{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:02:36Z","timestamp":1760234556124,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2021,5,28]],"date-time":"2021-05-28T00:00:00Z","timestamp":1622160000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Quantum metrology overcomes standard precision limits and has the potential to play a key role in quantum sensing. Quantum mechanics, through the Heisenberg uncertainty principle, imposes limits on the precision of measurements. Conventional bounds to the measurement precision such as the shot noise limit are not as fundamental as the Heisenberg limits, and can be beaten with quantum strategies that employ \u2018quantum tricks\u2019 such as squeezing and entanglement. Bipartite entangled quantum states with a positive partial transpose (PPT), i.e., PPT entangled states, are usually considered to be too weakly entangled for applications. Since no pure entanglement can be distilled from them, they are also called bound entangled states. We provide strategies, using which multipartite quantum states that have a positive partial transpose with respect to all bi-partitions of the particles can still outperform separable states in linear interferometers.<\/jats:p>","DOI":"10.3390\/e23060685","type":"journal-article","created":{"date-parts":[[2021,5,28]],"date-time":"2021-05-28T11:33:20Z","timestamp":1622201600000},"page":"685","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Strategies for Positive Partial Transpose (PPT) States in Quantum Metrologies with Noise"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2601-7084","authenticated-orcid":false,"given":"Arunava","family":"Majumder","sequence":"first","affiliation":[{"name":"Indian Institute of Technology Kharagpur, Kharagpur 721302, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Harshank","family":"Shrotriya","sequence":"additional","affiliation":[{"name":"Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0879-0591","authenticated-orcid":false,"given":"Leong-Chuan","family":"Kwek","sequence":"additional","affiliation":[{"name":"Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore"},{"name":"MajuLab, CNRS-UNS-NUS-NTU International Joint Research Unit, Singapore UMI 3654, Singapore"},{"name":"National Institute of Education, Nanyang Technological University, Singapore 637616, Singapore"},{"name":"Quantum Science and Engineering Center, Nanyang Technological University, Singapore 637616, Singapore"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,5,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"010401","DOI":"10.1103\/PhysRevLett.96.010401","article-title":"Quantum metrology","volume":"96","author":"Giovannetti","year":"2006","journal-title":"Phys. Rev. Lett."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"024703","DOI":"10.1116\/5.0007577","article-title":"Photonic quantum metrology","volume":"2","author":"Polino","year":"2020","journal-title":"AVS Quantum Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"424006","DOI":"10.1088\/1751-8113\/47\/42\/424006","article-title":"Quantum metrology from a quantum information science perspective","volume":"47","author":"Apellaniz","year":"2014","journal-title":"J. Phys. A Math. Theor."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"032333","DOI":"10.1103\/PhysRevA.97.032333","article-title":"Noise-dependent optimal strategies for quantum metrology","volume":"97","author":"Huang","year":"2018","journal-title":"Phys. Rev. A"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"012101","DOI":"10.1103\/PhysRevA.94.012101","article-title":"Usefulness of entanglement-assisted quantum metrology","volume":"94","author":"Huang","year":"2016","journal-title":"Phys. Rev. A"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2099","DOI":"10.1080\/09500340008235132","article-title":"An application of two-photon entangled states to quantum metrology","volume":"47","author":"Brida","year":"2000","journal-title":"J. Mod. Opt."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"865","DOI":"10.1103\/RevModPhys.81.865","article-title":"Quantum entanglement","volume":"81","author":"Horodecki","year":"2009","journal-title":"Rev. Mod. Phys."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Zatelli, F., Benedetti, C., and Paris, M.G. (2020). Scattering as a quantum metrology problem: A quantum walk approach. Entropy, 22.","DOI":"10.3390\/e22111321"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1413","DOI":"10.1103\/PhysRevLett.77.1413","article-title":"Separability criterion for density matrices","volume":"77","author":"Peres","year":"1996","journal-title":"Phys. Rev. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0375-9601(01)00142-6","article-title":"Separability of n-particle mixed states: Necessary and sufficient conditions in terms of linear maps","volume":"283","author":"Horodecki","year":"2001","journal-title":"Phys. Lett. A"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1056","DOI":"10.1103\/PhysRevLett.82.1056","article-title":"Bound entanglement can be activated","volume":"82","author":"Horodecki","year":"1999","journal-title":"Phys. Rev. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"150501","DOI":"10.1103\/PhysRevLett.96.150501","article-title":"All bipartite entangled states are useful for information processing","volume":"96","author":"Masanes","year":"2006","journal-title":"Phys. Rev. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"020506","DOI":"10.1103\/PhysRevLett.120.020506","article-title":"Quantum states with a positive partial transpose are useful for metrology","volume":"120","year":"2018","journal-title":"Phys. Rev. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"020402","DOI":"10.1103\/PhysRevLett.125.020402","article-title":"Activating hidden metrological usefulness","volume":"125","author":"Horodecki","year":"2020","journal-title":"Phys. Rev. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"012304","DOI":"10.1103\/PhysRevA.99.012304","article-title":"Entanglement criterion for multipartite systems based on quantum Fisher information","volume":"99","author":"Azhdargalam","year":"2019","journal-title":"Phys. Rev. A"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"012310","DOI":"10.1103\/PhysRevA.100.012310","article-title":"Class of genuinely high-dimensionally-entangled states with a positive partial transpose","volume":"100","year":"2019","journal-title":"Phys. Rev. A"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"P\u00e1l, K.F., T\u00f3th, G., Bene, E., and V\u00e9rtesi, T. (2020). Bound entangled \u201csinglets\u201d for quantum metrology. arXiv.","DOI":"10.1103\/PhysRevResearch.3.023101"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Petz, D., and Ghinea, C. (2011). Introduction to quantum Fisher information. Quantum Probability and Related Topics, World Scientific.","DOI":"10.1142\/9789814338745_0015"},{"key":"ref_19","unstructured":"Helstrom, C.W., and Helstrom, C.W. (1976). Quantum Detection and Estimation Theory, Academic Press."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1090\/S0273-0979-1985-15378-9","article-title":"Probabilistic and statistical aspects of quantum theory","volume":"13","author":"Gudder","year":"1985","journal-title":"Bull. (New Ser.) Am. Math. Soc."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"032324","DOI":"10.1103\/PhysRevA.87.032324","article-title":"Extremal properties of the variance and the quantum Fisher information","volume":"87","author":"Petz","year":"2013","journal-title":"Phys. Rev. A"},{"key":"ref_22","unstructured":"Yu, S. (2013). Quantum Fisher information as the convex roof of variance. arXiv."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"022321","DOI":"10.1103\/PhysRevA.85.022321","article-title":"Fisher information and multiparticle entanglement","volume":"85","author":"Hyllus","year":"2012","journal-title":"Phys. Rev. A"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"022322","DOI":"10.1103\/PhysRevA.85.022322","article-title":"Multipartite entanglement and high-precision metrology","volume":"85","year":"2012","journal-title":"Phys. Rev. A"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"4674","DOI":"10.1109\/TIT.2018.2790423","article-title":"Quantum error-correcting codes for qudit amplitude damping","volume":"64","author":"Grassl","year":"2018","journal-title":"IEEE Trans. Inf. Theory"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/6\/685\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:10:07Z","timestamp":1760163007000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/6\/685"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,5,28]]},"references-count":25,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2021,6]]}},"alternative-id":["e23060685"],"URL":"https:\/\/doi.org\/10.3390\/e23060685","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2021,5,28]]}}}