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arXiv:1811.12851 · Optica

Experimental certification of an informationally complete quantum measurement in a device-independent protocol

Massimiliano Smania, Piotr Mironowicz, Mohamed Nawareg, Marcin Pawłowski, Adán Cabello, Mohamed Bourennane

Published Dec 9, 2019• 36 citations
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Abstract

Minimal informationally complete positive operator-valued measures (MIC-POVMs) are special kinds of measurement in quantum theory in which the statistics of their d 2 -outcomes are enough to reconstruct any d -dimensional quantum state. For this reason, MIC-POVMs are referred to as standard measurements for quantum information. Here, we report an experiment with entangled photon pairs that certifies, for what we believe is the first time, a MIC-POVM for qubits following a device-independent protocol (i.e., modeling the state preparation and the measurement devices as black boxes, and using only the statistics of the inputs and outputs). Our certification is achieved under the assumption of freedom of choice, no communication, and fair sampling.

DOI
10.1364/optica.377959

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Minimal informationally complete positive operator-valued measures (MIC-POVMs) are special kinds of measurement in quantum theory in which the statistics of their d 2 -outcomes are enough to reconstruct any d -dimensional quantum state. For this reason, MIC-POVMs are referred to as standard measurements for quantum information. Here, we report an experiment with entangled photon pairs that certifies, for what we believe is the first time, a MIC-POVM for qubits following a device-independent protocol (i.e., modeling the state preparation and the measurement devices as black boxes, and using only the statistics of the inputs and outputs). Our certification is achieved under the assumption of freedom of choice, no communication, and fair sampling.
Minimal informationally complete positive operator-valued measures (MIC-POVMs) are special kinds of measurement in quantum theory in which the statistics of their d2-outcomes are enough to reconstruct any d-dimensional quantum state. For this reason, MIC-POVMs are referred to as standard measurements for quantum information. Here, we report an experiment with entangled photon pairs that certifies, for what we believe is the first time, a MIC-POVM for qubits following a device-independent protocol (i.e., modeling the state preparation and the measurement devices as black boxes, and using only the statistics of the inputs and outputs). Our certification is achieved under the assumption of freedom of choice, no communication, and fair sampling.
Certifying quantum measurements is increasingly important for foundational insights in quantum information science. Here, we report an experimental certification of unknown quantum measurements in a semi-device-independent setting. For the first time, we experimentally demonstrate that genuine three-outcome positive operator-valued measures (POVMs) can be certified under the assumption of a limited overlap between the prepared quantum states. The generalized quantum measurements are realized through discrete-time quantum walk and our experimental results clearly show that three-outcome POVMs can be certified even in the presence of noise. Finally, we experimentally investigate that optimal POVMs for performing unambiguous state discrimination can be self-tested. Our work opens new avenues for robust certification of quantum systems in the prepare-and-measure scenario.
Symmetric, informationally complete, positive operator-valued measurements (SIC-POVM) are fundamental in quantum information and foundations of quantum theory[1]. For example, SIC-POVMs are crucial for optimal quantum state tomography, quantum key distribution with optimal trade-off between security and key rate, device-independent certification of optimal randomness from one bit of entanglement, and information-based interpretations and operational reconstructions of quantum theory. Experimentally, photonic experiments of qubit and qutrit tomography, and quantum key distribution[2] have aimed for SIC-POVMs. However, these experiments rely on specific models for parts of the experimental setups and do not allow us to test whether the target measurements are truly SIC-POVMs in a "device independent" (DI) way that is, without relying on any modelling of the devices.
Self-testing represents the strongest form of certification of a quantum system. Here, we theoretically and experimentally investigate self-testing of nonprojective quantum measurements. That is, how can one certify, from observed data only, that an uncharacterized measurement device implements a desired nonprojective positive-operator valued measure (POVM). We consider a prepare-and-measure scenario with a bound on the Hilbert space dimension and develop methods for (i) robustly self-testing extremal qubit POVMs and (ii) certifying that an uncharacterized qubit measurement is nonprojective. 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 imply 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 certify a genuine four-outcome qubit POVM. Our results open interesting perspective for semi-device-independent certification of quantum devices.
Device-independent (DI) quantum protocols use Bell inequality violations to ensure security or certify quantum properties without assumptions on the devices’ internal workings. In this work, we study the role of rank-one qubit positive operator-valued measures (POVMs) in DI scenarios. This class includes all qubit extremal POVMs, i.e., those measurements that cannot be realized as mixtures of others, as well as part of non-extremal POVMs, recently shown to be useful in sequential quantum protocols. We demonstrate that any rank-one POVM can generate correlations in bipartite scenarios that saturate a Tsirelson inequality when two parties share an arbitrary entangled two-qubit state and perform specific self-tested measurements. For extremal POVMs, such saturation enables explicit computation of guessing probability and worst-case conditional von Neumann entropy. From the Tsirelson inequality, we establish a randomness certification method that facilitates numerical simulations and we validate it through a proof-of-concept experiment with three-outcome POVMs and tilted entangled states.
Among certification techniques, those based on the violation of Bell inequalities are appealing because they do not require assumptions on the underlying Hilbert space dimension and on the accuracy of calibration methods. Such device-independent techniques have been proposed to certify the quality of entangled states, unitary operations, projective measurements following von Neumann's model and rank-one positive-operator-valued measures (POVM). Here, we show that they can be extended to the characterization of quantum instruments with post-measurement states that are not fully determined by the Kraus operators but also depend on input states. We provide concrete certification recipes that are robust to noise.