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| Autori principali: | , , , , |
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| Natura: | Preprint |
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2024
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| Accesso online: | https://arxiv.org/abs/2412.09576 |
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| _version_ | 1866908417743912960 |
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| author | Giorgadze, Irakli Huang, Haixuan Gaines, Jordan König, Elio J. Väyrynen, Jukka I. |
| author_facet | Giorgadze, Irakli Huang, Haixuan Gaines, Jordan König, Elio J. Väyrynen, Jukka I. |
| contents | Fermionic Hamiltonians play a critical role in quantum chemistry, one of the most promising use cases for near-term quantum computers. However, since encoding nonlocal fermionic statistics using conventional qubits results in significant computational overhead, fermionic quantum hardware, such as fermion atom arrays, were proposed as a more efficient platform. In this context, we here study the many-body entanglement structure of fermionic $N$-particle states by concentrating on $M$-body reduced density matrices (DMs) across various bipartitions in Fock space. The von Neumann entropy of the reduced DM is a basis independent entanglement measure which generalizes the traditional quantum chemistry concept of the one-particle DM entanglement, which characterizes how a single fermion is entangled with the rest. We carefully examine upper bounds on the $M$-body entanglement, which are analogous to the volume law of conventional entanglement measures. To this end we establish a connection between $M$-body reduced DM and the mathematical structure of hypergraphs. Specifically, we show that a special class of hypergraphs, known as $t$-designs, corresponds to maximally entangled fermionic states. Finally, we explore fermionic many-body entanglement in random states. We semianalytically demonstrate that the distribution of reduced DMs associated with random fermionic states corresponds to the trace-fixed Wishart-Laguerre random matrix ensemble. In the limit of large single-particle dimension $D$ and a non-zero filling fraction, random states asymptotically become absolutely maximally entangled. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_09576 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Characterizing maximally many-body entangled fermionic states by using $M$-body density matrix Giorgadze, Irakli Huang, Haixuan Gaines, Jordan König, Elio J. Väyrynen, Jukka I. Quantum Physics Fermionic Hamiltonians play a critical role in quantum chemistry, one of the most promising use cases for near-term quantum computers. However, since encoding nonlocal fermionic statistics using conventional qubits results in significant computational overhead, fermionic quantum hardware, such as fermion atom arrays, were proposed as a more efficient platform. In this context, we here study the many-body entanglement structure of fermionic $N$-particle states by concentrating on $M$-body reduced density matrices (DMs) across various bipartitions in Fock space. The von Neumann entropy of the reduced DM is a basis independent entanglement measure which generalizes the traditional quantum chemistry concept of the one-particle DM entanglement, which characterizes how a single fermion is entangled with the rest. We carefully examine upper bounds on the $M$-body entanglement, which are analogous to the volume law of conventional entanglement measures. To this end we establish a connection between $M$-body reduced DM and the mathematical structure of hypergraphs. Specifically, we show that a special class of hypergraphs, known as $t$-designs, corresponds to maximally entangled fermionic states. Finally, we explore fermionic many-body entanglement in random states. We semianalytically demonstrate that the distribution of reduced DMs associated with random fermionic states corresponds to the trace-fixed Wishart-Laguerre random matrix ensemble. In the limit of large single-particle dimension $D$ and a non-zero filling fraction, random states asymptotically become absolutely maximally entangled. |
| title | Characterizing maximally many-body entangled fermionic states by using $M$-body density matrix |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2412.09576 |