{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,2]],"date-time":"2025-04-02T05:10:17Z","timestamp":1743570617613,"version":"3.40.3"},"publisher-location":"Cham","reference-count":32,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783031856990","type":"print"},{"value":"9783031857003","type":"electronic"}],"license":[{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025]]},"DOI":"10.1007\/978-3-031-85700-3_23","type":"book-chapter","created":{"date-parts":[[2025,4,2]],"date-time":"2025-04-02T04:57:28Z","timestamp":1743569848000},"page":"313-324","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Fredholm Determinants Approach to\u00a0the\u00a0Computations of\u00a0Quantum Entanglement"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8657-0829","authenticated-orcid":false,"given":"Roman","family":"Gielerak","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2119-3329","authenticated-orcid":false,"given":"Joanna","family":"Wi\u015bniewska","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8468-2456","authenticated-orcid":false,"given":"Marek","family":"Sawerwain","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,4,1]]},"reference":[{"key":"23_CR1","doi-asserted-by":"publisher","unstructured":"Barbieri, M., Diversi, R.: Recursive identification of noisy autoregressive models via a noise-compensated overdetermined instrumental variable method. Int. J. Appl. Math. Comput. Sci. 34(1), 65\u201379 (2024). https:\/\/doi.org\/10.61822\/amcs-2024-0005","DOI":"10.61822\/amcs-2024-0005"},{"key":"23_CR2","doi-asserted-by":"crossref","unstructured":"Bengtsson, I., \u017byczkowski, K.: Geometry of Quantum States: An Introduction to Quantum Entanglement, 2nd edn. Cambridge University Press, Cambridge (2017)","DOI":"10.1017\/9781139207010"},{"key":"23_CR3","doi-asserted-by":"crossref","unstructured":"Bott, R., Tu, L.W.: Differential Forms in Algebraic Topology. Graduate Texts in Mathematics, vol. 82. Springer (1982)","DOI":"10.1007\/978-1-4757-3951-0"},{"key":"23_CR4","doi-asserted-by":"publisher","unstructured":"Carlen, E.A., Lieb, E.H.: Minkowski type trace inequality and strong subadditivity of quantum entropy II: convexity and concavity. Lett. Math. Phys. 83, 107\u2013126 (2008). https:\/\/doi.org\/10.1007\/s11005-008-0223-1","DOI":"10.1007\/s11005-008-0223-1"},{"key":"23_CR5","doi-asserted-by":"publisher","unstructured":"Carlen, E.A., Cordero-Erausquin, D.: Subadditivity of the entropy and its relation to Brascamp-Lieb type inequalities. Geom. Funct. Anal. 19, 373\u2013405 (2009). https:\/\/doi.org\/10.1007\/s00039-009-0001-y","DOI":"10.1007\/s00039-009-0001-y"},{"key":"23_CR6","unstructured":"Dunford, N., Schwartz, J.T.: Linear Operators. Part II: Spectral Theory. Wiley (1963)"},{"key":"23_CR7","unstructured":"Fredholm, I.: Les \u00e9quations int\u00e9grales lin\u00e9aires. C. R. Congr\u00e9s des Math. tenu \u00e0 Stockholm (1909)"},{"key":"23_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1007\/978-3-030-77980-1_9","volume-title":"Computational Science \u2013 ICCS 2021","author":"R Gielerak","year":"2021","unstructured":"Gielerak, R., Sawerwain, M., Wi\u015bniewska, J., Wr\u00f3blewski, M.: EntDetector: entanglement detecting toolbox for bipartite quantum states. In: Paszynski, M., Kranzlm\u00fcller, D., Krzhizhanovskaya, V.V., Dongarra, J.J., Sloot, P.M.A. (eds.) ICCS 2021. LNCS, vol. 12747, pp. 113\u2013126. Springer, Cham (2021). https:\/\/doi.org\/10.1007\/978-3-030-77980-1_9"},{"key":"23_CR9","doi-asserted-by":"publisher","unstructured":"Gielerak, R.: Renormalized Von Neumann entropy with application to entanglement in genuine infinite dimensional systems. Quantum Inf. Process 22, 311 (2023). https:\/\/doi.org\/10.1007\/s11128-023-04059-1","DOI":"10.1007\/s11128-023-04059-1"},{"key":"23_CR10","unstructured":"Gielerak, R., Sawerwain, M.: Renormalized Fredholm determinants and their use in Continuous Variables Quantum Information Theory. In preparations"},{"key":"23_CR11","doi-asserted-by":"publisher","first-page":"319","DOI":"10.24033\/bsmf.1476","volume":"84","author":"A Grothendiek","year":"1956","unstructured":"Grothendiek, A.: La theorie de Fredholm. Bull. Soc. Math. France 84, 319\u2013384 (1956)","journal-title":"Bull. Soc. Math. France"},{"key":"23_CR12","unstructured":"Gielerak, R., Sawerwain, M., Wi\u015bniewska, J.: Source code repository. https:\/\/github.com\/qMSUZ\/EntDetector. Accessed 30 Oct 2024"},{"key":"23_CR13","doi-asserted-by":"crossref","unstructured":"Gielerak, R., W\u015bniewska, J., Sawerwain, M.: The Infinite-Dimensional Quantum Entropy: the Unified Entropy Case. arXiv:2406.17133 (2024)","DOI":"10.3390\/e26121070"},{"key":"23_CR14","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-8401-3","volume-title":"Traces and determinants of linear operators","author":"I Gohberg","year":"2000","unstructured":"Gohberg, I., Goldberg, S., Krupnik, N.: Traces and determinants of linear operators. Birkh\u00e4user Verlag, Basel (2000)"},{"key":"23_CR15","unstructured":"Hilbert, D.: Grundzuge einer allgemeinen Theorie der linearen Integralgleichungen (Erste Mitteilung). Nachr. Ges. Wiss. G\u00f6ttingen 49\u201391 (1904)"},{"issue":"2","key":"23_CR16","doi-asserted-by":"publisher","DOI":"10.1063\/1.2165794","volume":"47","author":"X Hu","year":"2006","unstructured":"Hu, X., Ye, Z.: Generalized quantum entropy. J. Math. Phys. 47(2), 023502 (2006). https:\/\/doi.org\/10.1063\/1.2165794","journal-title":"J. Math. Phys."},{"key":"23_CR17","doi-asserted-by":"publisher","unstructured":"Jeczmionek, E., Kowalski, P.A.: Choice of the p-norm for high level classification features pruning in modern convolutional neural networks with local sensitivity analysis. Int. J. Appl. Math. Comput. Sci. 33(4), 663\u2013672 (2023). https:\/\/doi.org\/10.34768\/amcs-2023-0047","DOI":"10.34768\/amcs-2023-0047"},{"key":"23_CR18","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1016\/0001-8708(73)90011-X","volume":"67","author":"EH Lieb","year":"1973","unstructured":"Lieb, E.H.: Convex trace functions and the Wigner-Yanase-Dyson conjecture. Adv. Math. 67, 267\u2013288 (1973)","journal-title":"Adv. Math."},{"key":"23_CR19","doi-asserted-by":"publisher","first-page":"1938","DOI":"10.1063\/1.1666274","volume":"14","author":"EH Lieb","year":"1973","unstructured":"Lieb, E.H., Ruskai, M.B.: Proof of the strong subadditivity of quantum-mechanical entropy. J. Math. Phys. 14, 1938\u20131941 (1973)","journal-title":"J. Math. Phys."},{"key":"23_CR20","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1090\/S0002-9904-1975-13621-4","volume":"81","author":"EH Lieb","year":"1975","unstructured":"Lieb, E.H.: Some convexity and subadditivity properties of entropy. Bull. Amer. Math. Soc. 81, 1\u201313 (1975)","journal-title":"Bull. Amer. Math. Soc."},{"key":"23_CR21","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-61409-5","volume-title":"Mathematische Grundlagen der Quantenmechanik","author":"J von Neumann","year":"1996","unstructured":"von Neumann, J.: Mathematische Grundlagen der Quantenmechanik. Springer, Heidelberg (1996)"},{"key":"23_CR22","unstructured":"von Neumann, J.: Mathematical Foundations of Quantum Mechanics. Princeton University Press (1955)"},{"key":"23_CR23","doi-asserted-by":"publisher","unstructured":"Nielsen, M.A., Chuang, I.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, The Edinburgh Building, Cambridge (2010). https:\/\/doi.org\/10.1017\/CBO9780511976667","DOI":"10.1017\/CBO9780511976667"},{"key":"23_CR24","unstructured":"Nielsen, M.A.: An introduction of majorization and its applications to quantum mechanics. Lecture Notes, Department of Physics, University of Queensland, Australia (2002). http:\/\/michaelnielsen.org\/blog\/talks\/2002\/maj\/book.ps"},{"key":"23_CR25","volume-title":"Quantum Information Theory and Quantum Statistics","author":"D Petz","year":"2008","unstructured":"Petz, D.: Quantum Information Theory and Quantum Statistics. Springer, Berlin (2008)"},{"key":"23_CR26","unstructured":"Plenio, B.M., Virnami, S.: An introduction to entanglement measures. arXiv:quant-ph\/0504.4163v3 (2006)"},{"key":"23_CR27","unstructured":"Reed, M., Simon, B.: Methods of modern mathematical physics I: Functional analysis. Academic Press (1980)"},{"key":"23_CR28","unstructured":"Reed, M., Simon, B.: Methods of modern mathematical physics IV: Analysis of operators. Academic Press (1978)"},{"key":"23_CR29","doi-asserted-by":"crossref","unstructured":"Ruskai, M.B.: Inequalities for quantum entropy: a review with conditions for equality. J. Math. Phys. 43, 4358\u20134375 (2002). Erratum ibid 46, pp. 019901","DOI":"10.1063\/1.1497701"},{"key":"23_CR30","doi-asserted-by":"publisher","first-page":"244","DOI":"10.1016\/S0001-8708(77)80044-3","volume":"24","author":"B Simon","year":"1977","unstructured":"Simon, B.: Notes on infinite determinants of Hilbert space operators. Adv. Math. 24, 244\u2013273 (1977)","journal-title":"Adv. Math."},{"key":"23_CR31","unstructured":"Simon, B.: Trace ideals and their applications. Mathematical Surveys and Monographs, 2nd edn, vol. 120. AMS (2005)"},{"issue":"8","key":"23_CR32","doi-asserted-by":"publisher","first-page":"4277","DOI":"10.1103\/PhysRevA.40.4277","volume":"40","author":"RF Werner","year":"1989","unstructured":"Werner, R.F.: Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model. Phys. Rev. A 40(8), 4277\u20134281 (1989)","journal-title":"Phys. Rev. A"}],"container-title":["Lecture Notes in Computer Science","Parallel Processing and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-85700-3_23","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,2]],"date-time":"2025-04-02T04:57:44Z","timestamp":1743569864000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-85700-3_23"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"ISBN":["9783031856990","9783031857003"],"references-count":32,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-85700-3_23","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025]]},"assertion":[{"value":"1 April 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"All authors declare that they have no conflicts of interest.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Disclosure of Interests"}},{"value":"PPAM","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Parallel Processing and Applied Mathematics","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Ostrava","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Czech Republic","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2024","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"9 September 2024","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"12 September 2024","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"15","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"ppam2024","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/ppam.edu.pl\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}