Entanglement of Three-Qubit Random Pure States
We study entanglement properties of generic three-qubit pure states. First, we obtain the distributions of both the coefficients and the only phase in the five-term decomposition of Acín et al. for an ensemble of random pure states generated by the Haar measure on U ( 8 ) . Further...
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| Format: | Article |
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MDPI AG
2018-09-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/20/10/745 |
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| author | Marco Enríquez Francisco Delgado Karol Życzkowski |
| author_facet | Marco Enríquez Francisco Delgado Karol Życzkowski |
| author_sort | Marco Enríquez |
| collection | DOAJ |
| description | We study entanglement properties of generic three-qubit pure states. First, we obtain the distributions of both the coefficients and the only phase in the five-term decomposition of Acín et al. for an ensemble of random pure states generated by the Haar measure on U ( 8 ) . Furthermore, we analyze the probability distributions of two sets of polynomial invariants. One of these sets allows us to classify three-qubit pure states into four classes. Entanglement in each class is characterized using the minimal Rényi-Ingarden-Urbanik entropy. Besides, the fidelity of a three-qubit random state with the closest state in each entanglement class is investigated. We also present a characterization of these classes in terms of the corresponding entanglement polytope. The entanglement classes related to stochastic local operations and classical communication (SLOCC) are analyzed as well from this geometric perspective. The numerical findings suggest some conjectures relating some of those invariants with entanglement properties to be ground in future analytical work. |
| first_indexed | 2024-04-11T22:26:24Z |
| format | Article |
| id | doaj.art-3b4e730328114178a16b211146308554 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T22:26:24Z |
| publishDate | 2018-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-3b4e730328114178a16b2111463085542022-12-22T03:59:38ZengMDPI AGEntropy1099-43002018-09-01201074510.3390/e20100745e20100745Entanglement of Three-Qubit Random Pure StatesMarco Enríquez0Francisco Delgado1Karol Życzkowski2Escuela de Ingeniería y Ciencias, Tecnológico de Monterrey, Atizapán 52926, MexicoEscuela de Ingeniería y Ciencias, Tecnológico de Monterrey, Atizapán 52926, MexicoFaculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków, PolandWe study entanglement properties of generic three-qubit pure states. First, we obtain the distributions of both the coefficients and the only phase in the five-term decomposition of Acín et al. for an ensemble of random pure states generated by the Haar measure on U ( 8 ) . Furthermore, we analyze the probability distributions of two sets of polynomial invariants. One of these sets allows us to classify three-qubit pure states into four classes. Entanglement in each class is characterized using the minimal Rényi-Ingarden-Urbanik entropy. Besides, the fidelity of a three-qubit random state with the closest state in each entanglement class is investigated. We also present a characterization of these classes in terms of the corresponding entanglement polytope. The entanglement classes related to stochastic local operations and classical communication (SLOCC) are analyzed as well from this geometric perspective. The numerical findings suggest some conjectures relating some of those invariants with entanglement properties to be ground in future analytical work.http://www.mdpi.com/1099-4300/20/10/745quantum entanglementthree-qubit random statesentanglement classesentanglement polytopeanisotropic invariants |
| spellingShingle | Marco Enríquez Francisco Delgado Karol Życzkowski Entanglement of Three-Qubit Random Pure States Entropy quantum entanglement three-qubit random states entanglement classes entanglement polytope anisotropic invariants |
| title | Entanglement of Three-Qubit Random Pure States |
| title_full | Entanglement of Three-Qubit Random Pure States |
| title_fullStr | Entanglement of Three-Qubit Random Pure States |
| title_full_unstemmed | Entanglement of Three-Qubit Random Pure States |
| title_short | Entanglement of Three-Qubit Random Pure States |
| title_sort | entanglement of three qubit random pure states |
| topic | quantum entanglement three-qubit random states entanglement classes entanglement polytope anisotropic invariants |
| url | http://www.mdpi.com/1099-4300/20/10/745 |
| work_keys_str_mv | AT marcoenriquez entanglementofthreequbitrandompurestates AT franciscodelgado entanglementofthreequbitrandompurestates AT karolzyczkowski entanglementofthreequbitrandompurestates |