Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W2004981493', 'doi': 'https://doi.org/10.1007/s11232-011-0080-4', 'title': 'Probability representation of spin states and inequalities for unitary matrices', 'display_name': 'Probability representation of spin states and inequalities for unitary matrices', 'publication_year': 2011, 'publication_date': '2011-07-01', 'ids': {'openalex': 'https://openalex.org/W2004981493', 'doi': 'https://doi.org/10.1007/s11232-011-0080-4', 'mag': '2004981493'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://doi.org/10.1007/s11232-011-0080-4', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S135066301', 'display_name': 'Theoretical and Mathematical Physics', 'issn_l': '0040-5779', 'issn': ['0040-5779', '1573-9333'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320267', 'host_organization_name': 'Pleiades Publishing', 'host_organization_lineage': ['https://openalex.org/P4310320267', 'https://openalex.org/P4310319965'], 'host_organization_lineage_names': ['Pleiades Publishing', 'Springer Nature'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['crossref'], 'open_access': {'is_oa': False, 'oa_status': 'closed', 'oa_url': None, 'any_repository_has_fulltext': False}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5065193506', 'display_name': 'Margarita A. Man’ko', 'orcid': 'https://orcid.org/0000-0003-1282-4560'}, 'institutions': [{'id': 'https://openalex.org/I118517470', 'display_name': 'P.N. Lebedev Physical Institute of the Russian Academy of Sciences', 'ror': 'https://ror.org/01jkd3546', 'country_code': 'RU', 'type': 'facility', 'lineage': ['https://openalex.org/I118517470', 'https://openalex.org/I1313323035', 'https://openalex.org/I2800498218', 'https://openalex.org/I4210096333']}], 'countries': ['RU'], 'is_corresponding': True, 'raw_author_name': 'M. A. Man’ko', 'raw_affiliation_strings': ['Lebedev Physical Institute, RAS, Moscow, Russia'], 'affiliations': [{'raw_affiliation_string': 'Lebedev Physical Institute, RAS, Moscow, Russia', 'institution_ids': ['https://openalex.org/I118517470']}]}], 'countries_distinct_count': 1, 'institutions_distinct_count': 1, 'corresponding_author_ids': ['https://openalex.org/A5065193506'], 'corresponding_institution_ids': ['https://openalex.org/I118517470'], 'apc_list': None, 'apc_paid': None, 'fwci': 0.688, 'has_fulltext': True, 'fulltext_origin': 'ngrams', 'cited_by_count': 6, 'citation_normalized_percentile': {'value': 0.557467, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 82, 'max': 83}, 'biblio': {'volume': '168', 'issue': '1', 'first_page': '985', 'last_page': '993'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T10622', 'display_name': 'Foundations of Quantum Mechanics and Interpretations', 'score': 0.9999, 'subfield': {'id': 'https://openalex.org/subfields/3107', 'display_name': 'Atomic and Molecular Physics, and Optics'}, 'field': {'id': 'https://openalex.org/fields/31', 'display_name': 'Physics and Astronomy'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, 'topics': [{'id': 'https://openalex.org/T10622', 'display_name': 'Foundations of Quantum Mechanics and Interpretations', 'score': 0.9999, 'subfield': {'id': 'https://openalex.org/subfields/3107', 'display_name': 'Atomic and Molecular Physics, and Optics'}, 'field': {'id': 'https://openalex.org/fields/31', 'display_name': 'Physics and Astronomy'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T10020', 'display_name': 'Quantum Information and Computation', 'score': 0.9986, 'subfield': {'id': 'https://openalex.org/subfields/1702', 'display_name': 'Artificial Intelligence'}, 'field': {'id': 'https://openalex.org/fields/17', 'display_name': 'Computer Science'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T12261', 'display_name': 'Statistical Mechanics with Long-Range Interactions and Nonextensivity', 'score': 0.9868, 'subfield': {'id': 'https://openalex.org/subfields/3109', 'display_name': 'Statistical and Nonlinear Physics'}, 'field': {'id': 'https://openalex.org/fields/31', 'display_name': 'Physics and Astronomy'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}], 'keywords': [{'id': 'https://openalex.org/keywords/unitary-representation', 'display_name': 'Unitary representation', 'score': 0.7200606}, {'id': 'https://openalex.org/keywords/representation', 'display_name': 'Representation (politics)', 'score': 0.50530463}, {'id': 'https://openalex.org/keywords/circular-ensemble', 'display_name': 'Circular ensemble', 'score': 0.4796867}, {'id': 'https://openalex.org/keywords/unitary-group', 'display_name': 'Unitary group', 'score': 0.47821066}, {'id': 'https://openalex.org/keywords/generalized-entropies', 'display_name': 'Generalized Entropies', 'score': 0.470001}], 'concepts': [{'id': 'https://openalex.org/C67820243', 'wikidata': 'https://www.wikidata.org/wiki/Q179164', 'display_name': 'Unitary state', 'level': 2, 'score': 0.8652997}, {'id': 'https://openalex.org/C2776122010', 'wikidata': 'https://www.wikidata.org/wiki/Q10359539', 'display_name': 'Unitary representation', 'level': 3, 'score': 0.7200606}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.5811926}, {'id': 'https://openalex.org/C96214315', 'wikidata': 'https://www.wikidata.org/wiki/Q727103', 'display_name': 'Unitary matrix', 'level': 3, 'score': 0.522413}, {'id': 'https://openalex.org/C2781311116', 'wikidata': 'https://www.wikidata.org/wiki/Q83306', 'display_name': 'Group (periodic table)', 'level': 2, 'score': 0.5184059}, {'id': 'https://openalex.org/C2776359362', 'wikidata': 'https://www.wikidata.org/wiki/Q2145286', 'display_name': 'Representation (politics)', 'level': 3, 'score': 0.50530463}, {'id': 'https://openalex.org/C42704618', 'wikidata': 'https://www.wikidata.org/wiki/Q910917', 'display_name': 'Spin (aerodynamics)', 'level': 2, 'score': 0.49881458}, {'id': 'https://openalex.org/C45555294', 'wikidata': 'https://www.wikidata.org/wiki/Q28113351', 'display_name': 'Inequality', 'level': 2, 'score': 0.47968885}, {'id': 'https://openalex.org/C11902944', 'wikidata': 'https://www.wikidata.org/wiki/Q5121662', 'display_name': 'Circular ensemble', 'level': 4, 'score': 0.4796867}, {'id': 'https://openalex.org/C99072794', 'wikidata': 'https://www.wikidata.org/wiki/Q1500617', 'display_name': 'Unitary group', 'level': 3, 'score': 0.47821066}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.41614494}, {'id': 'https://openalex.org/C62520636', 'wikidata': 'https://www.wikidata.org/wiki/Q944', 'display_name': 'Quantum mechanics', 'level': 1, 'score': 0.32894486}, {'id': 'https://openalex.org/C136119220', 'wikidata': 'https://www.wikidata.org/wiki/Q1000660', 'display_name': 'Algebra over a field', 'level': 2, 'score': 0.3218993}, {'id': 'https://openalex.org/C121332964', 'wikidata': 'https://www.wikidata.org/wiki/Q413', 'display_name': 'Physics', 'level': 0, 'score': 0.28980982}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.14927325}, {'id': 'https://openalex.org/C187915474', 'wikidata': 'https://www.wikidata.org/wiki/Q622679', 'display_name': 'Lie group', 'level': 2, 'score': 0.091958016}, {'id': 'https://openalex.org/C199539241', 'wikidata': 'https://www.wikidata.org/wiki/Q7748', 'display_name': 'Law', 'level': 1, 'score': 0.07287443}, {'id': 'https://openalex.org/C94625758', 'wikidata': 'https://www.wikidata.org/wiki/Q7163', 'display_name': 'Politics', 'level': 2, 'score': 0.0}, {'id': 'https://openalex.org/C17744445', 'wikidata': 'https://www.wikidata.org/wiki/Q36442', 'display_name': 'Political science', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C97355855', 'wikidata': 'https://www.wikidata.org/wiki/Q11473', 'display_name': 'Thermodynamics', 'level': 1, 'score': 0.0}], 'mesh': [], 'locations_count': 1, 'locations': [{'is_oa': False, 'landing_page_url': 'https://doi.org/10.1007/s11232-011-0080-4', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S135066301', 'display_name': 'Theoretical and Mathematical Physics', 'issn_l': '0040-5779', 'issn': ['0040-5779', '1573-9333'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320267', 'host_organization_name': 'Pleiades Publishing', 'host_organization_lineage': ['https://openalex.org/P4310320267', 'https://openalex.org/P4310319965'], 'host_organization_lineage_names': ['Pleiades Publishing', 'Springer Nature'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}], 'best_oa_location': None, 'sustainable_development_goals': [{'score': 0.67, 'id': 'https://metadata.un.org/sdg/10', 'display_name': 'Reduced inequalities'}], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 26, 'referenced_works': ['https://openalex.org/W1970213764', 'https://openalex.org/W1979001571', 'https://openalex.org/W1989288976', 'https://openalex.org/W1995875735', 'https://openalex.org/W2006638080', 'https://openalex.org/W2010199445', 'https://openalex.org/W2025842401', 'https://openalex.org/W2028815089', 'https://openalex.org/W2029692747', 'https://openalex.org/W2038389955', 'https://openalex.org/W2040794877', 'https://openalex.org/W2041015810', 'https://openalex.org/W2048880604', 'https://openalex.org/W2050594797', 'https://openalex.org/W2052876372', 'https://openalex.org/W2059108078', 'https://openalex.org/W2085255879', 'https://openalex.org/W2112236514', 'https://openalex.org/W2125991572', 'https://openalex.org/W2170942924', 'https://openalex.org/W2374631013', 'https://openalex.org/W2578414960', 'https://openalex.org/W2969734899', 'https://openalex.org/W3037786024', 'https://openalex.org/W3105530000', 'https://openalex.org/W3165898261'], 'related_works': ['https://openalex.org/W4293832529', 'https://openalex.org/W4292706183', 'https://openalex.org/W2499716529', 'https://openalex.org/W2064597394', 'https://openalex.org/W2048668967', 'https://openalex.org/W2044176161', 'https://openalex.org/W2023081713', 'https://openalex.org/W2019516429', 'https://openalex.org/W2010357651', 'https://openalex.org/W1482282520'], 'abstract_inverted_index': None, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2004981493', 'counts_by_year': [{'year': 2019, 'cited_by_count': 1}, {'year': 2017, 'cited_by_count': 1}, {'year': 2013, 'cited_by_count': 3}, {'year': 2012, 'cited_by_count': 1}], 'updated_date': '2024-08-15T05:23:22.774851', 'created_date': '2016-06-24'}