Trade-off Relations in Genuine Four-qubit Nonlocality Systems
Sk Sahadat Hossain
Dr. Sk Sahadat Hossain, Assistant Professor, Department of Mathematics, Nabagram Hiralal Paul College, Hooghly (West Bengal), India.
Manuscript received on 10 August 2026 | First Revised Manuscript received on 27 August 2026 | Second Revised Manuscript received on 17 September 2026 | Manuscript Accepted on 15 October 2026 | Manuscript published on 30 October 2026 | PP: 7-12 | Volume-6 Issue-2, October 2026 | Retrieval Number: 100.1/ijap.B107906021026 | DOI: 10.54105/ijap.B1079.06021026
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© The Authors. Published by Lattice Science Publication (LSP). This is an open-access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: We investigate trade-off relations governing genuine four-qubit nonlocality in multipartite quantum systems. By analyzing the reduced four-qubit density operators obtained from five-qubit generalized GHZ and MS states, we establish nontrivial constraints on the expectation values of the SeevinckSvetlichny operators associated with these subsystems. In particular, we demonstrate that genuine four-qubit nonlocal correlations across different four-qubit reductions are not mutually independent. For both classes of five-qubit states considered, we show that the sum of the maximal squared expectation values of the Seevinck-Svetlichny operators over all four-qubit reductions is subject to a state-dependent upper bound. Furthermore, this collective bound is shown to be tighter than the bounds obtained by independently imposing the maximal allowed expectation value of the Svetlichny operator on each four-qubit subsystem. These results reveal a monogamy-like trade-off structure for genuine four-qubit nonlocal correlations and provide tighter constraints on their simultaneous manifestation in multipartite quantum systems.
Keywords: GHZ State, Seevinck-Svetlichny Inequality, Multipartite Genuine Nonlocality, Four-Qubit System, Measurements.
Scope of the Article: Applied Physics