{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:52:45Z","timestamp":1760241165580,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2019,12,19]],"date-time":"2019-12-19T00:00:00Z","timestamp":1576713600000},"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>Geometry is often a valuable guide to complex problems in physics. In this paper, we introduce a novel geometric quantity called quantum reactivity (QR) to probe quantum correlations in higher-dimensional quantum systems. Much like quantum discord, QR is not a measure of quantum entanglement but can be useful in quantum information processes where a notion of quantum correlation in higher dimensions is needed. Both quantum discord and QR are extendable to an arbitrarily large number of qubits; however, unlike discord, QR satisfies the invariance under unitary operations. Our approach parallels Schumacher\u2019s singlet state triangle inequality, which used an information geometry-based entropic distance. We use a generalization of information distance to area, volume, and higher-dimensional volumes and then use these to define a quantity that we call QR, which is the familiar ratio of surface area to volume. We examine a spectrum of multipartite states (Werner, W, GHZ, randomly generated density matrices, etc.) and demonstrate that QR can provide an ordering of these quantum states as to their degree of quantum correlation.<\/jats:p>","DOI":"10.3390\/e22010006","type":"journal-article","created":{"date-parts":[[2019,12,20]],"date-time":"2019-12-20T09:50:33Z","timestamp":1576835433000},"page":"6","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Quantum Reactivity: An Indicator of Quantum Correlation"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5772-3937","authenticated-orcid":false,"given":"Shahabeddin M.","family":"Aslmarand","sequence":"first","affiliation":[{"name":"Department of Physics, Florida Atlantic University, Boca Raton, FL 33431, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5883-3596","authenticated-orcid":false,"given":"Warner A.","family":"Miller","sequence":"additional","affiliation":[{"name":"Department of Physics, Florida Atlantic University, Boca Raton, FL 33431, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Verinder S.","family":"Rana","sequence":"additional","affiliation":[{"name":"Naval Information Warfare Center Pacific (NIWC PAC), San Diego, CA 92152, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Paul M.","family":"Alsing","sequence":"additional","affiliation":[{"name":"Information Directorate, Air Force Research Laboratory, Rome, NY 13441, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,12,19]]},"reference":[{"key":"ref_1","unstructured":"Preskill, J. (2011, January 19\u201325). Quantum computing and the entanglement frontier. Proceedings of the 25th Solvay Conference on Physics (\u201cThe Theory of the Quantum World\u201d), Brussels, Belgium."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1070","DOI":"10.1103\/PhysRevA.59.1070","article-title":"Quantum nonlocality without entanglement","volume":"A59","author":"Bennett","year":"1999","journal-title":"Phys. Rev."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"042105","DOI":"10.1103\/PhysRevA.81.042105","article-title":"Erratum: Quantum discord for two-qubit X states","volume":"A81","author":"Ali","year":"2010","journal-title":"Phys. Rev."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1141","DOI":"10.1007\/s10701-010-9452-0","article-title":"The elusive source of quantum speedup","volume":"40","author":"Vedral","year":"2010","journal-title":"Found. Phys."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2011","DOI":"10.1098\/rspa.2002.1097","article-title":"On the role of entanglement in quantum-computational speed-up","volume":"459","author":"Jozsa","year":"2003","journal-title":"Proc. Math. Phys. Eng. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"062307","DOI":"10.1103\/PhysRevA.71.062307","article-title":"Local versus nonlocal information in quantum-information theory: Formalism and phenomena","volume":"A71","author":"Horodecki","year":"2005","journal-title":"Phys. Rev."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"052103","DOI":"10.1103\/PhysRevA.74.052103","article-title":"Multipartite nonlocality without entanglement in many dimensions","volume":"A74","author":"Niset","year":"2006","journal-title":"Phys. Rev."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"200501","DOI":"10.1103\/PhysRevLett.101.200501","article-title":"Experimental quantum computing without entanglement","volume":"101","author":"Lanyon","year":"2008","journal-title":"Phys. Rev. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1103\/PhysRevLett.67.661","article-title":"Quantum cryptography based on Bell\u2019s theorem","volume":"67","author":"Ekert","year":"1991","journal-title":"Phys. Rev. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1895","DOI":"10.1103\/PhysRevLett.70.1895","article-title":"Teleporting an unknown quantum state via dual classical and Einstein\u2013Podolsky\u2013Rosen channels","volume":"70","author":"Bennett","year":"1993","journal-title":"Phys. Rev. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1201","DOI":"10.1103\/PhysRevA.56.1201","article-title":"Substituting quantum entanglement for communication","volume":"A56","author":"Cleve","year":"1997","journal-title":"Phys. Rev."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"4452","DOI":"10.1103\/PhysRevA.56.4452","article-title":"Statistical inference, distinguishability of quantum states, and quantum entanglement","volume":"A56","author":"Vedral","year":"1997","journal-title":"Phys. Rev."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"017901","DOI":"10.1103\/PhysRevLett.88.017901","article-title":"Quantum Discord: A Measure of the Quantumness of Correlations","volume":"88","author":"Ollivier","year":"2001","journal-title":"Phys. Rev. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"042109","DOI":"10.1103\/PhysRevA.84.042109","article-title":"Global quantum discord in multipartite systems","volume":"84","author":"Rulli","year":"2011","journal-title":"Phys. Rev. A"},{"key":"ref_15","unstructured":"Nielson, M.A., and Chuang, I.L. (2000). Quantum Computation and Quantum Information, Cambridge University Press."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Vedral, V. (2017). Foundations of Quantum Discord. arXiv.","DOI":"10.1007\/978-3-319-53412-1_1"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"7047","DOI":"10.1103\/PhysRevA.44.7047","article-title":"Information and quantum nonseparability","volume":"A44","author":"Schumacher","year":"1991","journal-title":"Phys. Rev."},{"key":"ref_18","first-page":"152","article-title":"Lecture on the entropy theory of measure-preserving transformations","volume":"22","author":"Roklin","year":"1967","journal-title":"Russ. Math. Surv."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1016\/S0019-9958(61)80055-7","article-title":"A metric space of discrete probability distributions","volume":"4","author":"Rajski","year":"1961","journal-title":"Inf. Control"},{"key":"ref_20","first-page":"16","article-title":"Quantum Information Geometry in the Space of Measurements","volume":"10660","author":"Miller","year":"2018","journal-title":"Proc. SPIE"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"395","DOI":"10.4310\/AMSA.2019.v4.n2.a5","article-title":"Geometric measures of information for quantum state characterization","volume":"4","author":"Aslmarand","year":"2019","journal-title":"Ann. Math. Sci. Appl."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Aslmarand, S.M., Miller, W.A., Razaei, T., Alsing, P.M., and Rana, V.S. (2019). Properties of Quantum Reactivity for a Multipartite State. Quantum Information Science, Sensing, and Computation XI, International Society for Optics and Photonics.","DOI":"10.1117\/12.2524224"},{"key":"ref_23","first-page":"1345","article-title":"Quantum Theory, and Conceptions of the Universe","volume":"82","author":"Greenberger","year":"1999","journal-title":"Phys. Rev. Lett."},{"key":"ref_24","unstructured":"Kobayashi, S., Ezawa, H., Murayama, Y., and Nomura, S. (1989, January 28\u201331). Information, physics, quantum: The search for links. Proceedings of the 3rd International Symposium Foundations of Quantum Mechanics, Tokyo, Japan."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1038\/341119a0","article-title":"Thermodynamic cost of computation, algorithmic complexity and the information metric","volume":"341","author":"Zurek","year":"1989","journal-title":"Nature"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Shannon, C.E. (1948). A Mathematical Theory of Communication, Wiley Online Library.","DOI":"10.1002\/j.1538-7305.1948.tb00917.x"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"De Oliveira, T.R. (2017). Quantum Correlations in Multipartite Quantum Systems. Lectures on General Quantum Correlations and their Applications, Springer.","DOI":"10.1007\/978-3-319-53412-1_5"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"4277","DOI":"10.1103\/PhysRevA.40.4277","article-title":"Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model","volume":"A40","author":"Werner","year":"1989","journal-title":"Phys. Rev."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"5022","DOI":"10.1103\/PhysRevLett.78.5022","article-title":"Entanglement of a Pair of Quantum Bits","volume":"78","author":"Hill","year":"1997","journal-title":"Phys. Rev. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"062314","DOI":"10.1103\/PhysRevA.62.062314","article-title":"Three qubits can be entangled in two inequivalent ways","volume":"62","author":"Vidal","year":"2000","journal-title":"Phys. Rev. A"},{"key":"ref_31","first-page":"35","article-title":"Statistical properties of random density matrices","volume":"A37","author":"Sommers","year":"2004","journal-title":"J. Phys."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/1\/6\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:43:36Z","timestamp":1760190216000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/1\/6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,12,19]]},"references-count":31,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,1]]}},"alternative-id":["e22010006"],"URL":"https:\/\/doi.org\/10.3390\/e22010006","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2019,12,19]]}}}