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Register a new userDevice-independent tests of structures of measurement incompatibility
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Added by
Marco T\\'ulio Quintino
Publication date
2019
fields
Physics
and research's language is
English
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In contrast with classical physics, in quantum physics some sets of measurements are incompatible in the sense that they can not be performed simultaneously. Among other applications, incompatibility allows for contextuality and Bell nonlocality. This makes of crucial importance developing tools for certifying whether a set of measurements posses a certain structure of incompatibility. Here we show that, for quantum or nonsignaling models, if the measurements employed in a Bell test satisfy a given type of compatibility, then the amount of violation of some specific Bell inequalities become limited. Then, we show that correlations arising from local measurements on two-qubit states violate these limits, which rules out in a device-independent way such structures of incompatibility. In particular, we prove that quantum correlations allow for a device-independent demonstration of genuine triplewise incompatibility. Finally, we translate these results into a semi-device-independent Einstein-Podolsky-Rosen-steering scenario.
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Incompatible measurements, i.e., measurements that cannot be simultaneously performed, are necessary to observe nonlocal correlations. It is natural to ask, e.g., how incompatible the measurements have to be to achieve a certain violation of a Bell inequality. In this work, we provide the direct link between Bell nonlocality and the quantification of measurement incompatibility. This includes quantifiers for both incompatible and genuine-multipartite incompatible measurements. Our method straightforwardly generalizes to include constraints on the systems dimension (semi-device-independent approach) and on projective measurements, providing improved bounds on incompatibility quantifiers, and to include the prepare-and-measure scenario.
We show that the entropy of a message can be tested in a device-independent way. Specifically, we consider a prepare-and-measure scenario with classical or quantum communication, and develop two different methods for placing lower bounds on the communication entropy, given observable data. The first method is based on the framework of causal inference networks. The second technique, based on convex optimization, shows that quantum communication provides an advantage over classical, in the sense of requiring a lower entropy to reproduce given data. These ideas may serve as a basis for novel applications in device-independent quantum information processing.
Quantum tomography is currently the mainly employed method to assess the information of a system and therefore plays a fundamental role when trying to characterize the action of a particular channel. Nonetheless, quantum tomography requires the trust that the devices used in the laboratory perform state generation and measurements correctly. This work is based on the theoretical framework for the device-independent inference of quantum channels that was recently developed and experimentally implemented with superconducting qubits in [DallArno, Buscemi, Vedral, arXiv:1805.01159] and [DallArno, Brandsen, Buscemi, PRSA 473, 20160721 (2017)]. Here, we present a complete experimental test on a photonic setup of two device-independent quantum channels falsification and characterization protocols to analyze, validate, and enhance the results obtained by conventional quantum process tomography. This framework has fundamental implications in quantum information processing and may also lead to the development of new methods removing the assumptions typically taken for granted in all the previous protocols.
In this paper, we report an experiment about the device-independent tests of classical and quantum entropy based on a recent proposal [Phys. Rev. Lett. 115, 110501 (2015)], in which the states are encoded on the polarization of a biphoton system and measured by the state tomography technology. We also theoretically obtained the minimal quantum entropy for three widely used linear dimension witnesses. The experimental results agree well with the theoretical analysis, demonstrating that lower entropy is needed in quantum systems than that in classical systems under given values of the dimension witness.
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 can 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 that 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.
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