Random Sampling of Quantum States: a Survey of Methods. And Some Issues Regarding the Overparametrized Method
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| Format: | Artículo científico |
| Langue: | en |
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Sociedade Brasileira de Física
2015
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| _version_ | 1876482733958496256 |
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| author | Jonas Maziero |
| author_facet | Jonas Maziero |
| contents | Random Sampling of Quantum States: a Survey of Methods. And Some Issues Regarding the Overparametrized Method Jonas Maziero Física, Astronomía y Matemáticas Numerical generation Random quantum states Overparametrized method Concentration of measure The numerical generation of random quantum states (RQS) is an important procedure for investigations in quantum information science. Here, we review some meth- ods that may be used for performing that task. We start by presenting a simple procedure for generating random state vectors, for which the main tool is the random sam- pling of unbiased discrete probability distributions (DPD). Afterwards, the creation of random density matrices is addressed. In this context, we first present the standard method, which consists in using the spectral decomposition of a quantum state for getting RQS from random DPDs and random unitary matrices. In the sequence, the Bloch vector parametrization method is described. This approach, despite being useful in several instances, is not in general conve- nient for RQS generation. In the last part of the article, we regard the overparametrized method (OPM) and the related Ginibre and Bures techniques. The OPM can be used to cre- ate random positive semidefinite matrices with unit trace from randomly produced general complex matrices in a sim- ple way that is friendly for numerical implementations. We consider a physically relevant issue related to the possible domains that may be used for the real and imaginary parts Jonas Maziero jonas.maziero@ufsm.br 1 Departamento de F ́ ısica, Centro de Ci ˆ encias Naturais e Exatas, Universidade Federal de Santa Maria, Avenida Roraima 1000, 97105-900, Santa Maria, RS, Brazil 2 Instituto de F ́ ısica, Facultad de Ingenier ́ ıa, Universidad de la Rep ́ ublica, J. Herrera y Reissig 565, 11300, Montevideo, Uruguay of the elements of such general complex matrices. Subse- quently, a too fast concentration of measure in the quantum state space that appears in this parametrization is noticed. 2015 artículo científico 0103-9733 https://www.redalyc.org/articulo.oa?id=46442560002 en http://www.redalyc.org/revista.oa?id=464 Brazilian Journal of Physics application/pdf Sociedade Brasileira de Física Brazilian Journal of Physics (Brasil) Num.6 Vol.45 |
| format | Artículo científico |
| id | redalyc_46442560002 |
| institution | Redalyc |
| language | en |
| publishDate | 2015 |
| publisher | Sociedade Brasileira de Física |
| spellingShingle | Random Sampling of Quantum States: a Survey of Methods. And Some Issues Regarding the Overparametrized Method Jonas Maziero Física, Astronomía y Matemáticas Numerical generation Random quantum states Overparametrized method Concentration of measure Random Sampling of Quantum States: a Survey of Methods. And Some Issues Regarding the Overparametrized Method Jonas Maziero Física, Astronomía y Matemáticas Numerical generation Random quantum states Overparametrized method Concentration of measure The numerical generation of random quantum states (RQS) is an important procedure for investigations in quantum information science. Here, we review some meth- ods that may be used for performing that task. We start by presenting a simple procedure for generating random state vectors, for which the main tool is the random sam- pling of unbiased discrete probability distributions (DPD). Afterwards, the creation of random density matrices is addressed. In this context, we first present the standard method, which consists in using the spectral decomposition of a quantum state for getting RQS from random DPDs and random unitary matrices. In the sequence, the Bloch vector parametrization method is described. This approach, despite being useful in several instances, is not in general conve- nient for RQS generation. In the last part of the article, we regard the overparametrized method (OPM) and the related Ginibre and Bures techniques. The OPM can be used to cre- ate random positive semidefinite matrices with unit trace from randomly produced general complex matrices in a sim- ple way that is friendly for numerical implementations. We consider a physically relevant issue related to the possible domains that may be used for the real and imaginary parts Jonas Maziero jonas.maziero@ufsm.br 1 Departamento de F ́ ısica, Centro de Ci ˆ encias Naturais e Exatas, Universidade Federal de Santa Maria, Avenida Roraima 1000, 97105-900, Santa Maria, RS, Brazil 2 Instituto de F ́ ısica, Facultad de Ingenier ́ ıa, Universidad de la Rep ́ ublica, J. Herrera y Reissig 565, 11300, Montevideo, Uruguay of the elements of such general complex matrices. Subse- quently, a too fast concentration of measure in the quantum state space that appears in this parametrization is noticed. 2015 artículo científico 0103-9733 https://www.redalyc.org/articulo.oa?id=46442560002 en http://www.redalyc.org/revista.oa?id=464 Brazilian Journal of Physics application/pdf Sociedade Brasileira de Física Brazilian Journal of Physics (Brasil) Num.6 Vol.45 |
| title | Random Sampling of Quantum States: a Survey of Methods. And Some Issues Regarding the Overparametrized Method |
| topic | Física, Astronomía y Matemáticas Numerical generation Random quantum states Overparametrized method Concentration of measure |
| url | https://www.redalyc.org/articulo.oa?id=46442560002 |