A mathematical theory of resources
Many fields of science investigate states and processes as resources. Chemistry, thermodynamics, Shannon's theory of communication channels, and the theory of quantum entanglement are prominent examples. Questions addressed by these theories include: Which resources can be converted into which...
Uložené v:
| Vydané v: | Information and computation Ročník 250; s. 59 - 86 |
|---|---|
| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Elsevier Inc
01.10.2016
|
| ISSN: | 0890-5401, 1090-2651 |
| On-line prístup: | Získať plný text |
| Tagy: |
Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
|
| Abstract | Many fields of science investigate states and processes as resources. Chemistry, thermodynamics, Shannon's theory of communication channels, and the theory of quantum entanglement are prominent examples. Questions addressed by these theories include: Which resources can be converted into which others? At what rate can many copies of one resource be converted into many copies of another? Can a catalyst enable a conversion? How to quantify a resource? We propose a general mathematical definition of resource theory. We prove general theorems about how resource theories can be constructed from theories of processes with a subclass of processes that are freely implementable. These define the means by which costly states and processes can be interconverted. We outline how various existing resource theories fit into our framework, which is a first step in a project of identifying universal features and principles of resource theories. We develop a few general results concerning resource convertibility. |
|---|---|
| AbstractList | Many fields of science investigate states and processes as resources. Chemistry, thermodynamics, Shannon's theory of communication channels, and the theory of quantum entanglement are prominent examples. Questions addressed by these theories include: Which resources can be converted into which others? At what rate can many copies of one resource be converted into many copies of another? Can a catalyst enable a conversion? How to quantify a resource? We propose a general mathematical definition of resource theory. We prove general theorems about how resource theories can be constructed from theories of processes with a subclass of processes that are freely implementable. These define the means by which costly states and processes can be interconverted. We outline how various existing resource theories fit into our framework, which is a first step in a project of identifying universal features and principles of resource theories. We develop a few general results concerning resource convertibility. |
| Author | Spekkens, Robert W. Fritz, Tobias Coecke, Bob |
| Author_xml | – sequence: 1 givenname: Bob surname: Coecke fullname: Coecke, Bob email: Bob.Coecke@cs.ox.ac.uk organization: University of Oxford, Department of Computer Science, United Kingdom – sequence: 2 givenname: Tobias surname: Fritz fullname: Fritz, Tobias email: tfritz@perimeterinstitute.ca organization: Perimeter Institute for Theoretical Physics, Canada – sequence: 3 givenname: Robert W. surname: Spekkens fullname: Spekkens, Robert W. email: rspekkens@perimeterinstitute.ca organization: Perimeter Institute for Theoretical Physics, Canada |
| BookMark | eNp9j01LAzEQhoNUsK3ePS7ed53ZTcLGWyl-QcFL7yE7O8GUdleSVei_N6WeBL3MvPDyDPMsxGwYBxbiFqFCQH2_qwJVdU4V1BVAeyHmCAbKWiuciTm0OSsJeCUWKe0AEJXUc3G3Kg5ueuc8Arl9keMYj8Xoi8hp_IzE6VpcerdPfPOzl2L79Lhdv5Sbt-fX9WpTUtPoqWxYOkddi2iMbKgF1TquUXUq12y8UrU2nW_RgWx6zdQbMBJ77yUhQ7MU-nyW4phSZG8pTPmrcZiiC3uLYE-idmcD2ZOohdpm0QzCL_AjhoOLx_-QhzPC2ecrcLSJAg_EfYhMk-3H8Df8DTFPauc |
| CitedBy_id | crossref_primary_10_1088_1402_4896_ad977c crossref_primary_10_1088_1742_6596_2038_1_012008 crossref_primary_10_1007_s13538_022_01191_8 crossref_primary_10_1088_1751_8113_49_47_473001 crossref_primary_10_32408_compositionality_5_7 crossref_primary_10_1007_s10955_019_02344_x crossref_primary_10_1140_epjd_e2019_90693_y crossref_primary_10_3390_e25040574 crossref_primary_10_1007_s11467_018_0804_0 crossref_primary_10_1038_s41534_021_00402_5 crossref_primary_10_1007_s11128_019_2304_8 crossref_primary_10_1088_1367_2630_ad7f7c crossref_primary_10_1088_1751_8121_aa9100 crossref_primary_10_3390_e23060755 crossref_primary_10_1038_s41534_021_00444_9 crossref_primary_10_1016_S0034_4877_23_00081_2 crossref_primary_10_1103_PhysRevResearch_2_023039 crossref_primary_10_1088_1751_8121_aaa62f crossref_primary_10_1098_rsta_2023_0008 crossref_primary_10_1007_s11128_019_2284_8 crossref_primary_10_1007_s10773_022_05027_8 crossref_primary_10_3390_e24010074 crossref_primary_10_1038_s41598_020_79318_7 crossref_primary_10_1088_1367_2630_ab5020 crossref_primary_10_1103_PhysRevX_8_021011 crossref_primary_10_3389_fpsyg_2024_1361580 crossref_primary_10_1038_s42005_024_01649_y crossref_primary_10_1088_1751_8121_acec20 crossref_primary_10_1007_s11128_021_03251_5 crossref_primary_10_1007_s11128_019_2186_9 crossref_primary_10_1103_PhysRevA_104_052208 crossref_primary_10_1088_1751_8121_abafe5 crossref_primary_10_1103_PhysRevResearch_2_023400 crossref_primary_10_1007_s10676_017_9424_6 crossref_primary_10_1088_1367_2630_aa91c7 crossref_primary_10_1145_3594735 crossref_primary_10_1088_1751_8121_adf307 crossref_primary_10_1103_PhysRevX_8_041038 crossref_primary_10_1145_3326938_3326940 crossref_primary_10_1088_2058_9565_acb56a crossref_primary_10_1088_1367_2630_ada4d2 crossref_primary_10_3390_e27010029 crossref_primary_10_1103_PhysRevA_111_062407 crossref_primary_10_1007_s10701_018_0188_6 crossref_primary_10_1007_s11128_025_04866_8 crossref_primary_10_1088_1751_8121_ab8674 crossref_primary_10_1103_PhysRevResearch_2_023298 crossref_primary_10_1088_1367_2630_ab8ef7 crossref_primary_10_3390_e21030260 crossref_primary_10_1088_1367_2630_ad0d38 crossref_primary_10_1103_PhysRevA_111_L040402 crossref_primary_10_1088_1612_202X_abae02 crossref_primary_10_1038_s41467_019_13846_3 crossref_primary_10_1103_PhysRevResearch_2_012035 crossref_primary_10_1088_1612_202X_acf664 crossref_primary_10_1103_PhysRevX_8_041007 crossref_primary_10_1103_PhysRevX_9_031053 crossref_primary_10_1088_1751_8121_aabe9c crossref_primary_10_1103_PhysRevResearch_1_033174 crossref_primary_10_1016_j_physleta_2024_130106 crossref_primary_10_1007_s42979_023_02232_y crossref_primary_10_1134_S106456242370151X crossref_primary_10_3390_math7060543 crossref_primary_10_1007_s00220_022_04523_6 crossref_primary_10_1088_1751_8121_abb040 crossref_primary_10_1109_TIT_2021_3079938 crossref_primary_10_1007_s10699_020_09650_8 crossref_primary_10_1088_1751_8121_ad0bcc crossref_primary_10_1103_PhysRevX_8_021033 crossref_primary_10_1088_2399_6528_ac70a7 crossref_primary_10_1103_PRXQuantum_3_040323 crossref_primary_10_1109_TIT_2021_3070120 crossref_primary_10_1088_1751_8121_aacb4a crossref_primary_10_1016_j_pquantelec_2022_100395 crossref_primary_10_1007_s11128_020_02848_6 crossref_primary_10_1088_1367_2630_18_11_113028 crossref_primary_10_1007_s11128_023_04186_9 crossref_primary_10_1103_PhysRevA_111_012405 crossref_primary_10_1038_s41467_019_10572_8 crossref_primary_10_1088_1367_2630_aac484 crossref_primary_10_1007_s10701_020_00352_6 crossref_primary_10_1016_j_jlamp_2023_100942 crossref_primary_10_1088_1751_8121_abed67 crossref_primary_10_1007_s00023_023_01313_1 crossref_primary_10_1103_PRXQuantum_5_010340 crossref_primary_10_1103_PhysRevX_11_021014 crossref_primary_10_1088_1751_8121_ac99b0 crossref_primary_10_1007_s11128_020_02826_y crossref_primary_10_1088_1367_2630_ac7346 crossref_primary_10_1103_PRXQuantum_2_020318 |
| Cites_doi | 10.1016/0304-3975(87)90045-4 10.1103/PhysRevA.80.012307 10.1103/RevModPhys.81.865 10.1103/PhysRevLett.111.250404 10.1088/1367-2630/15/3/033001 10.1103/PhysRevA.53.2046 10.1038/ncomms4821 10.2307/1968871 10.1023/A:1026422630734 10.1016/0001-8708(91)90003-P 10.1103/PhysRevA.90.014102 10.3390/e13111945 10.1090/conm/092/1003201 10.1002/j.1538-7305.1948.tb00917.x 10.1038/ncomms3059 10.1088/1367-2630/10/3/033023 10.1080/00107510903257624 10.1103/PhysRevA.67.062104 10.1103/PhysRevLett.101.060401 10.1103/PhysRevA.84.012311 10.1109/TIT.2008.928980 10.1103/PhysRevLett.89.240403 10.1038/ncomms5185 10.1088/1367-2630/15/1/013057 10.1016/j.tcs.2006.08.002 10.1103/PhysRevLett.83.436 10.1007/BF01421922 |
| ContentType | Journal Article |
| Copyright | 2016 Elsevier Inc. |
| Copyright_xml | – notice: 2016 Elsevier Inc. |
| DBID | AAYXX CITATION |
| DOI | 10.1016/j.ic.2016.02.008 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Computer Science |
| EISSN | 1090-2651 |
| EndPage | 86 |
| ExternalDocumentID | 10_1016_j_ic_2016_02_008 S0890540116000353 |
| GroupedDBID | --K --M --Z -~X .~1 0R~ 1B1 1~. 1~5 29I 4.4 457 4G. 5GY 5VS 6I. 6TJ 7-5 71M 8P~ 9JN AACTN AAEDT AAEDW AAFTH AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AAXUO AAYFN ABAOU ABBOA ABFNM ABJNI ABMAC ABTAH ABVKL ABXDB ABYKQ ACAZW ACDAQ ACGFS ACNNM ACRLP ACZNC ADBBV ADEZE ADFGL ADMUD AEBSH AEKER AENEX AEXQZ AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AHZHX AIALX AIEXJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ AOUOD ARUGR ASPBG AVWKF AXJTR AZFZN BKOJK BLXMC CAG COF CS3 DM4 DU5 E3Z EBS EFBJH EFLBG EJD EO8 EO9 EP2 EP3 FDB FEDTE FGOYB FIRID FNPLU FYGXN G-Q G8K GBLVA GBOLZ HVGLF HZ~ H~9 IHE IXB J1W KOM LG5 LX9 M41 MHUIS MO0 MVM N9A NCXOZ O-L O9- OAUVE OK1 OZT P-8 P-9 P2P PC. Q38 R2- RIG RNS ROL RPZ SDF SDG SDP SES SEW SPC SPCBC SSV SSW SSZ T5K TN5 WH7 WUQ XJT XPP ZMT ZU3 ZY4 ~G- 9DU AATTM AAXKI AAYWO AAYXX ABDPE ABWVN ACLOT ACRPL ACVFH ADCNI ADNMO ADVLN AEIPS AEUPX AFJKZ AFPUW AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP CITATION EFKBS ~HD |
| ID | FETCH-LOGICAL-c336t-3e4aacb8119943c8058ae215b5336e9f55269bf81a043d6ecd90941dff4c1e03 |
| ISICitedReferencesCount | 212 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000383828000005&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0890-5401 |
| IngestDate | Sat Nov 29 01:56:33 EST 2025 Tue Nov 18 21:51:11 EST 2025 Fri Feb 23 02:25:06 EST 2024 |
| IsDoiOpenAccess | false |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c336t-3e4aacb8119943c8058ae215b5336e9f55269bf81a043d6ecd90941dff4c1e03 |
| OpenAccessLink | https://doi.org/10.1016/j.ic.2016.02.008 |
| PageCount | 28 |
| ParticipantIDs | crossref_citationtrail_10_1016_j_ic_2016_02_008 crossref_primary_10_1016_j_ic_2016_02_008 elsevier_sciencedirect_doi_10_1016_j_ic_2016_02_008 |
| PublicationCentury | 2000 |
| PublicationDate | October 2016 2016-10-00 |
| PublicationDateYYYYMMDD | 2016-10-01 |
| PublicationDate_xml | – month: 10 year: 2016 text: October 2016 |
| PublicationDecade | 2010 |
| PublicationTitle | Information and computation |
| PublicationYear | 2016 |
| Publisher | Elsevier Inc |
| Publisher_xml | – name: Elsevier Inc |
| References | Gour, Marvian, Spekkens (br0240) 2009; 80 Bellin, Hyland, Robinson, Urban (br0070) 2006; 364 Abeyesinghe, Devetak, Hayden, Winter (br0010) 2009; 465 Horodecki, Horodecki, Horodecki, Horodecki (br0300) Jun 2009; 81 Coecke (br0160) 2006; vol. 30 Borceux, Stubbe (br0110) 2000; vol. 111 Brandão, Horodecki, Oppenheim, Renes, Spekkens (br0130) 2013; 111 Coecke, Heunen, Kissinger (br0200) 2013 Benabou (br0080) 1963; 256 Chiribella, D'Ariano, Perinotti (br0140) 2008; 101 Joyal, Street (br0320) 1991; 88 Marvian, Spekkens (br0380) 2013; 15 Baez, Fritz, Leinster (br0050) 2011; 13 Skrzypczyk, Short, Popescu (br0460) 2014; 5 Cuntz (br0210) 1978; 233 Bennett, Bernstein, Popescu, Schumacher (br0090) 1996; 53 Baez, Stay (br0030) 2011 Baez, Fritz (br0040) 2014 Horodecki, Oppenheim (br0280) 2013; 4 Marvian, Spekkens (br0400) 2014; 90 Shannon (br0450) 1948; 27 Brandão, Horodecki, Ng, Oppenheim, Wehner (br0120) 2013 Mulvey (br0410) 1986; vol. 12 Ahmadi, Jennings, Rudolph (br0020) 2013; 15 Coecke (br0170) 2009; 51 Bandyopadhyay, Roychowdhury, Sen (br0060) 2002; 65 Horodecki, Horodecki, Oppenheim (br0270) 2003; 67 Coecke (br0180) 2013 nLab, Twisted arrow category, 2012. Devetak, Harrow, Winter (br0220) 2008; 54 Leinster (br0340) 2003 Horodecki, Oppenheim, Horodecki (br0290) 2002; 89 Marvian, Spekkens (br0370) 2013 Marvian, Spekkens (br0360) 2012 . Lambek (br0330) 1989; 92 Janzing, Wocjan, Zeier, Geiss, Beth (br0310) 2000; 39 Marvian, Spekkens (br0390) 2014; 5 Nielsen (br0420) 1999; 83 Selinger (br0440) 2011 Girard (br0230) 1987; 50 Chiribella, Mauro D'Ariano, Perinotti (br0150) 2011; 84 Gour, Müller, Narasimhachar, Spekkens, Halpern (br0250) 2013 Mac Lane (br0350) 1998 Birkhoff (br0100) 1942; 43 Coecke, Paquette (br0190) 2011 Gour, Spekkens (br0260) 2008; 10 Coecke (10.1016/j.ic.2016.02.008_br0170) 2009; 51 Gour (10.1016/j.ic.2016.02.008_br0250) Benabou (10.1016/j.ic.2016.02.008_br0080) 1963; 256 Nielsen (10.1016/j.ic.2016.02.008_br0420) 1999; 83 Coecke (10.1016/j.ic.2016.02.008_br0200) Janzing (10.1016/j.ic.2016.02.008_br0310) 2000; 39 Girard (10.1016/j.ic.2016.02.008_br0230) 1987; 50 Bellin (10.1016/j.ic.2016.02.008_br0070) 2006; 364 Mac Lane (10.1016/j.ic.2016.02.008_br0350) 1998 Marvian (10.1016/j.ic.2016.02.008_br0360) Ahmadi (10.1016/j.ic.2016.02.008_br0020) 2013; 15 Marvian (10.1016/j.ic.2016.02.008_br0370) Chiribella (10.1016/j.ic.2016.02.008_br0140) 2008; 101 Marvian (10.1016/j.ic.2016.02.008_br0400) 2014; 90 Leinster (10.1016/j.ic.2016.02.008_br0340) Brandão (10.1016/j.ic.2016.02.008_br0120) Mulvey (10.1016/j.ic.2016.02.008_br0410) 1986; vol. 12 Coecke (10.1016/j.ic.2016.02.008_br0160) 2006; vol. 30 Joyal (10.1016/j.ic.2016.02.008_br0320) 1991; 88 10.1016/j.ic.2016.02.008_br0430 Horodecki (10.1016/j.ic.2016.02.008_br0300) 2009; 81 Borceux (10.1016/j.ic.2016.02.008_br0110) 2000; vol. 111 Bandyopadhyay (10.1016/j.ic.2016.02.008_br0060) 2002; 65 Devetak (10.1016/j.ic.2016.02.008_br0220) 2008; 54 Brandão (10.1016/j.ic.2016.02.008_br0130) 2013; 111 Horodecki (10.1016/j.ic.2016.02.008_br0280) 2013; 4 Gour (10.1016/j.ic.2016.02.008_br0240) 2009; 80 Chiribella (10.1016/j.ic.2016.02.008_br0150) 2011; 84 Lambek (10.1016/j.ic.2016.02.008_br0330) 1989; 92 Skrzypczyk (10.1016/j.ic.2016.02.008_br0460) 2014; 5 Baez (10.1016/j.ic.2016.02.008_br0040) Selinger (10.1016/j.ic.2016.02.008_br0440) 2011 Coecke (10.1016/j.ic.2016.02.008_br0190) 2011 Marvian (10.1016/j.ic.2016.02.008_br0380) 2013; 15 Gour (10.1016/j.ic.2016.02.008_br0260) 2008; 10 Marvian (10.1016/j.ic.2016.02.008_br0390) 2014; 5 Bennett (10.1016/j.ic.2016.02.008_br0090) 1996; 53 Shannon (10.1016/j.ic.2016.02.008_br0450) 1948; 27 Baez (10.1016/j.ic.2016.02.008_br0050) 2011; 13 Coecke (10.1016/j.ic.2016.02.008_br0180) 2013 Horodecki (10.1016/j.ic.2016.02.008_br0270) 2003; 67 Cuntz (10.1016/j.ic.2016.02.008_br0210) 1978; 233 Horodecki (10.1016/j.ic.2016.02.008_br0290) 2002; 89 Baez (10.1016/j.ic.2016.02.008_br0030) 2011 Birkhoff (10.1016/j.ic.2016.02.008_br0100) 1942; 43 Abeyesinghe (10.1016/j.ic.2016.02.008_br0010) 2009; 465 |
| References_xml | – start-page: 167 year: 2011 end-page: 271 ident: br0190 article-title: Categories for the practicing physicist publication-title: New Structures for Physics – year: 2013 ident: br0250 article-title: The resource theory of informational nonequilibrium in thermodynamics – volume: 13 start-page: 1945 year: 2011 end-page: 1957 ident: br0050 article-title: A characterization of entropy in terms of information loss publication-title: Entropy – volume: 51 start-page: 59 year: 2009 end-page: 83 ident: br0170 article-title: Quantum picturalism publication-title: Contemp. Phys. – volume: 43 start-page: 298 year: 1942 end-page: 331 ident: br0100 article-title: Lattice-ordered groups publication-title: Ann. Math. – start-page: 275 year: 2011 end-page: 337 ident: br0440 article-title: A survey of graphical languages for monoidal categories publication-title: New Structures for Physics – year: 2014 ident: br0040 article-title: A Bayesian characterization of relative entropy – reference: nLab, Twisted arrow category, 2012. – volume: 80 year: 2009 ident: br0240 article-title: Measuring the quality of a quantum reference frame: the relative entropy of frameness publication-title: Phys. Rev. A – volume: 27 start-page: 623 year: 1948 end-page: 656 ident: br0450 article-title: A mathematical theory of communication publication-title: Bell Syst. Tech. J. – volume: 4 start-page: 1 year: 2013 end-page: 6 ident: br0280 article-title: Fundamental limitations for quantum and nanoscale thermodynamics publication-title: Nat. Commun. – volume: 53 start-page: 2046 year: 1996 ident: br0090 article-title: Concentrating partial entanglement by local operations publication-title: Phys. Rev. A – volume: 54 start-page: 4587 year: 2008 end-page: 4618 ident: br0220 article-title: A resource framework for quantum Shannon theory publication-title: IEEE Trans. Inf. Theory – volume: 465 start-page: 2537 year: 2009 end-page: 2563 ident: br0010 article-title: The mother of all protocols: restructuring quantum information's family tree publication-title: Proc. R. Soc. A, Math. Phys. Eng. Sci. – start-page: 1 year: 2013 end-page: 22 ident: br0180 article-title: An alternative Gospel of structure: order, composition, processes publication-title: Quantum Physics and Linguistics. A Compositional, Diagrammatic Discourse – volume: 83 start-page: 436 year: 1999 end-page: 439 ident: br0420 article-title: Conditions for a class of entanglement transformations publication-title: Phys. Rev. Lett. – volume: 111 year: 2013 ident: br0130 article-title: The resource theory of quantum states out of thermal equilibrium publication-title: Phys. Rev. Lett. – volume: 39 start-page: 2217 year: 2000 end-page: 2753 ident: br0310 article-title: The thermodynamic cost of reliability and low temperatures: tightening Landauer's principle and the second law publication-title: Int. J. Theor. Phys. – volume: vol. 111 start-page: 167 year: 2000 end-page: 194 ident: br0110 article-title: Short introduction to enriched categories publication-title: Current Research in Operational Quantum Logic: Algebras, Categories and Languages – volume: 84 year: 2011 ident: br0150 article-title: Informational derivation of quantum theory publication-title: Phys. Rev. A – volume: 50 start-page: 1 year: 1987 end-page: 101 ident: br0230 article-title: Linear logic publication-title: Theor. Comput. Sci. – volume: 5 start-page: 4185 year: 2014 ident: br0460 article-title: Work extraction and thermodynamics for individual quantum systems publication-title: Nat. Commun. – volume: 101 year: 2008 ident: br0140 article-title: Quantum circuit architecture publication-title: Phys. Rev. Lett. – volume: vol. 30 start-page: 45 year: 2006 end-page: 74 ident: br0160 article-title: Introducing categories to the practicing physicist publication-title: What Is Category Theory? – volume: 233 start-page: 145 year: 1978 end-page: 153 ident: br0210 article-title: Dimension functions on simple publication-title: Math. Ann. – volume: 88 start-page: 55 year: 1991 end-page: 112 ident: br0320 article-title: The geometry of tensor calculus, I publication-title: Adv. Math. – volume: 92 start-page: 217 year: 1989 end-page: 239 ident: br0330 article-title: Multicategories revisited publication-title: Contemp. Math. – volume: 15 year: 2013 ident: br0380 article-title: The theory of manipulations of pure state asymmetry: I. basic tools, equivalence classes and single copy transformations publication-title: New J. Phys. – volume: 90 year: 2014 ident: br0400 article-title: Asymmetry properties of pure quantum states publication-title: Phys. Rev. A – volume: 10 year: 2008 ident: br0260 article-title: The resource theory of quantum reference frames: manipulations and monotones publication-title: New J. Phys. – volume: 364 start-page: 146 year: 2006 end-page: 165 ident: br0070 article-title: Categorical proof theory of classical propositional calculus publication-title: Theor. Comput. Sci. – year: 2003 ident: br0340 article-title: Higher operads, higher categories – year: 2013 ident: br0200 article-title: Categories of quantum and classical channels – year: 1998 ident: br0350 article-title: Categories for the Working Mathematician – year: 2013 ident: br0120 article-title: The second laws of quantum thermodynamics – volume: 15 year: 2013 ident: br0020 article-title: The Wigner–Araki–Yanase theorem and the quantum resource theory of asymmetry publication-title: New J. Phys. – reference: . – volume: 256 start-page: 1887 year: 1963 end-page: 1890 ident: br0080 article-title: Categories avec multiplication publication-title: C. R. Séances Acad. Sci. – volume: 89 year: 2002 ident: br0290 article-title: Are the laws of entanglement theory thermodynamical? publication-title: Phys. Rev. Lett. – volume: 81 start-page: 865 year: Jun 2009 end-page: 942 ident: br0300 article-title: Quantum entanglement publication-title: Rev. Mod. Phys. – volume: 5 start-page: 3821 year: 2014 ident: br0390 article-title: Extending Noether's theorem by quantifying the asymmetry of quantum states publication-title: Nat. Commun. – year: 2012 ident: br0360 article-title: An information-theoretic account of the Wigner–Araki–Yanase theorem – volume: 65 year: 2002 ident: br0060 article-title: Classification of nonasymptotic bipartite pure-state entanglement transformations publication-title: Phys. Rev. A – volume: 67 year: 2003 ident: br0270 article-title: Reversible transformations from pure to mixed states and the unique measure of information publication-title: Phys. Rev. A – start-page: 95 year: 2011 end-page: 172 ident: br0030 article-title: Physics, topology, logic and computation: a Rosetta stone publication-title: New Structures for Physics – year: 2013 ident: br0370 article-title: Modes of asymmetry: the application of harmonic analysis to symmetric quantum dynamics and quantum reference frames – volume: vol. 12 start-page: 99 year: 1986 end-page: 104 ident: br0410 article-title: Rendiconti del Circolo Matematico di Palermo II – volume: 50 start-page: 1 issue: 1 year: 1987 ident: 10.1016/j.ic.2016.02.008_br0230 article-title: Linear logic publication-title: Theor. Comput. Sci. doi: 10.1016/0304-3975(87)90045-4 – volume: 80 issue: 1 year: 2009 ident: 10.1016/j.ic.2016.02.008_br0240 article-title: Measuring the quality of a quantum reference frame: the relative entropy of frameness publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.80.012307 – volume: 81 start-page: 865 issue: 2 year: 2009 ident: 10.1016/j.ic.2016.02.008_br0300 article-title: Quantum entanglement publication-title: Rev. Mod. Phys. doi: 10.1103/RevModPhys.81.865 – volume: 65 year: 2002 ident: 10.1016/j.ic.2016.02.008_br0060 article-title: Classification of nonasymptotic bipartite pure-state entanglement transformations publication-title: Phys. Rev. A – volume: 111 year: 2013 ident: 10.1016/j.ic.2016.02.008_br0130 article-title: The resource theory of quantum states out of thermal equilibrium publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.111.250404 – volume: 15 issue: 3 year: 2013 ident: 10.1016/j.ic.2016.02.008_br0380 article-title: The theory of manipulations of pure state asymmetry: I. basic tools, equivalence classes and single copy transformations publication-title: New J. Phys. doi: 10.1088/1367-2630/15/3/033001 – volume: 53 start-page: 2046 issue: 4 year: 1996 ident: 10.1016/j.ic.2016.02.008_br0090 article-title: Concentrating partial entanglement by local operations publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.53.2046 – volume: 5 start-page: 3821 year: 2014 ident: 10.1016/j.ic.2016.02.008_br0390 article-title: Extending Noether's theorem by quantifying the asymmetry of quantum states publication-title: Nat. Commun. doi: 10.1038/ncomms4821 – ident: 10.1016/j.ic.2016.02.008_br0430 – ident: 10.1016/j.ic.2016.02.008_br0340 – start-page: 95 year: 2011 ident: 10.1016/j.ic.2016.02.008_br0030 article-title: Physics, topology, logic and computation: a Rosetta stone – volume: 43 start-page: 298 issue: 2 year: 1942 ident: 10.1016/j.ic.2016.02.008_br0100 article-title: Lattice-ordered groups publication-title: Ann. Math. doi: 10.2307/1968871 – ident: 10.1016/j.ic.2016.02.008_br0120 – volume: 39 start-page: 2217 issue: 12 year: 2000 ident: 10.1016/j.ic.2016.02.008_br0310 article-title: The thermodynamic cost of reliability and low temperatures: tightening Landauer's principle and the second law publication-title: Int. J. Theor. Phys. doi: 10.1023/A:1026422630734 – volume: 88 start-page: 55 year: 1991 ident: 10.1016/j.ic.2016.02.008_br0320 article-title: The geometry of tensor calculus, I publication-title: Adv. Math. doi: 10.1016/0001-8708(91)90003-P – volume: 90 year: 2014 ident: 10.1016/j.ic.2016.02.008_br0400 article-title: Asymmetry properties of pure quantum states publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.90.014102 – volume: 13 start-page: 1945 year: 2011 ident: 10.1016/j.ic.2016.02.008_br0050 article-title: A characterization of entropy in terms of information loss publication-title: Entropy doi: 10.3390/e13111945 – volume: 92 start-page: 217 year: 1989 ident: 10.1016/j.ic.2016.02.008_br0330 article-title: Multicategories revisited publication-title: Contemp. Math. doi: 10.1090/conm/092/1003201 – start-page: 167 year: 2011 ident: 10.1016/j.ic.2016.02.008_br0190 article-title: Categories for the practicing physicist – volume: vol. 12 start-page: 99 year: 1986 ident: 10.1016/j.ic.2016.02.008_br0410 – volume: 27 start-page: 623 issue: 379–423 year: 1948 ident: 10.1016/j.ic.2016.02.008_br0450 article-title: A mathematical theory of communication publication-title: Bell Syst. Tech. J. doi: 10.1002/j.1538-7305.1948.tb00917.x – ident: 10.1016/j.ic.2016.02.008_br0250 – start-page: 275 year: 2011 ident: 10.1016/j.ic.2016.02.008_br0440 article-title: A survey of graphical languages for monoidal categories – volume: 4 start-page: 1 year: 2013 ident: 10.1016/j.ic.2016.02.008_br0280 article-title: Fundamental limitations for quantum and nanoscale thermodynamics publication-title: Nat. Commun. doi: 10.1038/ncomms3059 – volume: 10 year: 2008 ident: 10.1016/j.ic.2016.02.008_br0260 article-title: The resource theory of quantum reference frames: manipulations and monotones publication-title: New J. Phys. doi: 10.1088/1367-2630/10/3/033023 – volume: 51 start-page: 59 year: 2009 ident: 10.1016/j.ic.2016.02.008_br0170 article-title: Quantum picturalism publication-title: Contemp. Phys. doi: 10.1080/00107510903257624 – volume: 256 start-page: 1887 year: 1963 ident: 10.1016/j.ic.2016.02.008_br0080 article-title: Categories avec multiplication publication-title: C. R. Séances Acad. Sci. – volume: vol. 30 start-page: 45 year: 2006 ident: 10.1016/j.ic.2016.02.008_br0160 article-title: Introducing categories to the practicing physicist – volume: 67 issue: 6 year: 2003 ident: 10.1016/j.ic.2016.02.008_br0270 article-title: Reversible transformations from pure to mixed states and the unique measure of information publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.67.062104 – volume: 101 issue: 6 year: 2008 ident: 10.1016/j.ic.2016.02.008_br0140 article-title: Quantum circuit architecture publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.101.060401 – ident: 10.1016/j.ic.2016.02.008_br0200 – volume: 84 issue: 1 year: 2011 ident: 10.1016/j.ic.2016.02.008_br0150 article-title: Informational derivation of quantum theory publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.84.012311 – volume: 54 start-page: 4587 issue: 10 year: 2008 ident: 10.1016/j.ic.2016.02.008_br0220 article-title: A resource framework for quantum Shannon theory publication-title: IEEE Trans. Inf. Theory doi: 10.1109/TIT.2008.928980 – volume: 89 issue: 24 year: 2002 ident: 10.1016/j.ic.2016.02.008_br0290 article-title: Are the laws of entanglement theory thermodynamical? publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.89.240403 – volume: 5 start-page: 4185 year: 2014 ident: 10.1016/j.ic.2016.02.008_br0460 article-title: Work extraction and thermodynamics for individual quantum systems publication-title: Nat. Commun. doi: 10.1038/ncomms5185 – start-page: 1 year: 2013 ident: 10.1016/j.ic.2016.02.008_br0180 article-title: An alternative Gospel of structure: order, composition, processes – volume: 15 issue: 1 year: 2013 ident: 10.1016/j.ic.2016.02.008_br0020 article-title: The Wigner–Araki–Yanase theorem and the quantum resource theory of asymmetry publication-title: New J. Phys. doi: 10.1088/1367-2630/15/1/013057 – volume: 364 start-page: 146 year: 2006 ident: 10.1016/j.ic.2016.02.008_br0070 article-title: Categorical proof theory of classical propositional calculus publication-title: Theor. Comput. Sci. doi: 10.1016/j.tcs.2006.08.002 – ident: 10.1016/j.ic.2016.02.008_br0370 – volume: 83 start-page: 436 issue: 2 year: 1999 ident: 10.1016/j.ic.2016.02.008_br0420 article-title: Conditions for a class of entanglement transformations publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.83.436 – ident: 10.1016/j.ic.2016.02.008_br0040 – year: 1998 ident: 10.1016/j.ic.2016.02.008_br0350 – volume: vol. 111 start-page: 167 year: 2000 ident: 10.1016/j.ic.2016.02.008_br0110 article-title: Short introduction to enriched categories – volume: 233 start-page: 145 issue: 2 year: 1978 ident: 10.1016/j.ic.2016.02.008_br0210 article-title: Dimension functions on simple C⁎-algebras publication-title: Math. Ann. doi: 10.1007/BF01421922 – volume: 465 start-page: 2537 issue: 2108 year: 2009 ident: 10.1016/j.ic.2016.02.008_br0010 article-title: The mother of all protocols: restructuring quantum information's family tree publication-title: Proc. R. Soc. A, Math. Phys. Eng. Sci. – ident: 10.1016/j.ic.2016.02.008_br0360 |
| SSID | ssj0011546 |
| Score | 2.6064708 |
| Snippet | Many fields of science investigate states and processes as resources. Chemistry, thermodynamics, Shannon's theory of communication channels, and the theory of... |
| SourceID | crossref elsevier |
| SourceType | Enrichment Source Index Database Publisher |
| StartPage | 59 |
| Title | A mathematical theory of resources |
| URI | https://dx.doi.org/10.1016/j.ic.2016.02.008 |
| Volume | 250 |
| WOSCitedRecordID | wos000383828000005&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 customDbUrl: eissn: 1090-2651 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0011546 issn: 0890-5401 databaseCode: AIEXJ dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1NT8IwGG4MeNCDH6gRv7IYL4YM13Ub2xEJRj0QE0nktrRdlwx0I4CGn2-7dmUYMHLwspBlX-zp3j5t3_d5ALihQuEDE8I_JOLxAQqBJnGxYzJICEKR61IS5WYTrV7PHwyCF-XZPs3tBFpp6s_nwfhfoeb7ONiidHYDuPVF-Q7-m4POtxx2vv0T8O3Gh5ZiFZnkefG94IQTNVM_LRNSVY40K7KSae7ysLQ838kYlSk89xnReE-S3Am20c9IgjUxfx2z0YhJbi6TthtvzfLMAvR0jpoOQIElEidgOVraUidWxTul5q16Tm9lTJbTA8NmIhQjoSclUv1F_1Osuf_olnSyYJGHNgwTGoorhJYd5gXeVbvlBjyUVdtP3cGzXjyCqj6reHy1Oi3T-pafYjUbKTGM_gHYU0MDoy0hPQRbLK2B_cJ2w1BRuAZ2SxqSR-C6bZTxNiTeRhYbGu9j0H_o9juPpjK-MClC3sxEzMGYEh8K4WZEfcv1MePcjHBu7rEgdoUtPIl9iC0HRR6jUcBH6TCKY4dCZqETUEmzlJ0CowWx50QstijhXSJGxCbieMcRNgQ4xnVwV_z_kCpReOFN8h6ue-t1cKvPGEtBlF-ORcUrDRWhk0Qt5G1j7VlnG9zhHOwsWu4FqMwmn-wSbNOvWTKdXKmG8Q3c8Gey |
| linkProvider | Elsevier |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=A+mathematical+theory+of+resources&rft.jtitle=Information+and+computation&rft.au=Coecke%2C+Bob&rft.au=Fritz%2C+Tobias&rft.au=Spekkens%2C+Robert+W.&rft.date=2016-10-01&rft.issn=0890-5401&rft.volume=250&rft.spage=59&rft.epage=86&rft_id=info:doi/10.1016%2Fj.ic.2016.02.008&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_j_ic_2016_02_008 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0890-5401&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0890-5401&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0890-5401&client=summon |