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:1608.02675 · Physical Review Letters

Measurement-Device-Independent Approach to Entanglement Measures

Farid Shähandeh, Michael J. W. Hall, Timothy C. Ralph

Published Apr 13, 2017• 31 citations
arXivHTMLPDF

Abstract

Within the context of semiquantum nonlocal games, the trust can be removed from the measurement devices in an entanglement-detection procedure. Here, we show that a similar approach can be taken to quantify the amount of entanglement. To be specific, first, we show that in this context, a small subset of semiquantum nonlocal games is necessary and sufficient for entanglement detection in the local operations and classical communication paradigm. Second, we prove that the maximum payoff for these games is a universal measure of entanglement which is convex and continuous. Third, we show that for the quantification of negative-partial-transpose entanglement, this subset can be further reduced down to a single arbitrary element. Importantly, our measure is measurement device independent by construction and operationally accessible. Finally, our approach straightforwardly extends to quantify the entanglement within any partitioning of multipartite quantum states.

DOI
10.1103/physrevlett.118.150505

Related papers

Measurement-device-independent Schmidt number certification of all entangled states

Saheli Mukherjee, Bivas Mallick, Arun Kumar Das +2 more

Bipartite quantum states with higher Schmidt numbers have been shown to outperform those with lower Schmidt numbers in various quantum information-processing tasks, highlighting the operational advantage of entanglement dimensionality. Certifying the Schmidt number of such states is therefore crucial for efficient resource utilization. Ideally, this certification should rely as little as possible on the certifying devices to ensure robustness against their potential imperfections. Fully device-independent certification via Bell-nonlocal games offers strong robustness but suffers from fundamental limitations: It cannot certify the Schmidt number of all entangled states. We demonstrate that this insufficiency of Bell-nonlocal games is not limited to entangled states that do not exhibit Bell nonlocality. Specifically, we prove the existence of Bell-nonlocal states whose Schmidt number cannot be certified by any Bell-nonlocal game when the parties are restricted to local projective measurements. To overcome this, we develop a measurement-device-independent certification method based on semiquantum nonlocal games, which assume trusted preparation devices but treat measurement devices as black boxes. We prove that for any bipartite state with a Schmidt number exceeding $r$, a semiquantum nonlocal game exists that can certify its Schmidt number. Finally, we provide an explicit construction of such a semiquantum nonlocal game based on an optimal Schmidt number witness operator.

arXiv:2502.13296•Physical Review A•Nov 21, 2025•1 citation

Detection and quantification of entanglement with measurement-device-independent and universal entanglement witness*

Zhi‐Jin Ke, Yi‐Tao Wang, Shang Yu +10 more

Entanglement is the key resource in quantum information processing, and an entanglement witness (EW) is designed to detect whether a quantum system has any entanglement. However, prior knowledge of the target states should be known first to design a suitable EW, which weakens this method. Nevertheless, a recent theory shows that it is possible to design a universal entanglement witness (UEW) to detect negative-partial-transpose (NPT) entanglement in unknown bipartite states with measurement-device-independent (MDI) characteristic. The outcome of a UEW can also be upgraded to be an entanglement measure. In this study, we experimentally design and realize an MDI UEW for two-qubit entangled states. All of the tested states are well-detected without any prior knowledge. We also show that it is able to quantify entanglement by comparing it with concurrence estimated through state tomography. The relation between them is also revealed. The entire experimental framework ensures that the UEW is MDI.

Chinese Physics B•May 13, 2020•8 citations

Sequential measurement-device-independent entanglement detection by multiple observers

Chirag Srivastava, Shiladitya Mal, Aditi Sen +1 more

Violation of a Bell inequality certifies that the underlying state must be entangled in a device-independent way, although there exist some entangled states which do not violate such an inequality. However, for every entangled state, it is possible to find a Hermitian operator called an entanglement witness that can detect entanglement through some local measurements in a device-dependent method, but implementation of wrong measurements may lead to fake detection of entanglement. To avoid such difficulties, measurement-device-independent entanglement witness (MDI-EW) based on a semiquantum nonlocal game was proposed, which is not only robust against wrong measurements but also against a specific kind of lossy detectors. We employ here a measurement-device-independent entanglement witness to detect entanglement in a scenario where half of an entangled pair is possessed by a single observer while the other half is with multiple observers performing unsharp measurements, sequentially, independently, and preserving entanglement as much as possible. Interestingly, we find that the numbers of successful observers who can detect entanglement, measurement-device-independently, both with equal and unequal sharpness parameters of the noisy measurements, are greater than that obtained with standard and Bell-inequality-based entanglement detection methods, reflecting its robustness. The entanglement contents of the sequentially shared states are also analyzed. Unlike other scenarios, our investigations also reveal that in this measurement-device-independent situation, states having entanglement in proximity to maximal remain entangled until there are two sequential observers, even if they measure sharply.

arXiv:1911.02908•Physical Review A•Mar 10, 2021•30 citations

Witnessing arbitrary bipartite entanglement in a measurement-device-independent way

Arindam Mallick, Sibasish Ghosh A

Experimental detection of entanglement of an arbitrary state of a given bipartite system is crucial for exploring many areas of quantum information processing. But such a detection should be made in a device-independent way if the preparation process of the state is considered to be faithful, in order to avoid detection of a separable state as an entangled one. The recently developed scheme of detecting bipartite entanglement in a measurement-device-independent way [Phys. Rev. Lett. 110, 060405 (2013)] does require information about the state. Here, by using Auguisiak et al.'s universal entanglement witness scheme for two-qubit states [Phys. Rev. A 77, 030301 (2008)], we provide a universal entanglement detection scheme for two-qubit states in a measurement-device-independent way. We also provide a set of universal witness operators for detecting NPT-ness (negative under partial transpose) of two-qudit states in a measurement-device-independent way. We conjecture that no such universal entanglement witness scheme exists for PPT (positive under partial transpose) entangled states. We also analyze the robustness of some of the experimental schemes---for detecting entanglement in a measurement-device-independent way---under the influence of noise in the inputs (from the referee) as well as in the measurement operator.

arXiv:1506.03985•Physical Review A•Nov 16, 2017•8 citations

Quantum entanglement as a foundational and informational resource: A unified perspective for separability, nonlocal games, contextuality, decoherence, and measurement

Sachin .

Quantum entanglement is the defining feature of composite quantum systems, underpinning correlations beyond classical randomness and enabling quantum communication, cryptography, and error correction. Surveys treat entanglement, Bell nonlocality, contextuality, and decoherence in isolation or narrow subcommunities. This review advances a unified perspective analysing these phenomena as distinct but interrelated manifestations of nonclassical correlations with an operational structure. We organise bipartite entanglement through separability criteria, Schmidt decomposition, and partial-transpose techniques, and develop tools for nonlocal correlations based on Bell inequalities, Tsirelson’s bound, nonlocal games, and self-testing, emphasising device-independent protocols. We then examine contextuality and magic states as resources for quantum computational advantage beyond entanglement, clarifying their relationship to nonlocality. Finally, we characterise decoherence as environment-induced entanglement selecting classical records, and use this perspective to specify which aspects of the measurement problem it addresses and which require interpretational or dynamical extensions. Integrating these dimensions, the review clarifies how notions of nonclassicality relate, diverge, and underpin quantum technologies.

International Journal of Physics and Mathematics•Jul 1, 2025•0 citations

Device-independent entanglement quantification

Tobias Moroder, Jean-Daniel Bancal, Yeong-Cherng Liang +2 more

We present a general method to quantify both bipartite and multipartite entanglement in a device-independent manner, meaning that we put a lower bound on the amount of entanglement present in a system based on observed data only but independently of any quantum description of the employed devices. Some of the bounds we obtain, such as for the Clauser-Horne-Shimony-Holt Bell inequality or the Svetlichny inequality, are shown to be tight. Besides, device-independent entanglement quantification can serve as a basis for numerous tasks. We show in particular that our method provides a rigorous way to construct dimension witnesses, gives new insights into the question whether bound entangled states can violate a Bell inequality, and can be used to construct device independent entanglement witnesses involving an arbitrary number of parties.

•Feb 6, 2013•1 citation
Within the context of semiquantum nonlocal games, the trust can be removed from the measurement devices in an entanglement-detection procedure. Here, we show that a similar approach can be taken to quantify the amount of entanglement. To be specific, first, we show that in this context, a small subset of semiquantum nonlocal games is necessary and sufficient for entanglement detection in the local operations and classical communication paradigm. Second, we prove that the maximum payoff for these games is a universal measure of entanglement which is convex and continuous. Third, we show that for the quantification of negative-partial-transpose entanglement, this subset can be further reduced down to a single arbitrary element. Importantly, our measure is measurement device independent by construction and operationally accessible. Finally, our approach straightforwardly extends to quantify the entanglement within any partitioning of multipartite quantum states.
Bipartite quantum states with higher Schmidt numbers have been shown to outperform those with lower Schmidt numbers in various quantum information-processing tasks, highlighting the operational advantage of entanglement dimensionality. Certifying the Schmidt number of such states is therefore crucial for efficient resource utilization. Ideally, this certification should rely as little as possible on the certifying devices to ensure robustness against their potential imperfections. Fully device-independent certification via Bell-nonlocal games offers strong robustness but suffers from fundamental limitations: It cannot certify the Schmidt number of all entangled states. We demonstrate that this insufficiency of Bell-nonlocal games is not limited to entangled states that do not exhibit Bell nonlocality. Specifically, we prove the existence of Bell-nonlocal states whose Schmidt number cannot be certified by any Bell-nonlocal game when the parties are restricted to local projective measurements. To overcome this, we develop a measurement-device-independent certification method based on semiquantum nonlocal games, which assume trusted preparation devices but treat measurement devices as black boxes. We prove that for any bipartite state with a Schmidt number exceeding rrr, a semiquantum nonlocal game exists that can certify its Schmidt number. Finally, we provide an explicit construction of such a semiquantum nonlocal game based on an optimal Schmidt number witness operator.
Entanglement is the key resource in quantum information processing, and an entanglement witness (EW) is designed to detect whether a quantum system has any entanglement. However, prior knowledge of the target states should be known first to design a suitable EW, which weakens this method. Nevertheless, a recent theory shows that it is possible to design a universal entanglement witness (UEW) to detect negative-partial-transpose (NPT) entanglement in unknown bipartite states with measurement-device-independent (MDI) characteristic. The outcome of a UEW can also be upgraded to be an entanglement measure. In this study, we experimentally design and realize an MDI UEW for two-qubit entangled states. All of the tested states are well-detected without any prior knowledge. We also show that it is able to quantify entanglement by comparing it with concurrence estimated through state tomography. The relation between them is also revealed. The entire experimental framework ensures that the UEW is MDI.
Violation of a Bell inequality certifies that the underlying state must be entangled in a device-independent way, although there exist some entangled states which do not violate such an inequality. However, for every entangled state, it is possible to find a Hermitian operator called an entanglement witness that can detect entanglement through some local measurements in a device-dependent method, but implementation of wrong measurements may lead to fake detection of entanglement. To avoid such difficulties, measurement-device-independent entanglement witness (MDI-EW) based on a semiquantum nonlocal game was proposed, which is not only robust against wrong measurements but also against a specific kind of lossy detectors. We employ here a measurement-device-independent entanglement witness to detect entanglement in a scenario where half of an entangled pair is possessed by a single observer while the other half is with multiple observers performing unsharp measurements, sequentially, independently, and preserving entanglement as much as possible. Interestingly, we find that the numbers of successful observers who can detect entanglement, measurement-device-independently, both with equal and unequal sharpness parameters of the noisy measurements, are greater than that obtained with standard and Bell-inequality-based entanglement detection methods, reflecting its robustness. The entanglement contents of the sequentially shared states are also analyzed. Unlike other scenarios, our investigations also reveal that in this measurement-device-independent situation, states having entanglement in proximity to maximal remain entangled until there are two sequential observers, even if they measure sharply.
Experimental detection of entanglement of an arbitrary state of a given bipartite system is crucial for exploring many areas of quantum information processing. But such a detection should be made in a device-independent way if the preparation process of the state is considered to be faithful, in order to avoid detection of a separable state as an entangled one. The recently developed scheme of detecting bipartite entanglement in a measurement-device-independent way [Phys. Rev. Lett. 110, 060405 (2013)] does require information about the state. Here, by using Auguisiak et al.'s universal entanglement witness scheme for two-qubit states [Phys. Rev. A 77, 030301 (2008)], we provide a universal entanglement detection scheme for two-qubit states in a measurement-device-independent way. We also provide a set of universal witness operators for detecting NPT-ness (negative under partial transpose) of two-qudit states in a measurement-device-independent way. We conjecture that no such universal entanglement witness scheme exists for PPT (positive under partial transpose) entangled states. We also analyze the robustness of some of the experimental schemes---for detecting entanglement in a measurement-device-independent way---under the influence of noise in the inputs (from the referee) as well as in the measurement operator.
Quantum entanglement is the defining feature of composite quantum systems, underpinning correlations beyond classical randomness and enabling quantum communication, cryptography, and error correction. Surveys treat entanglement, Bell nonlocality, contextuality, and decoherence in isolation or narrow subcommunities. This review advances a unified perspective analysing these phenomena as distinct but interrelated manifestations of nonclassical correlations with an operational structure. We organise bipartite entanglement through separability criteria, Schmidt decomposition, and partial-transpose techniques, and develop tools for nonlocal correlations based on Bell inequalities, Tsirelson’s bound, nonlocal games, and self-testing, emphasising device-independent protocols. We then examine contextuality and magic states as resources for quantum computational advantage beyond entanglement, clarifying their relationship to nonlocality. Finally, we characterise decoherence as environment-induced entanglement selecting classical records, and use this perspective to specify which aspects of the measurement problem it addresses and which require interpretational or dynamical extensions. Integrating these dimensions, the review clarifies how notions of nonclassicality relate, diverge, and underpin quantum technologies.
We present a general method to quantify both bipartite and multipartite entanglement in a device-independent manner, meaning that we put a lower bound on the amount of entanglement present in a system based on observed data only but independently of any quantum description of the employed devices. Some of the bounds we obtain, such as for the Clauser-Horne-Shimony-Holt Bell inequality or the Svetlichny inequality, are shown to be tight. Besides, device-independent entanglement quantification can serve as a basis for numerous tasks. We show in particular that our method provides a rigorous way to construct dimension witnesses, gives new insights into the question whether bound entangled states can violate a Bell inequality, and can be used to construct device independent entanglement witnesses involving an arbitrary number of parties.