Quantum measurements on a two-level system can have more than two independent outcomes, and in this case, the measurement cannot be projective. Measurements of this general type are essential to an operational approach to quantum theory, but so far, the nonprojective character of a measurement could only be verified experimentally by already assuming a specific quantum model of parts of the experimental setup. Here, we overcome this restriction by using a device-independent approach. In an experiment on pairs of polarization-entangled photonic qubits we violate by more than 8 standard deviations a Bell-like correlation inequality which is valid for all sets of two-outcome measurements in any dimension. We combine this with a device-independent verification that the system is best described by two qubits, which therefore constitutes the first device-independent certification of a nonprojective quantum measurement.The qubit is the abstract notion for any system which can be modeled in quantum theory by a two-level system. In such a system, any observable has at most two eigenvalues and hence any projective measurement can have at most two outcomes. Still, a qubit allows for an infinite number of different two-outcome measurements, the value of which, in general, cannot be known to the observer beforehand, but rather follows a binomial distribution. In quantum information theory, additional properties reflecting this binary structure have been revealed, e.g., the information capacity of a qubit is one classical bit, even when using entangled qubits [1]. Nonetheless, the properties of a qubit sometimes break with the binary structure, e.g., transferring the quantum state of a qubit is only possible with the communication of two classical bits and the help of entanglement [2]. Moreover, it is well-known that general quantum measurements can be nonprojective and have more than two irreducible outcomes [3]. The most general quantum measurement with n outcomes is described by positive semidefinite, possibly nonprojective, operators E 1 , E 2 , . . . , E n with E k = 1 1. The number of outcomes is reducible, if it is possible to writen are measurements for each λ, p λ is a probability distribution over λ, and for each λ there is at least one k λ with E (λ) k λ = 0. Nonprojective measurements found first applications in quantum information processing in the context of the discrimination of nonorthogonal quantum states. Ivanovic [4] found that it is possible to discriminate two pure qubit states without error even if the two states are nonorthogonal, but at the cost of allowing a third measurement outcome that indicates a failure of the discrimination procedure. The strategy with the lowest failure probability can be shown to be an irreducible three-outcome measurement [5]. Also recently, nonprojective measurements proved to be essential in purely information theoretical tasks like improving randomness certification [6].A peculiarity of nonprojective qubit measurements with more than two irreducible outcomes is that there ...

We report on an optical setup generating more than one bit of randomness from one entangled bit (i.e. a maximally entangled state of two-qubits). The amount of randomness is certified through the observation of Bell non-local correlations. To attain this result we implemented a high-purity entanglement source and a non-projective three-outcome measurement. Our implementation achieves a gain of 27% of randomness as compared with the standard methods using projective measurements. Additionally we estimate the amount of randomness certified in a one-sided device independent scenario, through the observation of EPR steering. Our results prove that non-projective quantum measurements allows extending the limits for nonlocality-based certified randomness generation using current technology.

Recently, a protocol for quantum state discrimination (QSD) in a multi-party scenario has been introduced [Phys. Rev. Lett. 111, 100501 (2013)]. In this protocol, Alice generates a quantum system in one of two pre-defined non-orthogonal qubit states, and the goal is to send the generated state information to different parties without classical communication exchanged between them during the protocol's session. The interesting feature is that, by resorting to sequential generalized measurements onto this single system, there is a non-vanishing probability that all observers identify the state prepared by Alice. Here, we present the experimental implementation of this protocol based on polarization single-photon states. Our scheme works over an optical network, and since QSD lies in the core of many protocols, it represents a step towards experimental multi-party quantum information processing.

Previous theoretical works showed that all pure two-qubit entangled states can generate one bit of local randomness and can be self-tested through the violation of proper Bell inequalities. We report an experiment in which nearly pure partially entangled states of photonic qubits are produced to investigate these tasks in a practical scenario. We show that small deviations from the ideal situation make low entangled states impractical to self-testing and randomness generation using the available techniques. Our results show that in practice lower entanglement implies lower randomness generation, recovering the intuition that maximally entangled states are better candidates for deviceindependent quantum information processing.

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