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arXiv:1903.12533 · Physical Review Research

Semi-device-independent self-testing of unsharp measurements

Nikolai Miklin, Jakub J. Borkała, Marcin Pawłowski

Published Jul 6, 2020• 67 citations
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Abstract

This work studies unsharp quantum measurements as a resource in scenarios where one faces the trade-off between information gain and disturbance. The authors introduce a prepare-transform-measure scenario in which unsharp measurements outperform their sharp counterparts, as well as any stochastic strategy involving dichotomic projective measurements.

DOI
10.1103/physrevresearch.2.033014

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This work studies unsharp quantum measurements as a resource in scenarios where one faces the trade-off between information gain and disturbance. The authors introduce a prepare-transform-measure scenario in which unsharp measurements outperform their sharp counterparts, as well as any stochastic strategy involving dichotomic projective measurements.
A key aspect in quantum information is to understand the advantage offered by quantum systems over classical ones in communication tasks. In recent years, a fundamental approach to this problem has been developed, focusing on quantum correlations in prepare-and-measure scenarios. Inspired by the developments in Bell nonlocality and device-independent information processing, this line of research aims to characterize the possibilities and limits of quantum systems for communication, in particular to precisely capture the advantage they offer over classical systems. In addition to fundamental insights, these ideas also underpin the concept of semi-device-independent quantum information processing. Exploring trade-offs between security, performance and ease-of-implementation, this approach opens promising directions for novel quantum information processing technologies and devices. A number of protocols and proof-of-principle demonstrations have been reported in recent years, in particular for quantum randomness certification and key distribution. Here, we provide a comprehensive introduction to quantum prepare-and-measure correlations and semi-device independent applications.
Unsharp measurement is a unique type of measurement which provides a tradeoff between information gain and state disturbance. Such measurement is a crucial method in quantum theory and shows potential in various applications. We propose a device-independent scheme for certifying unsharp measurements with binary outcome in an efficient manner. Our scheme has low consumption of measurement resources and is robust against noise. In experiment, we demonstrate the certification of a typical kind of unsharp measurements. We achieve high fidelities above 0.9 when the strength of the unsharp measurement is less than 0.6 and get near unity fidelities in the low measurement strength range. Our scheme can be applied to enhance the feasibility and practicability of device-independent quantum information processing tasks.
Unsharp measurements are increasingly important in quantum information theory and tests of quantum theory. Here, in a semi-device-independent setting, we experimentally demonstrate their noise-robust characterisation while only assuming that the involved devices operate on qubits and that the detected events constitute a fair sample. Our experiment involves three parties; the first party prepares a qubit system, the second party performs operations which returns both a classical and quantum outcome and the later is measured by the third party. From the measured probabilities we show nearly-optimal quantum correlations for unsharp observales, falsify every model in which the operations are simulated with stochastic projective qubit measurements and obtain narrow intervals to which the sharpness parameter can be confined. Moreover, we also certify two sequential pairs of incompatible measurements and quantify their degree of incompatibility. Finally, we discuss our characterisation of the sharpness parameter as compared to that obtained from a tomographic scheme subjected to small errors.
Abstract Semi-device-independent certification of an unsharp instrument has recently been demonstrated (2019 New J. Phys. 21 083034) based on the sequential sharing of quantum advantages in a prepare-measure communication game by assuming the system to be qubit. In this work, we provide device-independent (DI) self-testing of the unsharp instrument through the quantum violation of two Bell inequalities where the devices are uncharacterized and the dimension of the system remains unspecified. We introduce an elegant sum-of-squares approach to derive the dimension-independent optimal quantum violation of Bell inequalities which plays a crucial role. Note that the standard Bell test cannot self-test the post-measurement states and consequently cannot self-test unsharp instrument. The sequential Bell test possess the potential to self-test an unsharp instrument. We demonstrate that there exists a trade-off between the maximum sequential quantum violations of the Clauser–Horne–Shimony–Holt inequality, and they form an optimal pair that enables the DI self-testing of the entangled state, the observables, and the unsharpness parameter. Further, we extend our study to the case of elegant Bell inequality and we argue that it has two classical bounds—the local bound and the non-trivial preparation non-contextual bound, lower than the local bound. Based on the sharing of preparation contextuality by three independent sequential observers, we demonstrate the DI self-testing of two unsharpness parameters. Since an actual experimental scenario involves losses and imperfection, we demonstrate robustness of our certification to noise.