Diagonalizability of Quantum Markov States on Trees
Abstract We introduce quantum Markov states (QMS) in a general tree graph %$G= (V, E)%$, extending the Cayley tree’s case. We investigate the Markov property w.r.t. the finer structure of the considered tree. The main result of the present paper concerns the diagonalizability of a locally faithful Q...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Mukhamedov, Farrukh [verfasserIn] Souissi, Abdessatar [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2021 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Journal of statistical physics - New York, NY [u.a.] : Springer Science + Business Media B.V., 1969, 182(2021), 1 vom: Jan. |
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| Übergeordnetes Werk: |
volume:182 ; year:2021 ; number:1 ; month:01 |
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| DOI / URN: |
10.1007/s10955-020-02674-1 |
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| Katalog-ID: |
SPR042608953 |
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| 100 | 1 | |a Mukhamedov, Farrukh |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a Diagonalizability of Quantum Markov States on Trees |
| 264 | 1 | |c 2021 | |
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| 520 | |a Abstract We introduce quantum Markov states (QMS) in a general tree graph %$G= (V, E)%$, extending the Cayley tree’s case. We investigate the Markov property w.r.t. the finer structure of the considered tree. The main result of the present paper concerns the diagonalizability of a locally faithful QMS %$\varphi %$ on a UHF-algebra %${\mathcal {A}}_V%$ over the considered tree by means of a suitable conditional expectation into a maximal abelian subalgebra. Namely, we prove the existence of a Umegaki conditional expectation %${\mathfrak {E}} : {\mathcal {A}}_V \rightarrow {\mathcal {D}}_V%$ such that %$\varphi =\varphi _{\lceil {\mathcal {D}}_V}\circ {\mathfrak {E}}%$. Moreover, it is clarified the Markovian structure of the associated classical measure on the spectrum of the diagonal algebra %${\mathcal {D}}_V%$. | ||
| 650 | 4 | |a Quantum Markov state |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Localized |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Conditional expectations |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Tree |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Maximal abelian subalgebra |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a C |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a -algebras |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a diagonalizability |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Souissi, Abdessatar |e verfasserin |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Journal of statistical physics |d New York, NY [u.a.] : Springer Science + Business Media B.V., 1969 |g 182(2021), 1 vom: Jan. |w (DE-627)320578437 |w (DE-600)2017302-7 |x 1572-9613 |7 nnns |
| 773 | 1 | 8 | |g volume:182 |g year:2021 |g number:1 |g month:01 |
| 856 | 4 | 0 | |u https://dx.doi.org/10.1007/s10955-020-02674-1 |z lizenzpflichtig |3 Volltext |
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10.1007/s10955-020-02674-1 doi (DE-627)SPR042608953 (DE-599)SPRs10955-020-02674-1-e (SPR)s10955-020-02674-1-e DE-627 ger DE-627 rakwb eng 530 ASE 31.00 bkl 33.00 bkl Mukhamedov, Farrukh verfasserin aut Diagonalizability of Quantum Markov States on Trees 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We introduce quantum Markov states (QMS) in a general tree graph %$G= (V, E)%$, extending the Cayley tree’s case. We investigate the Markov property w.r.t. the finer structure of the considered tree. The main result of the present paper concerns the diagonalizability of a locally faithful QMS %$\varphi %$ on a UHF-algebra %${\mathcal {A}}_V%$ over the considered tree by means of a suitable conditional expectation into a maximal abelian subalgebra. Namely, we prove the existence of a Umegaki conditional expectation %${\mathfrak {E}} : {\mathcal {A}}_V \rightarrow {\mathcal {D}}_V%$ such that %$\varphi =\varphi _{\lceil {\mathcal {D}}_V}\circ {\mathfrak {E}}%$. Moreover, it is clarified the Markovian structure of the associated classical measure on the spectrum of the diagonal algebra %${\mathcal {D}}_V%$. Quantum Markov state (dpeaa)DE-He213 Localized (dpeaa)DE-He213 Conditional expectations (dpeaa)DE-He213 Tree (dpeaa)DE-He213 Maximal abelian subalgebra (dpeaa)DE-He213 C (dpeaa)DE-He213 -algebras (dpeaa)DE-He213 diagonalizability (dpeaa)DE-He213 Souissi, Abdessatar verfasserin aut Enthalten in Journal of statistical physics New York, NY [u.a.] : Springer Science + Business Media B.V., 1969 182(2021), 1 vom: Jan. (DE-627)320578437 (DE-600)2017302-7 1572-9613 nnns volume:182 year:2021 number:1 month:01 https://dx.doi.org/10.1007/s10955-020-02674-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 ASE 33.00 ASE AR 182 2021 1 01 |
| spelling |
10.1007/s10955-020-02674-1 doi (DE-627)SPR042608953 (DE-599)SPRs10955-020-02674-1-e (SPR)s10955-020-02674-1-e DE-627 ger DE-627 rakwb eng 530 ASE 31.00 bkl 33.00 bkl Mukhamedov, Farrukh verfasserin aut Diagonalizability of Quantum Markov States on Trees 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We introduce quantum Markov states (QMS) in a general tree graph %$G= (V, E)%$, extending the Cayley tree’s case. We investigate the Markov property w.r.t. the finer structure of the considered tree. The main result of the present paper concerns the diagonalizability of a locally faithful QMS %$\varphi %$ on a UHF-algebra %${\mathcal {A}}_V%$ over the considered tree by means of a suitable conditional expectation into a maximal abelian subalgebra. Namely, we prove the existence of a Umegaki conditional expectation %${\mathfrak {E}} : {\mathcal {A}}_V \rightarrow {\mathcal {D}}_V%$ such that %$\varphi =\varphi _{\lceil {\mathcal {D}}_V}\circ {\mathfrak {E}}%$. Moreover, it is clarified the Markovian structure of the associated classical measure on the spectrum of the diagonal algebra %${\mathcal {D}}_V%$. Quantum Markov state (dpeaa)DE-He213 Localized (dpeaa)DE-He213 Conditional expectations (dpeaa)DE-He213 Tree (dpeaa)DE-He213 Maximal abelian subalgebra (dpeaa)DE-He213 C (dpeaa)DE-He213 -algebras (dpeaa)DE-He213 diagonalizability (dpeaa)DE-He213 Souissi, Abdessatar verfasserin aut Enthalten in Journal of statistical physics New York, NY [u.a.] : Springer Science + Business Media B.V., 1969 182(2021), 1 vom: Jan. (DE-627)320578437 (DE-600)2017302-7 1572-9613 nnns volume:182 year:2021 number:1 month:01 https://dx.doi.org/10.1007/s10955-020-02674-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 ASE 33.00 ASE AR 182 2021 1 01 |
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10.1007/s10955-020-02674-1 doi (DE-627)SPR042608953 (DE-599)SPRs10955-020-02674-1-e (SPR)s10955-020-02674-1-e DE-627 ger DE-627 rakwb eng 530 ASE 31.00 bkl 33.00 bkl Mukhamedov, Farrukh verfasserin aut Diagonalizability of Quantum Markov States on Trees 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We introduce quantum Markov states (QMS) in a general tree graph %$G= (V, E)%$, extending the Cayley tree’s case. We investigate the Markov property w.r.t. the finer structure of the considered tree. The main result of the present paper concerns the diagonalizability of a locally faithful QMS %$\varphi %$ on a UHF-algebra %${\mathcal {A}}_V%$ over the considered tree by means of a suitable conditional expectation into a maximal abelian subalgebra. Namely, we prove the existence of a Umegaki conditional expectation %${\mathfrak {E}} : {\mathcal {A}}_V \rightarrow {\mathcal {D}}_V%$ such that %$\varphi =\varphi _{\lceil {\mathcal {D}}_V}\circ {\mathfrak {E}}%$. Moreover, it is clarified the Markovian structure of the associated classical measure on the spectrum of the diagonal algebra %${\mathcal {D}}_V%$. Quantum Markov state (dpeaa)DE-He213 Localized (dpeaa)DE-He213 Conditional expectations (dpeaa)DE-He213 Tree (dpeaa)DE-He213 Maximal abelian subalgebra (dpeaa)DE-He213 C (dpeaa)DE-He213 -algebras (dpeaa)DE-He213 diagonalizability (dpeaa)DE-He213 Souissi, Abdessatar verfasserin aut Enthalten in Journal of statistical physics New York, NY [u.a.] : Springer Science + Business Media B.V., 1969 182(2021), 1 vom: Jan. (DE-627)320578437 (DE-600)2017302-7 1572-9613 nnns volume:182 year:2021 number:1 month:01 https://dx.doi.org/10.1007/s10955-020-02674-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 ASE 33.00 ASE AR 182 2021 1 01 |
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10.1007/s10955-020-02674-1 doi (DE-627)SPR042608953 (DE-599)SPRs10955-020-02674-1-e (SPR)s10955-020-02674-1-e DE-627 ger DE-627 rakwb eng 530 ASE 31.00 bkl 33.00 bkl Mukhamedov, Farrukh verfasserin aut Diagonalizability of Quantum Markov States on Trees 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We introduce quantum Markov states (QMS) in a general tree graph %$G= (V, E)%$, extending the Cayley tree’s case. We investigate the Markov property w.r.t. the finer structure of the considered tree. The main result of the present paper concerns the diagonalizability of a locally faithful QMS %$\varphi %$ on a UHF-algebra %${\mathcal {A}}_V%$ over the considered tree by means of a suitable conditional expectation into a maximal abelian subalgebra. Namely, we prove the existence of a Umegaki conditional expectation %${\mathfrak {E}} : {\mathcal {A}}_V \rightarrow {\mathcal {D}}_V%$ such that %$\varphi =\varphi _{\lceil {\mathcal {D}}_V}\circ {\mathfrak {E}}%$. Moreover, it is clarified the Markovian structure of the associated classical measure on the spectrum of the diagonal algebra %${\mathcal {D}}_V%$. Quantum Markov state (dpeaa)DE-He213 Localized (dpeaa)DE-He213 Conditional expectations (dpeaa)DE-He213 Tree (dpeaa)DE-He213 Maximal abelian subalgebra (dpeaa)DE-He213 C (dpeaa)DE-He213 -algebras (dpeaa)DE-He213 diagonalizability (dpeaa)DE-He213 Souissi, Abdessatar verfasserin aut Enthalten in Journal of statistical physics New York, NY [u.a.] : Springer Science + Business Media B.V., 1969 182(2021), 1 vom: Jan. (DE-627)320578437 (DE-600)2017302-7 1572-9613 nnns volume:182 year:2021 number:1 month:01 https://dx.doi.org/10.1007/s10955-020-02674-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 ASE 33.00 ASE AR 182 2021 1 01 |
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10.1007/s10955-020-02674-1 doi (DE-627)SPR042608953 (DE-599)SPRs10955-020-02674-1-e (SPR)s10955-020-02674-1-e DE-627 ger DE-627 rakwb eng 530 ASE 31.00 bkl 33.00 bkl Mukhamedov, Farrukh verfasserin aut Diagonalizability of Quantum Markov States on Trees 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We introduce quantum Markov states (QMS) in a general tree graph %$G= (V, E)%$, extending the Cayley tree’s case. We investigate the Markov property w.r.t. the finer structure of the considered tree. The main result of the present paper concerns the diagonalizability of a locally faithful QMS %$\varphi %$ on a UHF-algebra %${\mathcal {A}}_V%$ over the considered tree by means of a suitable conditional expectation into a maximal abelian subalgebra. Namely, we prove the existence of a Umegaki conditional expectation %${\mathfrak {E}} : {\mathcal {A}}_V \rightarrow {\mathcal {D}}_V%$ such that %$\varphi =\varphi _{\lceil {\mathcal {D}}_V}\circ {\mathfrak {E}}%$. Moreover, it is clarified the Markovian structure of the associated classical measure on the spectrum of the diagonal algebra %${\mathcal {D}}_V%$. Quantum Markov state (dpeaa)DE-He213 Localized (dpeaa)DE-He213 Conditional expectations (dpeaa)DE-He213 Tree (dpeaa)DE-He213 Maximal abelian subalgebra (dpeaa)DE-He213 C (dpeaa)DE-He213 -algebras (dpeaa)DE-He213 diagonalizability (dpeaa)DE-He213 Souissi, Abdessatar verfasserin aut Enthalten in Journal of statistical physics New York, NY [u.a.] : Springer Science + Business Media B.V., 1969 182(2021), 1 vom: Jan. (DE-627)320578437 (DE-600)2017302-7 1572-9613 nnns volume:182 year:2021 number:1 month:01 https://dx.doi.org/10.1007/s10955-020-02674-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 ASE 33.00 ASE AR 182 2021 1 01 |
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Quantum Markov state Localized Conditional expectations Tree Maximal abelian subalgebra C -algebras diagonalizability |
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Mukhamedov, Farrukh @@aut@@ Souissi, Abdessatar @@aut@@ |
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Mukhamedov, Farrukh |
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Mukhamedov, Farrukh ddc 530 bkl 31.00 bkl 33.00 misc Quantum Markov state misc Localized misc Conditional expectations misc Tree misc Maximal abelian subalgebra misc C misc -algebras misc diagonalizability Diagonalizability of Quantum Markov States on Trees |
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530 ASE 31.00 bkl 33.00 bkl Diagonalizability of Quantum Markov States on Trees Quantum Markov state (dpeaa)DE-He213 Localized (dpeaa)DE-He213 Conditional expectations (dpeaa)DE-He213 Tree (dpeaa)DE-He213 Maximal abelian subalgebra (dpeaa)DE-He213 C (dpeaa)DE-He213 -algebras (dpeaa)DE-He213 diagonalizability (dpeaa)DE-He213 |
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ddc 530 bkl 31.00 bkl 33.00 misc Quantum Markov state misc Localized misc Conditional expectations misc Tree misc Maximal abelian subalgebra misc C misc -algebras misc diagonalizability |
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ddc 530 bkl 31.00 bkl 33.00 misc Quantum Markov state misc Localized misc Conditional expectations misc Tree misc Maximal abelian subalgebra misc C misc -algebras misc diagonalizability |
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Diagonalizability of Quantum Markov States on Trees |
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Diagonalizability of Quantum Markov States on Trees |
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Mukhamedov, Farrukh |
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diagonalizability of quantum markov states on trees |
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Diagonalizability of Quantum Markov States on Trees |
| abstract |
Abstract We introduce quantum Markov states (QMS) in a general tree graph %$G= (V, E)%$, extending the Cayley tree’s case. We investigate the Markov property w.r.t. the finer structure of the considered tree. The main result of the present paper concerns the diagonalizability of a locally faithful QMS %$\varphi %$ on a UHF-algebra %${\mathcal {A}}_V%$ over the considered tree by means of a suitable conditional expectation into a maximal abelian subalgebra. Namely, we prove the existence of a Umegaki conditional expectation %${\mathfrak {E}} : {\mathcal {A}}_V \rightarrow {\mathcal {D}}_V%$ such that %$\varphi =\varphi _{\lceil {\mathcal {D}}_V}\circ {\mathfrak {E}}%$. Moreover, it is clarified the Markovian structure of the associated classical measure on the spectrum of the diagonal algebra %${\mathcal {D}}_V%$. |
| abstractGer |
Abstract We introduce quantum Markov states (QMS) in a general tree graph %$G= (V, E)%$, extending the Cayley tree’s case. We investigate the Markov property w.r.t. the finer structure of the considered tree. The main result of the present paper concerns the diagonalizability of a locally faithful QMS %$\varphi %$ on a UHF-algebra %${\mathcal {A}}_V%$ over the considered tree by means of a suitable conditional expectation into a maximal abelian subalgebra. Namely, we prove the existence of a Umegaki conditional expectation %${\mathfrak {E}} : {\mathcal {A}}_V \rightarrow {\mathcal {D}}_V%$ such that %$\varphi =\varphi _{\lceil {\mathcal {D}}_V}\circ {\mathfrak {E}}%$. Moreover, it is clarified the Markovian structure of the associated classical measure on the spectrum of the diagonal algebra %${\mathcal {D}}_V%$. |
| abstract_unstemmed |
Abstract We introduce quantum Markov states (QMS) in a general tree graph %$G= (V, E)%$, extending the Cayley tree’s case. We investigate the Markov property w.r.t. the finer structure of the considered tree. The main result of the present paper concerns the diagonalizability of a locally faithful QMS %$\varphi %$ on a UHF-algebra %${\mathcal {A}}_V%$ over the considered tree by means of a suitable conditional expectation into a maximal abelian subalgebra. Namely, we prove the existence of a Umegaki conditional expectation %${\mathfrak {E}} : {\mathcal {A}}_V \rightarrow {\mathcal {D}}_V%$ such that %$\varphi =\varphi _{\lceil {\mathcal {D}}_V}\circ {\mathfrak {E}}%$. Moreover, it is clarified the Markovian structure of the associated classical measure on the spectrum of the diagonal algebra %${\mathcal {D}}_V%$. |
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| title_short |
Diagonalizability of Quantum Markov States on Trees |
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https://dx.doi.org/10.1007/s10955-020-02674-1 |
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true |
| author2 |
Souissi, Abdessatar |
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Souissi, Abdessatar |
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| doi_str |
10.1007/s10955-020-02674-1 |
| up_date |
2024-07-03T13:50:32.640Z |
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| score |
7.4004107 |