Generalized Fusion of Qudit Graph States
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910047795150848 |
|---|---|
| author | Rimock, N. Oz, Y. |
| author_facet | Rimock, N. Oz, Y. |
| contents | We formalize a generalized type-II fusion operation for qudit cluster states within linear optics. Two designated qudits, one from each input cluster, interfere with optional ancilla qudits via a passive linear-optical network, followed by number-resolving detection; conditioned on measurement outcome, the remaining qudits form the post-selected fused state. We prove a general rank bound: for any such interferometer and outcome, the reduced density matrix across the two parent clusters has Schmidt rank at most $M$, the total number of measured qudits including ancillae. Consequently, a correct qudit fusion which requires rank $d$ is impossible without ancillae and requires at least $d-2$ ancilla qudits. Our analysis extends previous no-go results for Bell-type qubit fusion to the qudit setting and to generalized, non-Bell projections. We analyze the probabilities and entanglement of the relevant measurement outcomes, and discuss how our lower bound aligns with existing constructive schemes. These results set a clear resource threshold for high-dimensional, fusion-based photonic MBQC. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_16623 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized Fusion of Qudit Graph States Rimock, N. Oz, Y. Quantum Physics We formalize a generalized type-II fusion operation for qudit cluster states within linear optics. Two designated qudits, one from each input cluster, interfere with optional ancilla qudits via a passive linear-optical network, followed by number-resolving detection; conditioned on measurement outcome, the remaining qudits form the post-selected fused state. We prove a general rank bound: for any such interferometer and outcome, the reduced density matrix across the two parent clusters has Schmidt rank at most $M$, the total number of measured qudits including ancillae. Consequently, a correct qudit fusion which requires rank $d$ is impossible without ancillae and requires at least $d-2$ ancilla qudits. Our analysis extends previous no-go results for Bell-type qubit fusion to the qudit setting and to generalized, non-Bell projections. We analyze the probabilities and entanglement of the relevant measurement outcomes, and discuss how our lower bound aligns with existing constructive schemes. These results set a clear resource threshold for high-dimensional, fusion-based photonic MBQC. |
| title | Generalized Fusion of Qudit Graph States |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2510.16623 |