Asymptotic Error Rates in Quantum Hypothesis Testing
Abstract We consider the problem of discriminating between two different states of a finite quantum system in the setting of large numbers of copies, and find a closed form expression for the asymptotic exponential rate at which the error probability tends to zero. This leads to the identification o...
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| Autor*in: |
Audenaert, K. M. R. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2008 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag 2008 |
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| Übergeordnetes Werk: |
Enthalten in: Communications in mathematical physics - Springer-Verlag, 1965, 279(2008), 1 vom: 08. Feb., Seite 251-283 |
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| Übergeordnetes Werk: |
volume:279 ; year:2008 ; number:1 ; day:08 ; month:02 ; pages:251-283 |
| Links: |
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| DOI / URN: |
10.1007/s00220-008-0417-5 |
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OLC2038893292 |
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| 520 | |a Abstract We consider the problem of discriminating between two different states of a finite quantum system in the setting of large numbers of copies, and find a closed form expression for the asymptotic exponential rate at which the error probability tends to zero. This leads to the identification of the quantum generalisation of the classical Chernoff distance, which is the corresponding quantity in classical symmetric hypothesis testing. The proof relies on two new techniques introduced by the authors, which are also well suited to tackle the corresponding problem in asymmetric hypothesis testing, yielding the quantum generalisation of the classical Hoeffding bound. This has been done by Hayashi and Nagaoka for the special case where the states have full support. The goal of this paper is to present the proofs of these results in a unified way and in full generality, allowing hypothesis states with different supports. From the quantum Hoeffding bound, we then easily derive quantum Stein’s Lemma and quantum Sanov’s theorem. We give an in-depth treatment of the properties of the quantum Chernoff distance, and argue that it is a natural distance measure on the set of density operators, with a clear operational meaning. | ||
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| 700 | 1 | |a Szkoła, A. |4 aut | |
| 700 | 1 | |a Verstraete, F. |4 aut | |
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10.1007/s00220-008-0417-5 doi (DE-627)OLC2038893292 (DE-He213)s00220-008-0417-5-p DE-627 ger DE-627 rakwb eng 530 510 VZ Audenaert, K. M. R. verfasserin aut Asymptotic Error Rates in Quantum Hypothesis Testing 2008 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2008 Abstract We consider the problem of discriminating between two different states of a finite quantum system in the setting of large numbers of copies, and find a closed form expression for the asymptotic exponential rate at which the error probability tends to zero. This leads to the identification of the quantum generalisation of the classical Chernoff distance, which is the corresponding quantity in classical symmetric hypothesis testing. The proof relies on two new techniques introduced by the authors, which are also well suited to tackle the corresponding problem in asymmetric hypothesis testing, yielding the quantum generalisation of the classical Hoeffding bound. This has been done by Hayashi and Nagaoka for the special case where the states have full support. The goal of this paper is to present the proofs of these results in a unified way and in full generality, allowing hypothesis states with different supports. From the quantum Hoeffding bound, we then easily derive quantum Stein’s Lemma and quantum Sanov’s theorem. We give an in-depth treatment of the properties of the quantum Chernoff distance, and argue that it is a natural distance measure on the set of density operators, with a clear operational meaning. Density Operator Relative Entropy Error Exponent Quantum Hypothesis Quantum Relative Entropy Nussbaum, M. aut Szkoła, A. aut Verstraete, F. aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 279(2008), 1 vom: 08. Feb., Seite 251-283 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:279 year:2008 number:1 day:08 month:02 pages:251-283 https://doi.org/10.1007/s00220-008-0417-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_120 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 AR 279 2008 1 08 02 251-283 |
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10.1007/s00220-008-0417-5 doi (DE-627)OLC2038893292 (DE-He213)s00220-008-0417-5-p DE-627 ger DE-627 rakwb eng 530 510 VZ Audenaert, K. M. R. verfasserin aut Asymptotic Error Rates in Quantum Hypothesis Testing 2008 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2008 Abstract We consider the problem of discriminating between two different states of a finite quantum system in the setting of large numbers of copies, and find a closed form expression for the asymptotic exponential rate at which the error probability tends to zero. This leads to the identification of the quantum generalisation of the classical Chernoff distance, which is the corresponding quantity in classical symmetric hypothesis testing. The proof relies on two new techniques introduced by the authors, which are also well suited to tackle the corresponding problem in asymmetric hypothesis testing, yielding the quantum generalisation of the classical Hoeffding bound. This has been done by Hayashi and Nagaoka for the special case where the states have full support. The goal of this paper is to present the proofs of these results in a unified way and in full generality, allowing hypothesis states with different supports. From the quantum Hoeffding bound, we then easily derive quantum Stein’s Lemma and quantum Sanov’s theorem. We give an in-depth treatment of the properties of the quantum Chernoff distance, and argue that it is a natural distance measure on the set of density operators, with a clear operational meaning. Density Operator Relative Entropy Error Exponent Quantum Hypothesis Quantum Relative Entropy Nussbaum, M. aut Szkoła, A. aut Verstraete, F. aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 279(2008), 1 vom: 08. Feb., Seite 251-283 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:279 year:2008 number:1 day:08 month:02 pages:251-283 https://doi.org/10.1007/s00220-008-0417-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_120 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 AR 279 2008 1 08 02 251-283 |
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10.1007/s00220-008-0417-5 doi (DE-627)OLC2038893292 (DE-He213)s00220-008-0417-5-p DE-627 ger DE-627 rakwb eng 530 510 VZ Audenaert, K. M. R. verfasserin aut Asymptotic Error Rates in Quantum Hypothesis Testing 2008 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2008 Abstract We consider the problem of discriminating between two different states of a finite quantum system in the setting of large numbers of copies, and find a closed form expression for the asymptotic exponential rate at which the error probability tends to zero. This leads to the identification of the quantum generalisation of the classical Chernoff distance, which is the corresponding quantity in classical symmetric hypothesis testing. The proof relies on two new techniques introduced by the authors, which are also well suited to tackle the corresponding problem in asymmetric hypothesis testing, yielding the quantum generalisation of the classical Hoeffding bound. This has been done by Hayashi and Nagaoka for the special case where the states have full support. The goal of this paper is to present the proofs of these results in a unified way and in full generality, allowing hypothesis states with different supports. From the quantum Hoeffding bound, we then easily derive quantum Stein’s Lemma and quantum Sanov’s theorem. We give an in-depth treatment of the properties of the quantum Chernoff distance, and argue that it is a natural distance measure on the set of density operators, with a clear operational meaning. Density Operator Relative Entropy Error Exponent Quantum Hypothesis Quantum Relative Entropy Nussbaum, M. aut Szkoła, A. aut Verstraete, F. aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 279(2008), 1 vom: 08. Feb., Seite 251-283 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:279 year:2008 number:1 day:08 month:02 pages:251-283 https://doi.org/10.1007/s00220-008-0417-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_120 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 AR 279 2008 1 08 02 251-283 |
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10.1007/s00220-008-0417-5 doi (DE-627)OLC2038893292 (DE-He213)s00220-008-0417-5-p DE-627 ger DE-627 rakwb eng 530 510 VZ Audenaert, K. M. R. verfasserin aut Asymptotic Error Rates in Quantum Hypothesis Testing 2008 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2008 Abstract We consider the problem of discriminating between two different states of a finite quantum system in the setting of large numbers of copies, and find a closed form expression for the asymptotic exponential rate at which the error probability tends to zero. This leads to the identification of the quantum generalisation of the classical Chernoff distance, which is the corresponding quantity in classical symmetric hypothesis testing. The proof relies on two new techniques introduced by the authors, which are also well suited to tackle the corresponding problem in asymmetric hypothesis testing, yielding the quantum generalisation of the classical Hoeffding bound. This has been done by Hayashi and Nagaoka for the special case where the states have full support. The goal of this paper is to present the proofs of these results in a unified way and in full generality, allowing hypothesis states with different supports. From the quantum Hoeffding bound, we then easily derive quantum Stein’s Lemma and quantum Sanov’s theorem. We give an in-depth treatment of the properties of the quantum Chernoff distance, and argue that it is a natural distance measure on the set of density operators, with a clear operational meaning. Density Operator Relative Entropy Error Exponent Quantum Hypothesis Quantum Relative Entropy Nussbaum, M. aut Szkoła, A. aut Verstraete, F. aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 279(2008), 1 vom: 08. Feb., Seite 251-283 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:279 year:2008 number:1 day:08 month:02 pages:251-283 https://doi.org/10.1007/s00220-008-0417-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_120 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 AR 279 2008 1 08 02 251-283 |
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10.1007/s00220-008-0417-5 doi (DE-627)OLC2038893292 (DE-He213)s00220-008-0417-5-p DE-627 ger DE-627 rakwb eng 530 510 VZ Audenaert, K. M. R. verfasserin aut Asymptotic Error Rates in Quantum Hypothesis Testing 2008 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2008 Abstract We consider the problem of discriminating between two different states of a finite quantum system in the setting of large numbers of copies, and find a closed form expression for the asymptotic exponential rate at which the error probability tends to zero. This leads to the identification of the quantum generalisation of the classical Chernoff distance, which is the corresponding quantity in classical symmetric hypothesis testing. The proof relies on two new techniques introduced by the authors, which are also well suited to tackle the corresponding problem in asymmetric hypothesis testing, yielding the quantum generalisation of the classical Hoeffding bound. This has been done by Hayashi and Nagaoka for the special case where the states have full support. The goal of this paper is to present the proofs of these results in a unified way and in full generality, allowing hypothesis states with different supports. From the quantum Hoeffding bound, we then easily derive quantum Stein’s Lemma and quantum Sanov’s theorem. We give an in-depth treatment of the properties of the quantum Chernoff distance, and argue that it is a natural distance measure on the set of density operators, with a clear operational meaning. Density Operator Relative Entropy Error Exponent Quantum Hypothesis Quantum Relative Entropy Nussbaum, M. aut Szkoła, A. aut Verstraete, F. aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 279(2008), 1 vom: 08. Feb., Seite 251-283 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:279 year:2008 number:1 day:08 month:02 pages:251-283 https://doi.org/10.1007/s00220-008-0417-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_120 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 AR 279 2008 1 08 02 251-283 |
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Abstract We consider the problem of discriminating between two different states of a finite quantum system in the setting of large numbers of copies, and find a closed form expression for the asymptotic exponential rate at which the error probability tends to zero. This leads to the identification of the quantum generalisation of the classical Chernoff distance, which is the corresponding quantity in classical symmetric hypothesis testing. The proof relies on two new techniques introduced by the authors, which are also well suited to tackle the corresponding problem in asymmetric hypothesis testing, yielding the quantum generalisation of the classical Hoeffding bound. This has been done by Hayashi and Nagaoka for the special case where the states have full support. The goal of this paper is to present the proofs of these results in a unified way and in full generality, allowing hypothesis states with different supports. From the quantum Hoeffding bound, we then easily derive quantum Stein’s Lemma and quantum Sanov’s theorem. We give an in-depth treatment of the properties of the quantum Chernoff distance, and argue that it is a natural distance measure on the set of density operators, with a clear operational meaning. © Springer-Verlag 2008 |
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Abstract We consider the problem of discriminating between two different states of a finite quantum system in the setting of large numbers of copies, and find a closed form expression for the asymptotic exponential rate at which the error probability tends to zero. This leads to the identification of the quantum generalisation of the classical Chernoff distance, which is the corresponding quantity in classical symmetric hypothesis testing. The proof relies on two new techniques introduced by the authors, which are also well suited to tackle the corresponding problem in asymmetric hypothesis testing, yielding the quantum generalisation of the classical Hoeffding bound. This has been done by Hayashi and Nagaoka for the special case where the states have full support. The goal of this paper is to present the proofs of these results in a unified way and in full generality, allowing hypothesis states with different supports. From the quantum Hoeffding bound, we then easily derive quantum Stein’s Lemma and quantum Sanov’s theorem. We give an in-depth treatment of the properties of the quantum Chernoff distance, and argue that it is a natural distance measure on the set of density operators, with a clear operational meaning. © Springer-Verlag 2008 |
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Abstract We consider the problem of discriminating between two different states of a finite quantum system in the setting of large numbers of copies, and find a closed form expression for the asymptotic exponential rate at which the error probability tends to zero. This leads to the identification of the quantum generalisation of the classical Chernoff distance, which is the corresponding quantity in classical symmetric hypothesis testing. The proof relies on two new techniques introduced by the authors, which are also well suited to tackle the corresponding problem in asymmetric hypothesis testing, yielding the quantum generalisation of the classical Hoeffding bound. This has been done by Hayashi and Nagaoka for the special case where the states have full support. The goal of this paper is to present the proofs of these results in a unified way and in full generality, allowing hypothesis states with different supports. From the quantum Hoeffding bound, we then easily derive quantum Stein’s Lemma and quantum Sanov’s theorem. We give an in-depth treatment of the properties of the quantum Chernoff distance, and argue that it is a natural distance measure on the set of density operators, with a clear operational meaning. © Springer-Verlag 2008 |
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