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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2401.06472 |
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| _version_ | 1866929207616995328 |
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| author | Liu, Xinjian Wang, Yukun Han, Yunguang Wu, Xia |
| author_facet | Liu, Xinjian Wang, Yukun Han, Yunguang Wu, Xia |
| contents | In the standard Bell scenario, when making a local projective measurement on each system component, the amount of randomness generated is restricted. However, this limitation can be surpassed through the implementation of sequential measurements. Nonetheless, a rigorous definition of random numbers in the context of sequential measurements is yet to be established, except for the lower quantification in device-independent scenarios. In this paper, we define quantum intrinsic randomness in sequential measurements and quantify the randomness in the Collins-Gisin-Linden-Massar-Popescu (CGLMP) inequality sequential scenario. Initially, we investigate the quantum intrinsic randomness of the mixed states under sequential projective measurements and the intrinsic randomness of the sequential positive-operator-valued measure (POVM) under pure states. Naturally, we rigorously define quantum intrinsic randomness under sequential POVM for arbitrary quantum states. Furthermore, we apply our method to one-Alice and two-Bobs sequential measurement scenarios, and quantify the quantum intrinsic randomness of the maximally entangled state and maximally violated state by giving an extremal decomposition. Finally, using the sequential Navascues-Pironio-Acin (NPA) hierarchy in the device-independent scenario, we derive lower bounds on the quantum intrinsic randomness of the maximally entangled state and maximally violated state. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06472 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantifying the intrinsic randomness in sequential measurements Liu, Xinjian Wang, Yukun Han, Yunguang Wu, Xia Quantum Physics In the standard Bell scenario, when making a local projective measurement on each system component, the amount of randomness generated is restricted. However, this limitation can be surpassed through the implementation of sequential measurements. Nonetheless, a rigorous definition of random numbers in the context of sequential measurements is yet to be established, except for the lower quantification in device-independent scenarios. In this paper, we define quantum intrinsic randomness in sequential measurements and quantify the randomness in the Collins-Gisin-Linden-Massar-Popescu (CGLMP) inequality sequential scenario. Initially, we investigate the quantum intrinsic randomness of the mixed states under sequential projective measurements and the intrinsic randomness of the sequential positive-operator-valued measure (POVM) under pure states. Naturally, we rigorously define quantum intrinsic randomness under sequential POVM for arbitrary quantum states. Furthermore, we apply our method to one-Alice and two-Bobs sequential measurement scenarios, and quantify the quantum intrinsic randomness of the maximally entangled state and maximally violated state by giving an extremal decomposition. Finally, using the sequential Navascues-Pironio-Acin (NPA) hierarchy in the device-independent scenario, we derive lower bounds on the quantum intrinsic randomness of the maximally entangled state and maximally violated state. |
| title | Quantifying the intrinsic randomness in sequential measurements |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2401.06472 |