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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Trends in photonic quantum information follow closely the technical progress in classical optics and telecommunications. In this regard, advances in multiplexing optical communications channels have also been pursued for the generation of multidimensional quantum states (qudits), since their use is advantageous for several quantum information tasks. One current path leading in this direction is through the use of space-division multiplexing multicore optical fibers, which provides a platform for efficiently controlling path-encoded qudit states. Here, we report on a parametric down-conversion source of entangled qudits that is fully based on (and therefore compatible with) state-of-the-art multicore-fiber technology. The source design uses modern multicore-fiber beam splitters to prepare the pump-laser beam as well as measure the generated entangled state, achieving high spectral brightness while providing a stable architecture. In addition, it can be readily used with any core geometry, which is crucial since widespread standards for multicore fibers in telecommunications have yet to be established. Our source represents a step toward the compatibility of quantum communications with the next-generation optical networks.

We present a systematic method to introduce free parameters in sets of mutually unbiased bases.In particular, we demonstrate that any set of m real mutually unbiased bases in dimension N > 2 admits the introduction of (m − 1)N/2 free parameters which cannot be absorbed by a global unitary operation. As consequence, there are m = k + 1 mutually unbiased bases in every dimension N = k 2 with k 3 /2 free parameters, where k is even. We construct the maximal set of triplets of mutually unbiased bases for two-qubits systems and triplets, quadruplets and quintuplets of mutually unbiased bases with free parameters for three-qubits systems. Furthermore, we study the richness of the entanglement structure of such bases and we provide the quantum circuits required to implement all these bases with free parameters in the laboratory. Finally, we find the upper bound for the maximal number of real and complex mutually unbiased bases existing in every dimension. This proof is simple, short and it considers basic matrix algebra.

The problem of non-orthogonal state discrimination underlies crucial quantum information tasks, such as cryptography and computing protocols. Therefore, it is decisive to find optimal scenarios for discrimination among quantum states. We experimentally investigate the strategy for the optimal discrimination of two non-orthogonal states considering a fixed rate of inconclusive outcomes (FRIO). The main advantage of the FRIO strategy is to interpolate between unambiguous and minimum error discrimination by solely adjusting the rate of inconclusive outcomes. We present a versatile experimental scheme that performs the optimal FRIO measurement for any pair of generated non-orthogonal states with arbitrary a priori probabilities and any fixed rate of inconclusive outcomes. Considering different values of the free parameters in the FRIO protocol, we implement it upon qubit states encoded in the polarization mode of single photons generated in the spontaneous parametric down-conversion process. Moreover, we resort to a newfangled double-path Sagnac interferometer to perform a three-outcome non-projective measurement required for the discrimination task, showing excellent agreement with the theoretical prediction. This experiment provides a practical toolbox for a wide range of quantum state discrimination strategies using the FRIO scheme, which can significantly benefit quantum information applications and fundamental studies in quantum theory.