Detecting Entanglement by State Preparation and Local Measurements
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AbstractEntanglement witnesses (EWs) are a collection of observables that can characterize separable states and, experimentally, estimating EWs can verify entangled states. In this work, we show that a fixed measurement setting on a multipartite entangled state, which we introduce as a network state for the purpose, can estimate EWs. Namely, entangled states can be fully verified in a measurement-based manner, in which experimenters do not necessarily change measurement settings. We present a fixed measurement setting and network states for estimating decomposable EWs, equivalent to the partial transpose criteria. We also consider non-decomposable EWs that detect bound entangled states beyond the partial transpose criteria. The results can be extended to multipartite states such as graph states, a resource for measurement-based quantum computing, and readily applied to distributed settings such as quantum metrology or sensor networks where multipartite entangled states are resourceful.Popular summaryEntanglement is a key resource for quantum computing, communication, and sensing, making its verification a fundamental task in quantum technologies. The standard approach relies on entanglement witnesses—measurements whose outcomes certify entanglement. However, estimating a witness often requires multiple measurement settings, and precisely controlling these settings remains a major experimental challenge. The present work shows that this challenge can be avoided entirely. Rather than adapting measurements to a given witness, we introduce a tailored resource state, called a network state. A single fixed measurement performed on the network state together with the state under investigation is sufficient to determine whether the latter is entangled. In this sense, our approach is analogous to measurement-based quantum computing (MBQC), where state preparation and local measurements replace quantum circuits. Here, a network state and a fixed measurement replace the need for precisely controlled measurement settings. The framework naturally extends to distributed quantum settings, providing a practical route to entanglement verification across quantum networks. More broadly, it opens new opportunities for applications in distributed quantum metrology and quantum information processing.► BibTeX data@article{Kim2026detecting, doi = {10.22331/q-2026-06-08-2128}, url = {https://doi.org/10.22331/q-2026-06-08-2128}, title = {Detecting {E}ntanglement by {S}tate {P}reparation and {L}ocal {M}easurements}, author = {Kim, Jaemin and Bera, Anindita and Chru{\'{s}}ci{\'{n}}ski, Dariusz and Bae, Joonwoo}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2128}, month = jun, year = {2026} }► References [1] Antonio Acín, Nicolas Brunner, Nicolas Gisin, Serge Massar, Stefano Pironio, and Valerio Scarani. ``Device-independent security of quantum cryptography against collective attacks''. Phys. Rev. Lett. 98, 230501 (2007). https://doi.org/10.1103/PhysRevLett.98.230501 [2] Stefano Pironio, Antonio Acín, Nicolas Brunner, Nicolas Gisin, Serge Massar, and Valerio Scarani. ``Device-independent quantum key distribution secure against collective attacks''. New Journal of Physics 11, 045021 (2009). https://doi.org/10.1088/1367-2630/11/4/045021 [3] Cyril Branciard, Denis Rosset, Yeong-Cherng Liang, and Nicolas Gisin. ``Measurement-device-independent entanglement witnesses for all entangled quantum states''. Phys. Rev. Lett. 110, 060405 (2013). https://doi.org/10.1103/PhysRevLett.110.060405 [4] Francesco Buscemi. ``All entangled quantum states are nonlocal''. Phys. Rev. Lett. 108, 200401 (2012). https://doi.org/10.1103/PhysRevLett.108.200401 [5] Joseph Bowles, Ivan Šupić, Daniel Cavalcanti, and Antonio Acín. ``Device-independent entanglement certification of all entangled states''.
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The above citations are from SAO/NASA ADS (last updated successfully 2026-06-08 11:50:38). The list may be incomplete as not all publishers provide suitable and complete citation data.Could not fetch Crossref cited-by data during last attempt 2026-06-08 11:50:36: Could not fetch cited-by data for 10.22331/q-2026-06-08-2128 from Crossref. This is normal if the DOI was registered recently.This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions. AbstractEntanglement witnesses (EWs) are a collection of observables that can characterize separable states and, experimentally, estimating EWs can verify entangled states. In this work, we show that a fixed measurement setting on a multipartite entangled state, which we introduce as a network state for the purpose, can estimate EWs. Namely, entangled states can be fully verified in a measurement-based manner, in which experimenters do not necessarily change measurement settings. We present a fixed measurement setting and network states for estimating decomposable EWs, equivalent to the partial transpose criteria. We also consider non-decomposable EWs that detect bound entangled states beyond the partial transpose criteria. The results can be extended to multipartite states such as graph states, a resource for measurement-based quantum computing, and readily applied to distributed settings such as quantum metrology or sensor networks where multipartite entangled states are resourceful.Popular summaryEntanglement is a key resource for quantum computing, communication, and sensing, making its verification a fundamental task in quantum technologies. The standard approach relies on entanglement witnesses—measurements whose outcomes certify entanglement. However, estimating a witness often requires multiple measurement settings, and precisely controlling these settings remains a major experimental challenge. The present work shows that this challenge can be avoided entirely. Rather than adapting measurements to a given witness, we introduce a tailored resource state, called a network state. A single fixed measurement performed on the network state together with the state under investigation is sufficient to determine whether the latter is entangled. In this sense, our approach is analogous to measurement-based quantum computing (MBQC), where state preparation and local measurements replace quantum circuits. Here, a network state and a fixed measurement replace the need for precisely controlled measurement settings. The framework naturally extends to distributed quantum settings, providing a practical route to entanglement verification across quantum networks. More broadly, it opens new opportunities for applications in distributed quantum metrology and quantum information processing.► BibTeX data@article{Kim2026detecting, doi = {10.22331/q-2026-06-08-2128}, url = {https://doi.org/10.22331/q-2026-06-08-2128}, title = {Detecting {E}ntanglement by {S}tate {P}reparation and {L}ocal {M}easurements}, author = {Kim, Jaemin and Bera, Anindita and Chru{\'{s}}ci{\'{n}}ski, Dariusz and Bae, Joonwoo}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2128}, month = jun, year = {2026} }► References [1] Antonio Acín, Nicolas Brunner, Nicolas Gisin, Serge Massar, Stefano Pironio, and Valerio Scarani. ``Device-independent security of quantum cryptography against collective attacks''. Phys. Rev. Lett. 98, 230501 (2007). https://doi.org/10.1103/PhysRevLett.98.230501 [2] Stefano Pironio, Antonio Acín, Nicolas Brunner, Nicolas Gisin, Serge Massar, and Valerio Scarani. ``Device-independent quantum key distribution secure against collective attacks''. New Journal of Physics 11, 045021 (2009). https://doi.org/10.1088/1367-2630/11/4/045021 [3] Cyril Branciard, Denis Rosset, Yeong-Cherng Liang, and Nicolas Gisin. ``Measurement-device-independent entanglement witnesses for all entangled quantum states''. Phys. Rev. Lett. 110, 060405 (2013). https://doi.org/10.1103/PhysRevLett.110.060405 [4] Francesco Buscemi. ``All entangled quantum states are nonlocal''. Phys. Rev. Lett. 108, 200401 (2012). https://doi.org/10.1103/PhysRevLett.108.200401 [5] Joseph Bowles, Ivan Šupić, Daniel Cavalcanti, and Antonio Acín. ``Device-independent entanglement certification of all entangled states''.
Physical Review Letters 121, 180503– (2018). https://doi.org/10.1103/PhysRevLett.121.180503 [6] Yihui Quek and Peter W. Shor. ``Quantum and superquantum enhancements to two-sender, two-receiver channels''. Phys. Rev. A 95, 052329 (2017). https://doi.org/10.1103/PhysRevA.95.052329 [7] Jiyoung Yun, Ashutosh Rai, and Joonwoo Bae. ``Nonlocal network coding in interference channels''. Phys. Rev. Lett. 125, 150502 (2020). https://doi.org/10.1103/PhysRevLett.125.150502 [8] Robert Raussendorf and Hans J. Briegel. ``A one-way quantum computer''. Phys. Rev. Lett. 86, 5188–5191 (2001). https://doi.org/10.1103/PhysRevLett.86.5188 [9] H. J. Briegel, D. E. Browne, W. Dür, R. Raussendorf, and M. Van den Nest. ``Measurement-based quantum computation''. Nature Physics 5, 19–26 (2009). https://doi.org/10.1038/nphys1157 [10] Barbara M. Terhal. ``Bell inequalities and the separability criterion''. Physics Letters A 271, 319–326 (2000). https://doi.org/10.1016/S0375-9601(00)00401-1 [11] M. Lewenstein, B. Kraus, J. I. Cirac, and P. Horodecki. ``Optimization of entanglement witnesses''. Phys. Rev. A 62, 052310 (2000). https://doi.org/10.1103/PhysRevA.62.052310 [12] Michał Horodecki, Paweł Horodecki, and Ryszard Horodecki. ``Separability of mixed states: necessary and sufficient conditions''. Physics Letters A 223, 1–8 (1996). https://doi.org/10.1016/S0375-9601(96)00706-2 [13] Otfried Gühne and Géza Tóth. ``Entanglement detection''. Physics Reports 474, 1–75 (2009). https://doi.org/10.1016/j.physrep.2009.02.004 [14] Ryszard Horodecki, Paweł Horodecki, Michał Horodecki, and Karol Horodecki. ``Quantum entanglement''. Rev. Mod. Phys. 81, 865–942 (2009). https://doi.org/10.1103/RevModPhys.81.865 [15] Dariusz Chruściński and Gniewomir Sarbicki. ``Entanglement witnesses: construction, analysis and classification''. Journal of Physics A: Mathematical and Theoretical 47, 483001 (2014). https://doi.org/10.1088/1751-8113/47/48/483001 [16] Nicolai Friis, Giuseppe Vitagliano, Mehul Malik, and Marcus Huber. ``Entanglement certification from theory to experiment''.
Nature Reviews Physics 1, 72–87 (2019). https://doi.org/10.1038/s42254-018-0003-5 [17] Lluís Masanes. ``All bipartite entangled states are useful for information processing''. Phys. Rev. Lett. 96, 150501 (2006). https://doi.org/10.1103/PhysRevLett.96.150501 [18] Dariusz Chruściński. ``A class of symmetric bell diagonal entanglement witnesses—a geometric perspective''. Journal of Physics A: Mathematical and Theoretical 47, 424033 (2014). https://doi.org/10.1088/1751-8113/47/42/424033 [19] Anindita Bera, Filip A. Wudarski, Gniewomir Sarbicki, and Dariusz Chruściński. ``Class of bell-diagonal entanglement witnesses in ${C}^{4}{\bigotimes}{C}^{4}$: Optimization and the spanning property''. Phys. Rev. A 105, 052401 (2022). https://doi.org/10.1103/PhysRevA.105.052401 [20] Man-Duen Choi. ``Completely positive linear maps on complex matrices''. Linear Algebra and its Applications 10, 285–290 (1975). https://doi.org/10.1016/0024-3795(75)90075-0 [21] Kil-Chan Ha and Seung-Hyeok Kye. ``One-parameter family of indecomposable optimal entanglement witnesses arising from generalized choi maps''. Phys. Rev. A 84, 024302 (2011). https://doi.org/10.1103/PhysRevA.84.024302 [22] Heinz-Peter Breuer. ``Optimal entanglement criterion for mixed quantum states''. Phys. Rev. Lett. 97, 080501 (2006). https://doi.org/10.1103/PhysRevLett.97.080501 [23] William Hall. ``A new criterion for indecomposability of positive maps''. Journal of Physics A: Mathematical and General 39, 14119–14131 (2006). https://doi.org/10.1088/0305-4470/39/45/020 [24] M. Hein, J. Eisert, and H. J. Briegel. ``Multiparty entanglement in graph states''. Phys. Rev. A 69, 062311 (2004). https://doi.org/10.1103/PhysRevA.69.062311 [25] Krzysztof Chabuda, Jacek Dziarmaga, Tobias J. Osborne, and Rafał Demkowicz-Dobrzański. ``Tensor-network approach for quantum metrology in many-body quantum systems''. Nature Communications 11, 250 (2020). https://doi.org/10.1038/s41467-019-13735-9 [26] Zheshen Zhang and Quntao Zhuang. ``Distributed quantum sensing''. Quantum Science and Technology 6, 043001 (2021). https://doi.org/10.1088/2058-9565/abd4c3 [27] Yink Loong Len, Tuvia Gefen, Alex Retzker, and Jan Kołodyński. ``Quantum metrology with imperfect measurements''. Nature Communications 13, 6971 (2022). https://doi.org/10.1038/s41467-022-33563-8 [28] Wenchao Ge, Kurt Jacobs, Zachary Eldredge, Alexey V. Gorshkov, and Michael Foss-Feig. ``Distributed quantum metrology with linear networks and separable inputs''. Phys. Rev. Lett. 121, 043604 (2018). https://doi.org/10.1103/PhysRevLett.121.043604 [29] M. Zwerger, W. Dür, and H. J. Briegel. ``Measurement-based quantum repeaters''. Phys. Rev. A 85, 062326 (2012). https://doi.org/10.1103/PhysRevA.85.062326 [30] Nicolai Friis, Davide Orsucci, Michalis Skotiniotis, Pavel Sekatski, Vedran Dunjko, Hans J Briegel, and Wolfgang Dür. ``Flexible resources for quantum metrology''. New Journal of Physics 19, 063044 (2017). https://doi.org/10.1088/1367-2630/aa7144 [31] Timothy J. Proctor, Paul A. Knott, and Jacob A. Dunningham. ``Multiparameter estimation in networked quantum sensors''. Phys. Rev. Lett. 120, 080501 (2018). https://doi.org/10.1103/PhysRevLett.120.080501 [32] Elias Amselem and Mohamed Bourennane. ``Experimental four-qubit bound entanglement''. Nature Physics 5, 748–752 (2009). https://doi.org/10.1038/nphys1372 [33] Jonathan Lavoie, Rainer Kaltenbaek, Marco Piani, and Kevin J. Resch. ``Experimental bound entanglement in a four-photon state''. Phys. Rev. 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