Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1904.05692 · Physical Review A

Semi-device-independent characterization of quantum measurements under a minimum overlap assumption

Weixu Shi, Yu Cai, Jonatan Bohr Brask, Hugo Zbinden, Nicolas Brunner

Published Oct 10, 2019• 14 citations
arXivHTMLPDF

Abstract

Recently, a novel framework for semi-device-independent quantum prepare-and-measure protocols has been proposed, based on the assumption of a limited distinguishability between the prepared quantum states. Here, we discuss the problem of characterizing an unknown quantum measurement device in this setting. We present several methods to attack the problem. Considering the simplest scenario of two preparations with lower bounded overlap, we show that genuine three-outcome positive-operator valued measures (POVMs) can be certified, even in the presence of noise. Moreover, we show that the optimal POVM for performing unambiguous state discrimination can be self-tested.

DOI
10.1103/physreva.100.042108

Related papers

Experimental certification of nonprojective quantum measurements under a minimum overlap assumption

Qin Fan, Meng-Yun Ma, Yong-Nan Sun +2 more

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.

Optics Express•Aug 26, 2022•4 citations

Self-testing nonprojective quantum measurements in prepare-and-measure experiments

Armin Tavakoli, Massimiliano Smania, Tamás Vértesi +2 more

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.

arXiv:1811.12712•Science Advances•Apr 17, 2020•84 citations

Towards minimal self-testing of qubit states and measurements in prepare-and-measure scenarios

Gábor Drótos, Károly F. Pál, Abdelmalek Taoutioui +1 more

Abstract Self-testing is a promising approach to certifying quantum states or measurements. Originally, it relied solely on the outcome statistics of the measurements involved in a device-independent (DI) setup. Extra physical assumptions about the system make the setup semi-DI. In the latter approach, we consider a prepare-and-measure scenario in which the dimension of the mediating particle is assumed to be two. In a setup involving four (three) preparations and three (two) projective measurements in addition to the target, we exemplify how to self-test any four- (three-) outcome extremal positive operator-valued measure using a linear witness. One of our constructions also achieves self-testing of any number of states with the help of as many projective measurements as the dimensionality of the space spanned by the corresponding Bloch vectors. These constructions are conjectured to be minimal in terms of the number of preparations and measurements required. In addition, we implement one of our prepare-and-measure constructionson IBM and IonQ quantum processors and certify the existence of a complex qubit Hilbert space based on the data obtained from these experiments.

arXiv:2406.08661•New Journal of Physics•May 21, 2024•3 citations

Minimal scheme for certifying three-outcome qubit measurements in the prepare-and-measure scenario

Jonathan Steinberg, H. Chau Nguyen, Matthias Kleinmann

The number of outcomes is a defining property of a quantum measurement, in particular, if the measurement cannot be decomposed into simpler measurements with fewer outcomes. Importantly, the number of outcomes of a quantum measurement can be irreducibly higher than the dimension of the system. The certification of this property is possible in a semi-device-independent way either based on a Bell-like scenario or by utilizing the simpler prepare-and-measure scenario. Here we show that in the latter scenario the minimal scheme for certifying an irreducible three-outcome qubit measurement requires three state preparations and only two measurements and we provide experimentally feasible examples for this minimal certification scheme. We also discuss the dimension assumption characteristic of the semi-device-independent approach and to what extent it can be mitigated.

arXiv:2105.09925•Physical Review A•Dec 17, 2021•3 citations

Semi-device-independent characterization of multipartite entanglement of states and measurements

Armin Tavakoli, Alastair A. Abbott, Marc-Olivier Renou +2 more

The semi-device-independent framework allows one to draw conclusions about properties of an unknown quantum system under weak assumptions. Here we present a semi-device-independent scheme for the characterization of multipartite entanglement based around a game played by several isolated parties whose devices are uncharacterized beyond an assumption about the dimension of their Hilbert spaces. Our scheme can simultaneously certify that an $n$-partite high-dimensional quantum state features genuine multipartite entanglement, and that a joint measurement on $n$ subsystems is entangled. Moreover, it provides a lower bound on the number of entangled measurement operators. These tests are strongly robust to noise, and even optimal for certain classes of states and measurements, as we demonstrate with illustrative examples. Notably, our scheme allows the certification of many entangled states admitting a local model, which therefore cannot violate any Bell inequality.

arXiv:1805.00377•Physical Review A•Nov 26, 2018•30 citations

Self-testing of semisymmetric informationally complete measurements in a qubit prepare-and-measure scenario

Gábor Drótos, Károly F. Pál, Tamás Vértesi

Self-testing is a powerful method for certifying quantum systems. Initially proposed in the device-independent (DI) setting, self-testing has since been relaxed to the semi-device-independent (semi-DI) setting. In this study, we focus on the self-testing of a specific type of nonprojective qubit measurements belonging to a one-parameter family, using the semi-DI prepare-and-measure (PM) scenario. Remarkably, we identify the simplest PM scenario discovered so far, involving only four preparations and four measurements, for self-testing the fourth measurement. This particular measurement is a four-outcome nonprojective positive operator-valued measure (POVM) and falls in the class of semisymmetric informationally complete POVMs introduced by Geng et al. [Phys. Rev. Lett. 126, 100401 (2021)]. To achieve this, we develop analytic techniques for semi-DI self-testing in the PM scenario. Our results pave the way toward self-testing any extremal qubit POVM within a potentially minimal PM scenario.

arXiv:2306.07248•Physical Review A•Sep 20, 2024•6 citations
Recently, a novel framework for semi-device-independent quantum prepare-and-measure protocols has been proposed, based on the assumption of a limited distinguishability between the prepared quantum states. Here, we discuss the problem of characterizing an unknown quantum measurement device in this setting. We present several methods to attack the problem. Considering the simplest scenario of two preparations with lower bounded overlap, we show that genuine three-outcome positive-operator valued measures (POVMs) can be certified, even in the presence of noise. Moreover, we show that the optimal POVM for performing unambiguous state discrimination can be self-tested.
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.
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.
Abstract Self-testing is a promising approach to certifying quantum states or measurements. Originally, it relied solely on the outcome statistics of the measurements involved in a device-independent (DI) setup. Extra physical assumptions about the system make the setup semi-DI. In the latter approach, we consider a prepare-and-measure scenario in which the dimension of the mediating particle is assumed to be two. In a setup involving four (three) preparations and three (two) projective measurements in addition to the target, we exemplify how to self-test any four- (three-) outcome extremal positive operator-valued measure using a linear witness. One of our constructions also achieves self-testing of any number of states with the help of as many projective measurements as the dimensionality of the space spanned by the corresponding Bloch vectors. These constructions are conjectured to be minimal in terms of the number of preparations and measurements required. In addition, we implement one of our prepare-and-measure constructionson IBM and IonQ quantum processors and certify the existence of a complex qubit Hilbert space based on the data obtained from these experiments.
The number of outcomes is a defining property of a quantum measurement, in particular, if the measurement cannot be decomposed into simpler measurements with fewer outcomes. Importantly, the number of outcomes of a quantum measurement can be irreducibly higher than the dimension of the system. The certification of this property is possible in a semi-device-independent way either based on a Bell-like scenario or by utilizing the simpler prepare-and-measure scenario. Here we show that in the latter scenario the minimal scheme for certifying an irreducible three-outcome qubit measurement requires three state preparations and only two measurements and we provide experimentally feasible examples for this minimal certification scheme. We also discuss the dimension assumption characteristic of the semi-device-independent approach and to what extent it can be mitigated.
The semi-device-independent framework allows one to draw conclusions about properties of an unknown quantum system under weak assumptions. Here we present a semi-device-independent scheme for the characterization of multipartite entanglement based around a game played by several isolated parties whose devices are uncharacterized beyond an assumption about the dimension of their Hilbert spaces. Our scheme can simultaneously certify that an nnn-partite high-dimensional quantum state features genuine multipartite entanglement, and that a joint measurement on nnn subsystems is entangled. Moreover, it provides a lower bound on the number of entangled measurement operators. These tests are strongly robust to noise, and even optimal for certain classes of states and measurements, as we demonstrate with illustrative examples. Notably, our scheme allows the certification of many entangled states admitting a local model, which therefore cannot violate any Bell inequality.
Self-testing is a powerful method for certifying quantum systems. Initially proposed in the device-independent (DI) setting, self-testing has since been relaxed to the semi-device-independent (semi-DI) setting. In this study, we focus on the self-testing of a specific type of nonprojective qubit measurements belonging to a one-parameter family, using the semi-DI prepare-and-measure (PM) scenario. Remarkably, we identify the simplest PM scenario discovered so far, involving only four preparations and four measurements, for self-testing the fourth measurement. This particular measurement is a four-outcome nonprojective positive operator-valued measure (POVM) and falls in the class of semisymmetric informationally complete POVMs introduced by Geng et al. [Phys. Rev. Lett. 126, 100401 (2021)]. To achieve this, we develop analytic techniques for semi-DI self-testing in the PM scenario. Our results pave the way toward self-testing any extremal qubit POVM within a potentially minimal PM scenario.