we predict key rates using postselection of the heterodyne measurement results.
Self-testing represents the strongest form of certification of a quantum system. Here we investigate theoretically and experimentally the question of self-testing non-projective quantum measurements. That is, how can one certify, from observed data only, that an uncharacterised measurement device implements a desired non-projective positive-operator-valued-measure (POVM). We consider a prepare-and-measure scenario with a bound on the Hilbert space dimension, which we argue is natural for this problem since any measurement can be made projective by artificially increasing the Hilbert space dimension. We develop methods for (i) robustly self-testing extremal qubit POVMs (which feature either three or four outcomes), and (ii) certify that an uncharacterised qubit measurement is non-projective, or even a genuine four-outcome POVM. Our methods are robust to noise and thus applicable in practice, as we demonstrate in a photonic experiment. Specifically, we show that our experimental data implies that the implemented measurements are very close to certain ideal three and four outcome qubit POVMs, and hence non-projective. In the latter case, the data certifies a genuine four-outcome qubit POVM. Our results open interesting perspective for strong `black-box certification of quantum devices.
Contextuality has been identified as a potential resource responsible for the quantum advantage in several tasks. It is then necessary to develop a resource-theoretic framework for contextuality, both in its standard and generalized forms. Here we provide a formal resource-theoretic approach for generalized contextuality based on a physically motivated set of free operations with an explicit parametrisation. Then, using an efficient linear programming characterization for the contextual set of prepared-and-measured statistics, we adapt known resource quantifiers for contextuality and nonlocality to obtain natural monotones for generalized contextuality in arbitrary prepare-and-measure experiments.
Starting from arbitrary sets of quantum states and measurements, referred to as the prepare-and-measure scenario, a generalized Spekkens non-contextual ontological model representation of the quantum statistics associated to the prepare-and-measure scenario is constructed. The generalization involves the new notion of a reduced space which is non-trivial for non-tomographically complete scenarios. A new 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 two separate converging hierarchies of algorithmic tests to witness non-classicality or certify classicality are obtained. We relate the complexity of these algorithmic tests to that of a class of vertex enumeration problems. Finally, we reformulate our results in the framework of generalized probabilistic theories and discuss the implications for simplex-embeddability in such theories.
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